{"group":{"id":1,"name":"Community","lockable":false,"created_at":"2012-01-18T18:02:15.000Z","updated_at":"2025-12-14T01:33:56.000Z","description":"Problems submitted by members of the MATLAB Central community.","is_default":true,"created_by":161519,"badge_id":null,"featured":false,"trending":false,"solution_count_in_trending_period":0,"trending_last_calculated":"2025-12-14T00:00:00.000Z","image_id":null,"published":true,"community_created":false,"status_id":2,"is_default_group_for_player":false,"deleted_by":null,"deleted_at":null,"restored_by":null,"restored_at":null,"description_opc":null,"description_html":null,"published_at":null},"problems":[{"id":2358,"title":"Word Search Solver","description":"There are n words (minimum of three letters in each word) supplied with a given word search board. The answer will contain n rows where each row contains the row and column indices where the word starts followed by an integer indicating the direction of the word. The direction integer runs from 1 to 8 and starts at 12 o'clock, running clockwise. So, a word spelled to the right (normal fashion) would be indexed as a 3 and facing downward to the left (SW) would be a 6.\r\nThe first board is included here for reference:\r\n board = [\r\n  'xcupa'\r\n  'dyrng'\r\n  'osbaq'\r\n  'exbid'\r\n  'wgamv'\r\n ];\r\n\r\n words = {'aim'; 'bid'; 'cup'; 'doe'};\r\n\r\n loc_ans = [\r\n  3 4 5\r\n  4 3 3\r\n  1 2 3\r\n  2 1 5\r\n ];","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 450.933px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 225.467px; transform-origin: 407px 225.467px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 84px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 42px; text-align: left; transform-origin: 384px 42px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 365px 8px; transform-origin: 365px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThere are n words (minimum of three letters in each word) supplied with a given word search board. The answer will contain n rows where each row contains the row and column indices where the word starts followed by an integer indicating the direction of the word. The direction integer runs from 1 to 8 and starts at 12 o'clock, running clockwise. So, a word spelled to the right (normal fashion) would be indexed as a 3 and facing downward to the left (SW) would be a 6.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 143.5px 8px; transform-origin: 143.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe first board is included here for reference:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 326.933px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 404px 163.467px; transform-origin: 404px 163.467px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 40px 8.5px; tab-size: 4; transform-origin: 40px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e board = [\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 36px 8.5px; tab-size: 4; transform-origin: 36px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 8px 8.5px; transform-origin: 8px 8.5px; \"\u003e  \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); perspective-origin: 28px 8.5px; text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); transform-origin: 28px 8.5px; \"\u003e'xcupa'\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 36px 8.5px; tab-size: 4; transform-origin: 36px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 8px 8.5px; transform-origin: 8px 8.5px; \"\u003e  \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); perspective-origin: 28px 8.5px; text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); transform-origin: 28px 8.5px; \"\u003e'dyrng'\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 36px 8.5px; tab-size: 4; transform-origin: 36px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 8px 8.5px; transform-origin: 8px 8.5px; \"\u003e  \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); perspective-origin: 28px 8.5px; text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); transform-origin: 28px 8.5px; \"\u003e'osbaq'\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 36px 8.5px; tab-size: 4; transform-origin: 36px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 8px 8.5px; transform-origin: 8px 8.5px; \"\u003e  \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); perspective-origin: 28px 8.5px; text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); transform-origin: 28px 8.5px; \"\u003e'exbid'\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 36px 8.5px; tab-size: 4; transform-origin: 36px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 8px 8.5px; transform-origin: 8px 8.5px; \"\u003e  \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); perspective-origin: 28px 8.5px; text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); transform-origin: 28px 8.5px; \"\u003e'wgamv'\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 12px 8.5px; tab-size: 4; transform-origin: 12px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e ];\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 8.5px; tab-size: 4; transform-origin: 0px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 152px 8.5px; tab-size: 4; transform-origin: 152px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 40px 8.5px; transform-origin: 40px 8.5px; \"\u003e words = {\u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); perspective-origin: 20px 8.5px; text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); transform-origin: 20px 8.5px; \"\u003e'aim'\u003c/span\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 8px 8.5px; transform-origin: 8px 8.5px; \"\u003e; \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); perspective-origin: 20px 8.5px; text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); transform-origin: 20px 8.5px; \"\u003e'bid'\u003c/span\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 8px 8.5px; transform-origin: 8px 8.5px; \"\u003e; \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); perspective-origin: 20px 8.5px; text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); transform-origin: 20px 8.5px; \"\u003e'cup'\u003c/span\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 8px 8.5px; transform-origin: 8px 8.5px; \"\u003e; \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); perspective-origin: 20px 8.5px; text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); transform-origin: 20px 8.5px; \"\u003e'doe'\u003c/span\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 8px 8.5px; transform-origin: 8px 8.5px; \"\u003e};\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 8.5px; tab-size: 4; transform-origin: 0px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 48px 8.5px; tab-size: 4; transform-origin: 48px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e loc_ans = [\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 28px 8.5px; tab-size: 4; transform-origin: 28px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e  3 4 5\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 28px 8.5px; tab-size: 4; transform-origin: 28px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e  4 3 3\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 28px 8.5px; tab-size: 4; transform-origin: 28px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e  1 2 3\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 28px 8.5px; tab-size: 4; transform-origin: 28px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e  2 1 5\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 12px 8.5px; tab-size: 4; transform-origin: 12px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e ];\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function loc = WordSearch(board,words)\r\n loc = [-1 -1];\r\nend","test_suite":"%%\r\nboard = [\r\n 'xcupa';\r\n 'dyrng';\r\n 'osbaq';\r\n 'exbid';\r\n 'wgamv';\r\n];\r\nwords = {'aim'; 'bid'; 'cup'; 'doe'};\r\nloc_ans = [\r\n 3 4 5;\r\n 4 3 3;\r\n 1 2 3;\r\n 2 1 5;\r\n];\r\nassert(isequal(WordSearch(board,words),loc_ans))\r\n\r\n%%\r\nboard = [\r\n 'okeanpbirf';\r\n 'qicwnafehu';\r\n 'wniazcgame';\r\n 'egaxjelbiv';\r\n 'bnomelvmcr';\r\n];\r\nwords = {'fair'; 'game'; 'hall'; 'ice'; 'jack'; 'king'; 'lemon'};\r\nloc_ans = [\r\n 2 7 4;\r\n 3 7 3;\r\n 2 9 6;\r\n 3 3 1;\r\n 4 5 8;\r\n 1 2 5;\r\n 5 6 7;\r\n];\r\nassert(isequal(WordSearch(board,words),loc_ans))\r\n\r\n%%\r\nboard = [\r\n 'werojea';\r\n 'cafefls';\r\n 'apufrbw';\r\n 'hrleaan';\r\n 'aoltgbb';\r\n 'aoaevdr';\r\n 'mdzoece';\r\n];\r\nwords = {'able'; 'bare'; 'cafe'; 'door'; 'edge'; 'full'};\r\nloc_ans = [\r\n 4 6 1;\r\n 5 7 8;\r\n 2 1 3;\r\n 7 2 1;\r\n 7 7 8;\r\n 2 3 5;\r\n];\r\nassert(isequal(WordSearch(board,words),loc_ans))\r\n\r\n%%\r\nboard = [\r\n 'anmjwfpnyo';\r\n 'wasgijsaen';\r\n 'akigyqaekl';\r\n 'doorbellci';\r\n 'loiapucfdx';\r\n 'loepalirri';\r\n 'alzhheagle';\r\n 'mgxmsovnpr';\r\n 'aiqtbovgee';\r\n 'juyhctahnr';\r\n];\r\nwords = {'airplane'; 'board'; 'clasp'; 'doorbell'; 'eagle'; 'fiesty'; 'graph'; 'hatch'; 'igloo'; 'jigsaw'; 'key'; 'llama'};\r\nloc_ans = [\r\n 2 2 4;\r\n 9 5 2;\r\n 5 7 1;\r\n 4 1 3;\r\n 7 6 3;\r\n 5 8 6;\r\n 3 4 5;\r\n 10 8 7;\r\n 9 2 1;\r\n 2 6 7;\r\n 3 9 1;\r\n 5 1 5;\r\n];\r\nassert(isequal(WordSearch(board,words),loc_ans))","published":true,"deleted":false,"likes_count":3,"comments_count":2,"created_by":26769,"edited_by":223089,"edited_at":"2022-09-19T13:13:49.000Z","deleted_by":null,"deleted_at":null,"solvers_count":17,"test_suite_updated_at":"2022-09-19T13:13:50.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2014-06-11T13:58:10.000Z","updated_at":"2025-12-15T20:16:04.000Z","published_at":"2014-06-11T13:58:44.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThere are n words (minimum of three letters in each word) supplied with a given word search board. The answer will contain n rows where each row contains the row and column indices where the word starts followed by an integer indicating the direction of the word. The direction integer runs from 1 to 8 and starts at 12 o'clock, running clockwise. So, a word spelled to the right (normal fashion) would be indexed as a 3 and facing downward to the left (SW) would be a 6.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe first board is included here for reference:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ board = [\\n  'xcupa'\\n  'dyrng'\\n  'osbaq'\\n  'exbid'\\n  'wgamv'\\n ];\\n\\n words = {'aim'; 'bid'; 'cup'; 'doe'};\\n\\n loc_ans = [\\n  3 4 5\\n  4 3 3\\n  1 2 3\\n  2 1 5\\n ];]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":3043,"title":"Fill-a-pix - Solver (basic)","description":"\u003chttp://www.conceptispuzzles.com/index.aspx?uri=puzzle/fill-a-pix/rules Fill-a-pix\u003e is a logic puzzle game similar to Pic-a-Pix (aka Logic art) and Minesweeper. An example starting board is shown below on the left with the completed board shown to its right. Each number in the board indicates how many surrounding cells, including itself, are to be filled in. There are (up to) nine total cells associated with each number: four immediately adjacent (up, down, left, and right), four diagonally adjacent (one touching each corner), and the central cell (where the number is located).\r\n\r\nBased on this logic, all 0's and 9's are determinant, as all nine cells are either empty or filled, respectively, for these numbers. Also, all 6's on the board edges and 4's in the corners should be completely filled in, as they only involve 6 or 4 cells, respectively.\r\n\r\n\u003c\u003chttp://www.conceptispuzzles.com/picture/27/1558.gif\u003e\u003e\r\n\r\n\u003c\u003chttp://www.conceptispuzzles.com/picture/27/1574.gif\u003e\u003e\r\n\r\nThis problem deals with basic-logic Fill-a-pix problems; a sample step-by-step solution is found \u003chttp://www.conceptispuzzles.com/index.aspx?uri=puzzle/fill-a-pix/techniques here\u003e. These problems are basic in that each clue can be solved independent of all other clues, though some looping or iteration over the board will be required to solve all the clues. Basic logic can be summarized in the following two cases, regarding the cells associated with each clue: (1) if the sum of filled-in cells equals the clue, all other associated cells should be marked as empty, and (2) if the sum of empty cells equals the total number of associated cells minus the clue, all other associated cells should be marked as filled in.\r\n\r\nFor this problem, you will be presented with a board full of clues. Write a function to solve the Fill-a-pix puzzle based on those clues, returning a solution of the same size as the board filled with 1's (filled) and 0's (empty).\r\n\r\nA related problem is \u003chttps://www.mathworks.com/matlabcentral/cody/problems/3042-fill-a-pix-solution-checker Fill-a-pix - Solution Checker\u003e.","description_html":"\u003cp\u003e\u003ca href = \"http://www.conceptispuzzles.com/index.aspx?uri=puzzle/fill-a-pix/rules\"\u003eFill-a-pix\u003c/a\u003e is a logic puzzle game similar to Pic-a-Pix (aka Logic art) and Minesweeper. An example starting board is shown below on the left with the completed board shown to its right. Each number in the board indicates how many surrounding cells, including itself, are to be filled in. There are (up to) nine total cells associated with each number: four immediately adjacent (up, down, left, and right), four diagonally adjacent (one touching each corner), and the central cell (where the number is located).\u003c/p\u003e\u003cp\u003eBased on this logic, all 0's and 9's are determinant, as all nine cells are either empty or filled, respectively, for these numbers. Also, all 6's on the board edges and 4's in the corners should be completely filled in, as they only involve 6 or 4 cells, respectively.\u003c/p\u003e\u003cimg src = \"http://www.conceptispuzzles.com/picture/27/1558.gif\"\u003e\u003cimg src = \"http://www.conceptispuzzles.com/picture/27/1574.gif\"\u003e\u003cp\u003eThis problem deals with basic-logic Fill-a-pix problems; a sample step-by-step solution is found \u003ca href = \"http://www.conceptispuzzles.com/index.aspx?uri=puzzle/fill-a-pix/techniques\"\u003ehere\u003c/a\u003e. These problems are basic in that each clue can be solved independent of all other clues, though some looping or iteration over the board will be required to solve all the clues. Basic logic can be summarized in the following two cases, regarding the cells associated with each clue: (1) if the sum of filled-in cells equals the clue, all other associated cells should be marked as empty, and (2) if the sum of empty cells equals the total number of associated cells minus the clue, all other associated cells should be marked as filled in.\u003c/p\u003e\u003cp\u003eFor this problem, you will be presented with a board full of clues. Write a function to solve the Fill-a-pix puzzle based on those clues, returning a solution of the same size as the board filled with 1's (filled) and 0's (empty).\u003c/p\u003e\u003cp\u003eA related problem is \u003ca href = \"https://www.mathworks.com/matlabcentral/cody/problems/3042-fill-a-pix-solution-checker\"\u003eFill-a-pix - Solution Checker\u003c/a\u003e.\u003c/p\u003e","function_template":"function [solution] = fill_a_pix_solver_basic(board)\r\n\r\nsolution = ones(size(board));\r\n\r\nend\r\n","test_suite":"%%\r\nboard = [-1,-1,-1,-1,1; -1,9,-1,-1,-1; -1,8,8,-1,-1; -1,-1,-1,-1,4; 4,-1,5,-1,2];\r\nboard(board==-1) = NaN;\r\nsolution = [1,1,1,0,0; 1,1,1,1,0; 1,1,1,1,1; 1,1,0,1,0; 1,1,1,1,0];\r\nassert(isequal(fill_a_pix_solver_basic(board),solution))\r\n\r\n%%\r\nboard = [-1,-1,-1,-1,-1,-1,-1,-1,0,-1; -1,8,8,-1,2,-1,0,-1,-1,-1; 5,-1,8,-1,-1,-1,-1,-1,-1,-1; -1,-1,-1,-1,-1,2,-1,-1,-1,2; 1,-1,-1,-1,4,5,6,-1,-1,-1; -1,0,-1,-1,-1,7,9,-1,-1,6; -1,-1,-1,6,-1,-1,9,-1,-1,6; -1,-1,6,6,8,7,8,7,-1,5; -1,4,-1,6,6,6,-1,6,-1,4; -1,-1,-1,-1,-1,-1,3,-1,-1,-1];\r\nboard(board==-1) = NaN;\r\nsolution = [0,1,1,0,0,0,0,0,0,0; 1,1,1,1,0,0,0,0,0,0; 1,1,1,1,0,0,0,0,0,0; 0,1,1,0,0,0,0,0,0,0; 0,0,0,0,0,1,1,1,1,1; 0,0,0,1,1,1,1,1,1,1; 0,0,0,1,0,1,1,1,1,1; 0,1,1,1,1,1,1,1,1,1; 0,1,0,1,1,1,0,1,0,1; 0,0,1,0,0,0,1,0,1,0];\r\nassert(isequal(fill_a_pix_solver_basic(board),solution))\r\n\r\n%%\r\nboard = [-1,2,3,-1,-1,0,-1,-1,-1,-1; -1,-1,-1,-1,3,-1,2,-1,-1,6; -1,-1,5,-1,5,3,-1,5,7,4; -1,4,-1,5,-1,5,-1,6,-1,3; -1,-1,4,-1,5,-1,6,-1,-1,3; -1,-1,-1,2,-1,5,-1,-1,-1,-1; 4,-1,1,-1,-1,-1,1,1,-1,-1; 4,-1,1,-1,-1,-1,1,-1,4,-1; -1,-1,-1,-1,6,-1,-1,-1,-1,4; -1,4,4,-1,-1,-1,-1,4,-1,-1];\r\nboard(board==-1) = NaN;\r\nsolution = [0,1,1,0,0,0,0,0,1,1; 0,0,0,1,0,0,0,1,1,1; 0,0,1,1,1,0,0,1,1,1; 0,1,1,0,1,1,0,1,0,0; 0,1,0,0,0,1,1,1,1,0; 1,1,0,0,1,1,0,0,1,1; 1,0,0,0,1,0,0,0,0,1;  1,0,0,0,1,0,0,0,0,1; 1,1,0,0,1,1,0,0,1,1; 0,1,1,1,1,1,1,1,1,0];\r\nassert(isequal(fill_a_pix_solver_basic(board),solution))\r\n\r\n%%\r\nboard = [0,-1,-1,4,3,2,1,-1,-1,-1,-1,-1,3,-1,-1; -1,-1,5,-1,-1,4,-1,-1,4,4,-1,-1,-1,-1,3; -1,5,4,5,4,5,5,-1,5,3,-1,1,2,-1,3; 4,-1,-1,-1,4,-1,-1,4,2,-1,1,-1,-1,-1,-1; -1,-1,5,4,-1,2,2,-1,1,0,-1,-1,7,5,-1; -1,-1,-1,5,-1,-1,0,-1,-1,-1,-1,4,5,-1,2; 4,-1,-1,5,4,2,0,0,-1,-1,-1,5,6,-1,-1; 5,-1,-1,6,5,-1,-1,-1,-1,-1,3,3,3,-1,3; -1,-1,5,-1,5,3,-1,-1,-1,-1,-1,-1,3,-1,-1; 5,-1,-1,6,5,-1,3,5,-1,6,-1,-1,0,-1,0; -1,-1,5,-1,4,3,2,4,5,-1,4,-1,-1,1,-1; -1,7,-1,-1,5,-1,-1,1,-1,5,5,5,-1,-1,-1; -1,-1,6,4,4,4,3,1,2,4,-1,-1,6,4,-1; -1,5,-1,6,-1,-1,-1,-1,-1,4,6,-1,-1,-1,-1; -1,-1,-1,-1,-1,-1,3,2,0,-1,4,4,3,-1,2];\r\nboard(board==-1) = NaN;\r\nsolution = [0,0,0,1,1,0,0,0,0,0,1,1,1,1,0; 0,0,1,0,1,0,0,1,1,1,0,0,0,0,1; 1,1,1,1,0,1,1,0,1,0,0,0,0,0,1; 1,0,0,0,1,0,1,1,0,0,0,0,1,1,0; 0,1,1,1,0,0,0,0,0,0,0,1,1,0,0; 0,1,0,1,0,0,0,0,0,0,0,1,1,1,0; 1,1,1,0,1,0,0,0,0,0,0,0,0,0,1; 1,0,0,1,1,0,0,0,0,0,1,1,1,1,1; 1,1,1,1,0,1,0,0,1,1,0,0,0,0,0; 1,0,0,1,0,0,1,1,1,1,0,0,0,0,0; 1,1,1,1,1,0,0,0,1,0,1,0,0,0,0; 1,1,0,0,1,0,0,0,0,1,0,1,1,0,0; 0,1,1,1,0,1,0,0,0,1,1,0,1,1,0; 0,1,1,0,0,1,1,0,0,0,1,1,0,1,0; 0,0,1,1,1,0,1,0,0,0,1,1,0,0,1];\r\nassert(isequal(fill_a_pix_solver_basic(board),solution))\r\n\r\n%% anti-cheating test case\r\nboard = NaN(9);\r\nsolution = NaN(9);\r\nfor i = 1:3\r\n\tfor j = 1:3\r\n\t\tif randi(2) == 2\r\n\t\t\tboard(i*3-1,j*3-1) = 9;\r\n\t\t\tsolution((i*3-2):(i*3),(j*3-2):(j*3)) = 1;\r\n\t\telse\r\n\t\t\tboard(i*3-1,j*3-1) = 0;\r\n\t\t\tsolution((i*3-2):(i*3),(j*3-2):(j*3)) = 0;\r\n\t\tend\r\n\tend\r\nend\r\nassert(isequal(fill_a_pix_solver_basic(board),solution))\r\n","published":true,"deleted":false,"likes_count":2,"comments_count":11,"created_by":26769,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":10,"test_suite_updated_at":"2015-02-25T19:14:45.000Z","rescore_all_solutions":true,"group_id":1,"created_at":"2015-02-25T04:24:32.000Z","updated_at":"2026-04-01T15:40:48.000Z","published_at":"2015-02-25T04:24:32.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/image\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/media/image1.gif\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/image\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/media/image2.gif\"}],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:hyperlink w:docLocation=\\\"http://www.conceptispuzzles.com/index.aspx?uri=puzzle/fill-a-pix/rules\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eFill-a-pix\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e is a logic puzzle game similar to Pic-a-Pix (aka Logic art) and Minesweeper. An example starting board is shown below on the left with the completed board shown to its right. Each number in the board indicates how many surrounding cells, including itself, are to be filled in. There are (up to) nine total cells associated with each number: four immediately adjacent (up, down, left, and right), four diagonally adjacent (one touching each corner), and the central cell (where the number is located).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eBased on this logic, all 0's and 9's are determinant, as all nine cells are either empty or filled, respectively, for these numbers. Also, all 6's on the board edges and 4's in the corners should be completely filled in, as they only involve 6 or 4 cells, respectively.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"-1\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"-1\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"-1\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"-1\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId2\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis problem deals with basic-logic Fill-a-pix problems; a sample step-by-step solution is found\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://www.conceptispuzzles.com/index.aspx?uri=puzzle/fill-a-pix/techniques\\\"\u003e\u003cw:r\u003e\u003cw:t\u003ehere\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e. These problems are basic in that each clue can be solved independent of all other clues, though some looping or iteration over the board will be required to solve all the clues. Basic logic can be summarized in the following two cases, regarding the cells associated with each clue: (1) if the sum of filled-in cells equals the clue, all other associated cells should be marked as empty, and (2) if the sum of empty cells equals the total number of associated cells minus the clue, all other associated cells should be marked as filled in.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor this problem, you will be presented with a board full of clues. Write a function to solve the Fill-a-pix puzzle based on those clues, returning a solution of the same size as the board filled with 1's (filled) and 0's (empty).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA related problem is\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/3042-fill-a-pix-solution-checker\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eFill-a-pix - Solution Checker\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" 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Boggle","description":"Description\r\nIn the classic Parker Brothers game Boggle, players find words from a 4x4 game board of letters. This exercise is to make sure that a particular solution to a boggle board is actually available on the board.\r\nThe program does not need to check to make sure if the input word is a valid english word. Furthermore, all inputs will be in all uppercase, so the user does not need to check/convert for case differences. The game board will always be 4x4.\r\nNote: This does not perfectly align with the rules of Boggle. Specifically, all solutions in the original game must be 3 or more letters, which this problem is not asking to account for, and the atomic \"Qu\" is present (which I have avoided in the test suite).\r\nHappy MATLABing!\r\nExample\r\n    x = ['TIPE'\r\n         'YECV'\r\n         'LSRA'\r\n         'WOTU'];\r\n    y = 'RACIEST';\r\n    TF = true;","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 387.6px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 193.8px; transform-origin: 407px 193.8px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 40.5px 8px; transform-origin: 40.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eDescription\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 112px 8px; transform-origin: 112px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eIn the classic Parker Brothers game\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"/#null\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eBoggle\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 247px 8px; transform-origin: 247px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, players find words from a 4x4 game board of letters. This exercise is to make sure that a particular solution to a boggle board is actually available on the board.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 41px 8px; transform-origin: 41px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe program\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 27.5px 8px; transform-origin: 27.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003edoes not\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 311px 8px; transform-origin: 311px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e need to check to make sure if the input word is a valid english word. Furthermore, all inputs will be in all uppercase, so the user does not need to check/convert for case differences. The game board will always be 4x4.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 370px 8px; transform-origin: 370px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eNote: This does not perfectly align with the rules of Boggle. Specifically, all solutions in the original game must be 3 or more letters, which this problem is not asking to account for, and the atomic \"Qu\" is present (which I have avoided in the test suite).\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 61px 8px; transform-origin: 61px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eHappy MATLABing!\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 29.5px 8px; transform-origin: 29.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eExample\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 122.6px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 404px 61.3px; transform-origin: 404px 61.3px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 60px 8.5px; tab-size: 4; transform-origin: 60px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 36px 8.5px; transform-origin: 36px 8.5px; \"\u003e    x = [\u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); perspective-origin: 24px 8.5px; text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); transform-origin: 24px 8.5px; \"\u003e'TIPE'\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 60px 8.5px; tab-size: 4; transform-origin: 60px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 36px 8.5px; transform-origin: 36px 8.5px; \"\u003e         \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); perspective-origin: 24px 8.5px; text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); transform-origin: 24px 8.5px; \"\u003e'YECV'\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 60px 8.5px; tab-size: 4; transform-origin: 60px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 36px 8.5px; transform-origin: 36px 8.5px; \"\u003e         \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); perspective-origin: 24px 8.5px; text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); transform-origin: 24px 8.5px; \"\u003e'LSRA'\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 68px 8.5px; tab-size: 4; transform-origin: 68px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 36px 8.5px; transform-origin: 36px 8.5px; \"\u003e         \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); perspective-origin: 24px 8.5px; text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); transform-origin: 24px 8.5px; \"\u003e'WOTU'\u003c/span\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 8px 8.5px; transform-origin: 8px 8.5px; \"\u003e];\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 72px 8.5px; tab-size: 4; transform-origin: 72px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 32px 8.5px; transform-origin: 32px 8.5px; \"\u003e    y = \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); perspective-origin: 36px 8.5px; text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); transform-origin: 36px 8.5px; \"\u003e'RACIEST'\u003c/span\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 4px 8.5px; transform-origin: 4px 8.5px; \"\u003e;\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 56px 8.5px; tab-size: 4; transform-origin: 56px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e    TF = true;\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function tf = boggle_checker(x,y)\r\n  tf = true;\r\nend","test_suite":"%%\r\nx = ['TIPE'\r\n     'YECV'\r\n     'LSRA'\r\n     'WOTU'];\r\ny = 'RACIEST';\r\nassert(isequal(boggle_checker(x,y),true))\r\n\r\n%%\r\nx = ['TIPE'\r\n     'YECV'\r\n     'LSRA'\r\n     'WOTU'];\r\ny = 'RACIESTS';\r\nassert(isequal(boggle_checker(x,y),false))\r\n\r\n%%\r\nx = ['TIPE'\r\n     'YECV'\r\n     'LSRA'\r\n     'WOTU'];\r\ny = 'RACIESTW';\r\nassert(isequal(boggle_checker(x,y),false))\r\n\r\n%%\r\nx = ['TIPE'\r\n     'YECV'\r\n     'LSRA'\r\n     'WOTU'];\r\ny = 'AUTOLYTIC';\r\nassert(isequal(boggle_checker(x,y),true))\r\n\r\n%%\r\nx = ['TIPE'\r\n     'YECV'\r\n     'LSRA'\r\n     'WOTU'];\r\ny = 'RESTAR';\r\nassert(isequal(boggle_checker(x,y),false))\r\n\r\n%%\r\nx = ['OCEW'\r\n     'LRIR'\r\n     'GYSI'\r\n     'KREM'];\r\ny = 'SIRI';\r\nassert(isequal(boggle_checker(x,y),true))\r\n\r\n%%\r\nx = ['OCEW'\r\n     'LRIR'\r\n     'GYSI'\r\n     'KREM'];\r\ny = 'SIRIM';\r\nassert(isequal(boggle_checker(x,y),true))\r\n\r\n%%\r\nx = ['OCEW'\r\n     'LRIR'\r\n     'GYSI'\r\n     'KREM'];\r\ny = 'GLORY';\r\nassert(isequal(boggle_checker(x,y),true))\r\n\r\n%%\r\nx = ['OCEW'\r\n     'LRIR'\r\n     'GYSI'\r\n     'KREM'];\r\ny = 'ROME';\r\nassert(isequal(boggle_checker(x,y),false))","published":true,"deleted":false,"likes_count":3,"comments_count":2,"created_by":134,"edited_by":223089,"edited_at":"2023-02-02T11:43:47.000Z","deleted_by":null,"deleted_at":null,"solvers_count":60,"test_suite_updated_at":"2023-02-02T11:43:47.000Z","rescore_all_solutions":false,"group_id":40,"created_at":"2012-01-28T22:27:00.000Z","updated_at":"2026-04-02T08:30:49.000Z","published_at":"2012-02-01T01:02:17.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eDescription\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIn the classic Parker Brothers game\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eBoggle\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, players find words from a 4x4 game board of letters. This exercise is to make sure that a particular solution to a boggle board is actually available on the board.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe program\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003edoes not\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e need to check to make sure if the input word is a valid english word. Furthermore, all inputs will be in all uppercase, so the user does not need to check/convert for case differences. The game board will always be 4x4.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eNote: This does not perfectly align with the rules of Boggle. Specifically, all solutions in the original game must be 3 or more letters, which this problem is not asking to account for, and the atomic \\\"Qu\\\" is present (which I have avoided in the test suite).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eHappy MATLABing!\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eExample\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[    x = ['TIPE'\\n         'YECV'\\n         'LSRA'\\n         'WOTU'];\\n    y = 'RACIEST';\\n    TF = true;]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":54750,"title":"Find the length of stream affected by a spill","description":"When a contaminant is spilled into a stream, one might want to know how much of the stream is affected—e.g., the length over which the concentration exceeds a specified threshold. The concentration  is often computed as a function of time  and distance  from the spill using the advection-dispersion equation:\r\n\r\nwhere  is the mean velocity of the river and  is a dispersion coefficient, which describes spreading by several mechanisms. For an instantaneous spill of mass  mixed over the cross section (with area ) at , the concentration can be shown—using some of the math needed for Cody Problem 51625—to be\r\n\r\nWrite a function to compute the length of stream affected by the spill. In other words, find the position  (say) beyond which the concentration never exceeds a threshold . ","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 282.7px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 141.35px; transform-origin: 407px 141.35px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 378.317px 8px; transform-origin: 378.317px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWhen a contaminant is spilled into a stream, one might want to know how much of the stream is affected—e.g., the length over which the concentration exceeds a specified threshold. The concentration \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eC\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 123.675px 8px; transform-origin: 123.675px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is often computed as a function of time \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003et\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and distance \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ex\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 168.833px 8px; transform-origin: 168.833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e from the spill using the advection-dispersion equation:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 36.6px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 18.3px; text-align: left; transform-origin: 384px 18.3px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-16px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"dC/dt + U dC/dx = K d^2C/dx^2\" style=\"width: 126.5px; height: 36.5px;\" width=\"126.5\" height=\"36.5\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 21.0083px 8px; transform-origin: 21.0083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ewhere \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eU\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 113.958px 8px; transform-origin: 113.958px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the mean velocity of the river and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eK\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 202.158px 8px; transform-origin: 202.158px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is a dispersion coefficient, which describes spreading by several mechanisms. For an instantaneous spill of mass \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eM\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 125.242px 8px; transform-origin: 125.242px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e mixed over the cross section (with area \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eA\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 12.05px 8px; transform-origin: 12.05px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e) at \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"x = 0\" style=\"width: 36.5px; height: 18px;\" width=\"36.5\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 59.5083px 8px; transform-origin: 59.5083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, the concentration can be shown—using some of the math needed for \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/51625\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003eCody Problem 51625\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 22.5583px 8px; transform-origin: 22.5583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e—to be\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 40.1px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 20.05px; text-align: left; transform-origin: 384px 20.05px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-17px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"C = (M/(A sqrt(4 pi K t))) exp(-(x-U t)^2/(4 K t))\" style=\"width: 204.5px; height: 40px;\" width=\"204.5\" height=\"40\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 44px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 22px; text-align: left; transform-origin: 384px 22px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 313.617px 8px; transform-origin: 313.617px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to compute the length of stream affected by the spill. In other words, find the position \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"x = L_a\" style=\"width: 42.5px; height: 20px;\" width=\"42.5\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 44.3417px 8px; transform-origin: 44.3417px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e (say) beyond which the concentration never exceeds a threshold \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"C = C_t\" style=\"width: 46px; height: 20px;\" width=\"46\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function La = affectedReach(U,K,M,A,Ct)\r\n% La = length of affected reach of stream [L]\r\n% U  = mean velocity [L/T]\r\n% K  = dispersion coefficient [L^2/T]\r\n% M  = mass of contaminant [M]\r\n% A  = cross-sectional area (L^2)\r\n% Ct = threshold concentration (M/L^3)\r\n\r\n  La = M/(Ct*A);\r\nend","test_suite":"%%\r\nM = 100;                    %  Mass (kg)\r\nA = 30;                     %  Cross-sectional area (m2)\r\nU = 0.3;                    %  Mean velocity (m/s)\r\nK = 2;                      %  Dispersion coefficient (m2/s)\r\nCt = 0.01;                  %  Target concentration (kg/m3)\r\nLa_correct = 1329.62;       %  Length of affected reach (m)\r\nassert(abs(affectedReach(U,K,M,A,Ct)-La_correct)\u003c1e-2)\r\n\r\n%%\r\nM = 50;                     %  Mass (kg)\r\nA = 15;                     %  Cross-sectional area (m2)\r\nU = 0.25;                   %  Mean velocity (m/s)\r\nK = 8.4;                    %  Dispersion coefficient (m2/s)\r\nCt = 0.001;                 %  Target concentration (kg/m3)\r\nLa_correct = 26332.1;       %  Length of affected reach (m)\r\nassert(abs(affectedReach(U,K,M,A,Ct)-La_correct)\u003c1e-2)\r\n\r\n%%\r\nM = 15;                     %  Mass (kg)\r\nA = 25;                     %  Cross-sectional area (m2)\r\nU = 0.25;                   %  Mean velocity (m/s)\r\nK = 11;                     %  Dispersion coefficient (m2/s)\r\nCt = 0.003;                 %  Target concentration (kg/m3)\r\nLa_correct = 91.59;         %  Length of affected reach (m)\r\nassert(abs(affectedReach(U,K,M,A,Ct)-La_correct)\u003c1e-2)\r\n\r\n%%\r\nM = 15;                     %  Mass (kg)\r\nA = 25;                     %  Cross-sectional area (m2)\r\nU = 0.25;                   %  Mean velocity (m/s)\r\nK = 11;                     %  Dispersion coefficient (m2/s)\r\nCt = 3e-4;                  %  Target concentration (kg/m3)\r\nLa_correct = 7256.28;       %  Length of affected reach (m)\r\nassert(abs(affectedReach(U,K,M,A,Ct)-La_correct)\u003c1e-2)\r\n\r\n%%\r\nM = 70;                     %  Mass (kg)\r\nA = 21;                     %  Cross-sectional area (m2)\r\nU = 0.15;                   %  Mean velocity (m/s)\r\nK = 1;                      %  Dispersion coefficient (m2/s)\r\nCt = 0.01;                  %  Target concentration (kg/m3)\r\nLa_correct = 1329.62;       %  Length of affected reach (m)\r\nassert(abs(affectedReach(U,K,M,A,Ct)-La_correct)\u003c1e-2)\r\n\r\n%%\r\nM = 280;                    %  Mass (kg)\r\nA = 21;                     %  Cross-sectional area (m2)\r\nU = 0.54;                   %  Mean velocity (m/s)\r\nK = 3.7;                    %  Dispersion coefficient (m2/s)\r\nCt = 0.007;                 %  Target concentration (kg/m3)\r\nLa_correct = 42140.42;      %  Length of affected reach (m)\r\nassert(abs(affectedReach(U,K,M,A,Ct)-La_correct)\u003c1e-2)\r\n\r\n%% Approximately plug flow\r\nM = 5*rand;                 %  Mass (kg)\r\nA = 40;                     %  Cross-sectional area (m2)\r\nU = 0.3*(1+rand);           %  Mean velocity (m/s)\r\nK = rand*1e-3;              %  Dispersion coefficient (m2/s)\r\nCt = 0.02*rand;             %  Target concentration (kg/m3)\r\nLa_approx = (U/(4*pi*K))*(M/(Ct*A))^2;\r\nassert(abs(affectedReach(U,K,M,A,Ct)-La_approx)/La_approx\u003c1e-3)\r\n\r\n%%\r\nfiletext = fileread('affectedReach.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'assert') || contains(filetext,'switch') || contains(filetext,'regexp') || contains(filetext,'if'); \r\nassert(~illegal)\r\n","published":true,"deleted":false,"likes_count":2,"comments_count":1,"created_by":46909,"edited_by":46909,"edited_at":"2022-06-14T05:04:44.000Z","deleted_by":null,"deleted_at":null,"solvers_count":4,"test_suite_updated_at":"2022-06-14T05:04:44.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2022-06-14T04:57:20.000Z","updated_at":"2022-06-14T05:04:44.000Z","published_at":"2022-06-14T04:59:16.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWhen a contaminant is spilled into a stream, one might want to know how much of the stream is affected—e.g., the length over which the concentration exceeds a specified threshold. The concentration \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"C\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eC\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is often computed as a function of time \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"t\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003et\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and distance \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"x\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e from the spill using the advection-dispersion equation:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"dC/dt + U dC/dx = K d^2C/dx^2\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\frac{\\\\partial C}{\\\\partial t} + U \\\\frac{\\\\partial C}{\\\\partial x} = K \\\\frac{\\\\partial^2 C}{\\\\partial x^2}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"U\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eU\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the mean velocity of the river and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"K\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eK\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is a dispersion coefficient, which describes spreading by several mechanisms. For an instantaneous spill of mass \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"M\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eM\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e mixed over the cross section (with area \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"A\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eA\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e) at \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"x = 0\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex = 0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, the concentration can be shown—using some of the math needed for \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/51625\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eCody Problem 51625\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e—to be\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"C = (M/(A sqrt(4 pi K t))) exp(-(x-U t)^2/(4 K t))\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eC = \\\\frac{M}{A\\\\sqrt{4\\\\pi K t}} \\\\exp\\\\left(-\\\\frac{(x-U t)^2}{4 K t}\\\\right)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function to compute the length of stream affected by the spill. In other words, find the position \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"x = L_a\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex = L_a\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e (say) beyond which the concentration never exceeds a threshold \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"C = C_t\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eC = C_t\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":46938,"title":"Numerical computation of the optimal shooting angle of a catapult","description":null,"description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 879.667px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 406.5px 439.833px; transform-origin: 406.5px 439.833px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 64.3333px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.5px 32.1667px; text-align: left; transform-origin: 383.5px 32.1667px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eConsider a capapult that fires a projects into the air with an initial velocity\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"56.5\" height=\"20\" style=\"width: 56.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e. The free-flying projectile is subjected to air friction and a gravitional force. Given a desired target \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"109\" height=\"21\" style=\"width: 109px; height: 21px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e and an initial velocity \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"56.5\" height=\"20\" style=\"width: 56.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e, find the optimal shooting angle \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"16\" height=\"18.5\" style=\"width: 16px; height: 18.5px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eof the catapult that minimizes the distance between the target and the trajectory of the fired projectile. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42.5px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.5px 21.25px; text-align: left; transform-origin: 383.5px 21.25px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003etip 1:\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e Consider the states \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"14.5\" height=\"20\" style=\"width: 14.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"14.5\" height=\"20\" style=\"width: 14.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e as the x- and y-position of the projectile, and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"14.5\" height=\"20\" style=\"width: 14.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"14.5\" height=\"20\" style=\"width: 14.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e as the x- and y-velocity. Then, the trajectory of the projectile can be found by solving the following ordinary differential equation (ODE):\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 22px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.5px 11px; text-align: left; transform-origin: 383.5px 11px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e        \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"45\" height=\"22\" style=\"width: 45px; height: 22px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e,     \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 22px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.5px 11px; text-align: left; transform-origin: 383.5px 11px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e        \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"45.5\" height=\"22\" style=\"width: 45.5px; height: 22px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e      \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 22px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.5px 11px; text-align: left; transform-origin: 383.5px 11px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; 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height: 19.5px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e, and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"47.5\" height=\"17.5\" style=\"width: 47.5px; height: 17.5px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eis the friction coefficient between the air and the projectile. Use the ode45.m function to compute the trajectory of the projectile with initial conditions \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" 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Plotting \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"14.5\" height=\"20\" style=\"width: 14.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e vs. \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"14.5\" height=\"20\" style=\"width: 14.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e will result in the x-y trajectory of the projectile, as shown in the figure below.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21.8333px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.5px 10.9167px; text-align: left; transform-origin: 383.5px 10.9167px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003etip 2: \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eUse the following update law, to incrementally update the shooting angle \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"15\" height=\"20\" style=\"width: 15px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21.8333px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.5px 10.9167px; text-align: left; transform-origin: 383.5px 10.9167px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e        \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" 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width=\"44\" height=\"20\" style=\"width: 44px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e the smallest Euclidean distance between the trajectory of the projectile and the target \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg 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\" width=\"298\" height=\"20\" style=\"width: 298px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eis a difference angle, and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"55.5\" height=\"17.5\" style=\"width: 55.5px; height: 17.5px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003ean update parameter.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.6667px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.5px 10.3333px; text-align: left; transform-origin: 383.5px 10.3333px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.6667px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.5px 10.3333px; text-align: left; transform-origin: 383.5px 10.3333px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.6667px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.5px 10.3333px; text-align: left; transform-origin: 383.5px 10.3333px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eExample of algorithm's numerical result:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 80px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 403.5px 40px; transform-origin: 403.5px 40px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 403.5px 10px; transform-origin: 403.5px 10px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003etheta = catapult(25,3,25)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 403.5px 10px; transform-origin: 403.5px 10px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003etheta = \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 403.5px 10px; transform-origin: 403.5px 10px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e    0.8431\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 403.5px 10px; transform-origin: 403.5px 10px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e    \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 264.333px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 10px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 10px; perspective-origin: 383.5px 132.167px; text-align: left; transform-origin: 383.5px 132.167px; white-space: pre-wrap; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cimg class=\"imageNode\" width=\"570\" height=\"259\" style=\"vertical-align: baseline;width: 570px;height: 259px\" 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\" data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function theta = catapult(xd,yd,v0) \r\n  \r\n    global g nu;\r\n    \r\n    g   = -9.81;  % grav. acceleration\r\n    nu  = 0.5;    % air friction coeff.\r\n    k   = 0;      % solver increments\r\n    dt  = 1e-2;   % timesteps\r\n    T   = 10;     % simulation time\r\n    TOL = 1e-2;   % absolute tolerance\r\n    \r\n    [~,y] = ode45(@ODECatapult,0:dt:T,[v0,0,0]); \r\n    \r\n    % solver for optimal angle\r\n    while (e \u003e= TOL) \u0026\u0026 (k \u003e 150)        \r\n        \r\n        %theta = theta + beta;\r\n        \r\n        k = k+1;    % add increment\r\n    end\r\n  \r\n    function dx = ODECatapult(t,x)\r\n        global g nu;\r\n        %% fill in ordinary differential equation %%\r\n    end\r\n    \r\n    function e = EuclideanDistance(y,xd,yd)\r\n        %% fill in computation of smallest euclidean distance %%\r\n    end\r\n    \r\n    function beta = UpdateLaw(y,e,lambda)\r\n        %% fill in update law to update the shooting angle %%\r\n    end\r\nend","test_suite":"xd = 8;\r\nyd = 2;\r\nv0 = 35;\r\ny_correct = 1.446;\r\n\r\nassert(isequal(round(catapult(xd,yd,v0),3),y_correct))\r\n\r\n%%\r\nxd = 15;\r\nyd = 5;\r\nv0 = 35;\r\ny_correct = 1.33;\r\n\r\nassert(isequal(round(catapult(xd,yd,v0),2),y_correct))\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":2,"created_by":636373,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":7,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2020-10-19T12:41:43.000Z","updated_at":"2025-01-02T11:31:42.000Z","published_at":"2020-10-19T13:39:36.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eConsider a capapult that fires a projects into the air with an initial velocity\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ev_0 \\\\in \\\\mathbb{R}_{\\\\ge 0}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. The free-flying projectile is subjected to air friction and a gravitional force. Given a desired target \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e$z_d = [x_d, y_d] \\\\in \\\\mathbb{R}^2$\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and an initial velocity \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ev_0 \\\\in \\\\mathbb{R}_{\\\\ge 0}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, find the optimal shooting angle \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\theta^*\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003eof the catapult that minimizes the distance between the target and the trajectory of the fired projectile. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003etip 1:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e Consider the states \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex_1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex_2\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e as the x- and y-position of the projectile, and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex_3\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex_4\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e as the x- and y-velocity. Then, the trajectory of the projectile can be found by solving the following ordinary differential equation (ODE):\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e        \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\dot{x_1} = x_3\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e,     \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e        \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\dot{x}_2 = x_4\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e      \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e        \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\dot{x}_3 = -\\\\nu x_3\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e,  \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e    \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e        \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\dot{x}_4 = -g - \\\\nu x_4\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e.   \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eg = 9.81\\\\; (\\\\text{m/s}^2)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\nu = 0.5\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003eis the friction coefficient between the air and the projectile. Use the ode45.m function to compute the trajectory of the projectile with initial conditions \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex(t = 0) = (0,0,v_0 \\\\cos(\\\\theta_k), v_0 \\\\sin(\\\\theta_k))\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. Plotting \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex_1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e vs. \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex_2\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e will result in the x-y trajectory of the projectile, as shown in the figure below.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003etip 2: \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eUse the following update law, to incrementally update the shooting angle \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\theta_k\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e        \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\theta_{k+1} = \\\\theta_k + \\\\lambda \\\\, \\\\text{sign}(\\\\theta_{e,k})\\\\,e_k\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ee_k \\\\in \\\\mathbb{R}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e the smallest Euclidean distance between the trajectory of the projectile and the target \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ez_d\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\theta_{e,k} = \\\\text{atan2}(d_y,d_x) - \\\\text{atan2}(v_0\\\\sin(\\\\theta_k),v_0\\\\cos(\\\\theta_k))\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003eis a difference angle, and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e$\\\\lambda = 0.01$\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003ean update parameter.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eExample of algorithm's numerical result:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[theta = catapult(25,3,25)\\ntheta = \\n    0.8431\\n    ]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"259\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"570\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" 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\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"}],"problem_search":{"errors":[],"problems":[{"id":2358,"title":"Word Search Solver","description":"There are n words (minimum of three letters in each word) supplied with a given word search board. The answer will contain n rows where each row contains the row and column indices where the word starts followed by an integer indicating the direction of the word. The direction integer runs from 1 to 8 and starts at 12 o'clock, running clockwise. So, a word spelled to the right (normal fashion) would be indexed as a 3 and facing downward to the left (SW) would be a 6.\r\nThe first board is included here for reference:\r\n board = [\r\n  'xcupa'\r\n  'dyrng'\r\n  'osbaq'\r\n  'exbid'\r\n  'wgamv'\r\n ];\r\n\r\n words = {'aim'; 'bid'; 'cup'; 'doe'};\r\n\r\n loc_ans = [\r\n  3 4 5\r\n  4 3 3\r\n  1 2 3\r\n  2 1 5\r\n ];","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 450.933px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 225.467px; transform-origin: 407px 225.467px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 84px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 42px; text-align: left; transform-origin: 384px 42px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 365px 8px; transform-origin: 365px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThere are n words (minimum of three letters in each word) supplied with a given word search board. The answer will contain n rows where each row contains the row and column indices where the word starts followed by an integer indicating the direction of the word. The direction integer runs from 1 to 8 and starts at 12 o'clock, running clockwise. So, a word spelled to the right (normal fashion) would be indexed as a 3 and facing downward to the left (SW) would be a 6.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 143.5px 8px; transform-origin: 143.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe first board is included here for reference:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 326.933px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 404px 163.467px; transform-origin: 404px 163.467px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 40px 8.5px; tab-size: 4; transform-origin: 40px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e board = [\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 36px 8.5px; tab-size: 4; transform-origin: 36px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 8px 8.5px; transform-origin: 8px 8.5px; \"\u003e  \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); perspective-origin: 28px 8.5px; text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); transform-origin: 28px 8.5px; \"\u003e'xcupa'\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 36px 8.5px; tab-size: 4; transform-origin: 36px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 8px 8.5px; transform-origin: 8px 8.5px; \"\u003e  \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); perspective-origin: 28px 8.5px; text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); transform-origin: 28px 8.5px; \"\u003e'dyrng'\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 36px 8.5px; tab-size: 4; transform-origin: 36px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 8px 8.5px; transform-origin: 8px 8.5px; \"\u003e  \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); perspective-origin: 28px 8.5px; text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); transform-origin: 28px 8.5px; \"\u003e'osbaq'\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 36px 8.5px; tab-size: 4; transform-origin: 36px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 8px 8.5px; transform-origin: 8px 8.5px; \"\u003e  \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); perspective-origin: 28px 8.5px; text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); transform-origin: 28px 8.5px; \"\u003e'exbid'\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 36px 8.5px; tab-size: 4; transform-origin: 36px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 8px 8.5px; transform-origin: 8px 8.5px; \"\u003e  \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); perspective-origin: 28px 8.5px; text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); transform-origin: 28px 8.5px; \"\u003e'wgamv'\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 12px 8.5px; tab-size: 4; transform-origin: 12px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e ];\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 8.5px; tab-size: 4; transform-origin: 0px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 152px 8.5px; tab-size: 4; transform-origin: 152px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 40px 8.5px; transform-origin: 40px 8.5px; \"\u003e words = {\u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); perspective-origin: 20px 8.5px; text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); transform-origin: 20px 8.5px; \"\u003e'aim'\u003c/span\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 8px 8.5px; transform-origin: 8px 8.5px; \"\u003e; \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); perspective-origin: 20px 8.5px; text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); transform-origin: 20px 8.5px; \"\u003e'bid'\u003c/span\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 8px 8.5px; transform-origin: 8px 8.5px; \"\u003e; \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); perspective-origin: 20px 8.5px; text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); transform-origin: 20px 8.5px; \"\u003e'cup'\u003c/span\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 8px 8.5px; transform-origin: 8px 8.5px; \"\u003e; \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); perspective-origin: 20px 8.5px; text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); transform-origin: 20px 8.5px; \"\u003e'doe'\u003c/span\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 8px 8.5px; transform-origin: 8px 8.5px; \"\u003e};\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 8.5px; tab-size: 4; transform-origin: 0px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 48px 8.5px; tab-size: 4; transform-origin: 48px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e loc_ans = [\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 28px 8.5px; tab-size: 4; transform-origin: 28px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e  3 4 5\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 28px 8.5px; tab-size: 4; transform-origin: 28px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e  4 3 3\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 28px 8.5px; tab-size: 4; transform-origin: 28px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e  1 2 3\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 28px 8.5px; tab-size: 4; transform-origin: 28px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e  2 1 5\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 12px 8.5px; tab-size: 4; transform-origin: 12px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e ];\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function loc = WordSearch(board,words)\r\n loc = [-1 -1];\r\nend","test_suite":"%%\r\nboard = [\r\n 'xcupa';\r\n 'dyrng';\r\n 'osbaq';\r\n 'exbid';\r\n 'wgamv';\r\n];\r\nwords = {'aim'; 'bid'; 'cup'; 'doe'};\r\nloc_ans = [\r\n 3 4 5;\r\n 4 3 3;\r\n 1 2 3;\r\n 2 1 5;\r\n];\r\nassert(isequal(WordSearch(board,words),loc_ans))\r\n\r\n%%\r\nboard = [\r\n 'okeanpbirf';\r\n 'qicwnafehu';\r\n 'wniazcgame';\r\n 'egaxjelbiv';\r\n 'bnomelvmcr';\r\n];\r\nwords = {'fair'; 'game'; 'hall'; 'ice'; 'jack'; 'king'; 'lemon'};\r\nloc_ans = [\r\n 2 7 4;\r\n 3 7 3;\r\n 2 9 6;\r\n 3 3 1;\r\n 4 5 8;\r\n 1 2 5;\r\n 5 6 7;\r\n];\r\nassert(isequal(WordSearch(board,words),loc_ans))\r\n\r\n%%\r\nboard = [\r\n 'werojea';\r\n 'cafefls';\r\n 'apufrbw';\r\n 'hrleaan';\r\n 'aoltgbb';\r\n 'aoaevdr';\r\n 'mdzoece';\r\n];\r\nwords = {'able'; 'bare'; 'cafe'; 'door'; 'edge'; 'full'};\r\nloc_ans = [\r\n 4 6 1;\r\n 5 7 8;\r\n 2 1 3;\r\n 7 2 1;\r\n 7 7 8;\r\n 2 3 5;\r\n];\r\nassert(isequal(WordSearch(board,words),loc_ans))\r\n\r\n%%\r\nboard = [\r\n 'anmjwfpnyo';\r\n 'wasgijsaen';\r\n 'akigyqaekl';\r\n 'doorbellci';\r\n 'loiapucfdx';\r\n 'loepalirri';\r\n 'alzhheagle';\r\n 'mgxmsovnpr';\r\n 'aiqtbovgee';\r\n 'juyhctahnr';\r\n];\r\nwords = {'airplane'; 'board'; 'clasp'; 'doorbell'; 'eagle'; 'fiesty'; 'graph'; 'hatch'; 'igloo'; 'jigsaw'; 'key'; 'llama'};\r\nloc_ans = [\r\n 2 2 4;\r\n 9 5 2;\r\n 5 7 1;\r\n 4 1 3;\r\n 7 6 3;\r\n 5 8 6;\r\n 3 4 5;\r\n 10 8 7;\r\n 9 2 1;\r\n 2 6 7;\r\n 3 9 1;\r\n 5 1 5;\r\n];\r\nassert(isequal(WordSearch(board,words),loc_ans))","published":true,"deleted":false,"likes_count":3,"comments_count":2,"created_by":26769,"edited_by":223089,"edited_at":"2022-09-19T13:13:49.000Z","deleted_by":null,"deleted_at":null,"solvers_count":17,"test_suite_updated_at":"2022-09-19T13:13:50.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2014-06-11T13:58:10.000Z","updated_at":"2025-12-15T20:16:04.000Z","published_at":"2014-06-11T13:58:44.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThere are n words (minimum of three letters in each word) supplied with a given word search board. The answer will contain n rows where each row contains the row and column indices where the word starts followed by an integer indicating the direction of the word. The direction integer runs from 1 to 8 and starts at 12 o'clock, running clockwise. So, a word spelled to the right (normal fashion) would be indexed as a 3 and facing downward to the left (SW) would be a 6.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe first board is included here for reference:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ board = [\\n  'xcupa'\\n  'dyrng'\\n  'osbaq'\\n  'exbid'\\n  'wgamv'\\n ];\\n\\n words = {'aim'; 'bid'; 'cup'; 'doe'};\\n\\n loc_ans = [\\n  3 4 5\\n  4 3 3\\n  1 2 3\\n  2 1 5\\n ];]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":3043,"title":"Fill-a-pix - Solver (basic)","description":"\u003chttp://www.conceptispuzzles.com/index.aspx?uri=puzzle/fill-a-pix/rules Fill-a-pix\u003e is a logic puzzle game similar to Pic-a-Pix (aka Logic art) and Minesweeper. An example starting board is shown below on the left with the completed board shown to its right. Each number in the board indicates how many surrounding cells, including itself, are to be filled in. There are (up to) nine total cells associated with each number: four immediately adjacent (up, down, left, and right), four diagonally adjacent (one touching each corner), and the central cell (where the number is located).\r\n\r\nBased on this logic, all 0's and 9's are determinant, as all nine cells are either empty or filled, respectively, for these numbers. Also, all 6's on the board edges and 4's in the corners should be completely filled in, as they only involve 6 or 4 cells, respectively.\r\n\r\n\u003c\u003chttp://www.conceptispuzzles.com/picture/27/1558.gif\u003e\u003e\r\n\r\n\u003c\u003chttp://www.conceptispuzzles.com/picture/27/1574.gif\u003e\u003e\r\n\r\nThis problem deals with basic-logic Fill-a-pix problems; a sample step-by-step solution is found \u003chttp://www.conceptispuzzles.com/index.aspx?uri=puzzle/fill-a-pix/techniques here\u003e. These problems are basic in that each clue can be solved independent of all other clues, though some looping or iteration over the board will be required to solve all the clues. Basic logic can be summarized in the following two cases, regarding the cells associated with each clue: (1) if the sum of filled-in cells equals the clue, all other associated cells should be marked as empty, and (2) if the sum of empty cells equals the total number of associated cells minus the clue, all other associated cells should be marked as filled in.\r\n\r\nFor this problem, you will be presented with a board full of clues. Write a function to solve the Fill-a-pix puzzle based on those clues, returning a solution of the same size as the board filled with 1's (filled) and 0's (empty).\r\n\r\nA related problem is \u003chttps://www.mathworks.com/matlabcentral/cody/problems/3042-fill-a-pix-solution-checker Fill-a-pix - Solution Checker\u003e.","description_html":"\u003cp\u003e\u003ca href = \"http://www.conceptispuzzles.com/index.aspx?uri=puzzle/fill-a-pix/rules\"\u003eFill-a-pix\u003c/a\u003e is a logic puzzle game similar to Pic-a-Pix (aka Logic art) and Minesweeper. An example starting board is shown below on the left with the completed board shown to its right. Each number in the board indicates how many surrounding cells, including itself, are to be filled in. There are (up to) nine total cells associated with each number: four immediately adjacent (up, down, left, and right), four diagonally adjacent (one touching each corner), and the central cell (where the number is located).\u003c/p\u003e\u003cp\u003eBased on this logic, all 0's and 9's are determinant, as all nine cells are either empty or filled, respectively, for these numbers. Also, all 6's on the board edges and 4's in the corners should be completely filled in, as they only involve 6 or 4 cells, respectively.\u003c/p\u003e\u003cimg src = \"http://www.conceptispuzzles.com/picture/27/1558.gif\"\u003e\u003cimg src = \"http://www.conceptispuzzles.com/picture/27/1574.gif\"\u003e\u003cp\u003eThis problem deals with basic-logic Fill-a-pix problems; a sample step-by-step solution is found \u003ca href = \"http://www.conceptispuzzles.com/index.aspx?uri=puzzle/fill-a-pix/techniques\"\u003ehere\u003c/a\u003e. These problems are basic in that each clue can be solved independent of all other clues, though some looping or iteration over the board will be required to solve all the clues. Basic logic can be summarized in the following two cases, regarding the cells associated with each clue: (1) if the sum of filled-in cells equals the clue, all other associated cells should be marked as empty, and (2) if the sum of empty cells equals the total number of associated cells minus the clue, all other associated cells should be marked as filled in.\u003c/p\u003e\u003cp\u003eFor this problem, you will be presented with a board full of clues. Write a function to solve the Fill-a-pix puzzle based on those clues, returning a solution of the same size as the board filled with 1's (filled) and 0's (empty).\u003c/p\u003e\u003cp\u003eA related problem is \u003ca href = \"https://www.mathworks.com/matlabcentral/cody/problems/3042-fill-a-pix-solution-checker\"\u003eFill-a-pix - Solution Checker\u003c/a\u003e.\u003c/p\u003e","function_template":"function [solution] = fill_a_pix_solver_basic(board)\r\n\r\nsolution = ones(size(board));\r\n\r\nend\r\n","test_suite":"%%\r\nboard = [-1,-1,-1,-1,1; -1,9,-1,-1,-1; -1,8,8,-1,-1; -1,-1,-1,-1,4; 4,-1,5,-1,2];\r\nboard(board==-1) = NaN;\r\nsolution = [1,1,1,0,0; 1,1,1,1,0; 1,1,1,1,1; 1,1,0,1,0; 1,1,1,1,0];\r\nassert(isequal(fill_a_pix_solver_basic(board),solution))\r\n\r\n%%\r\nboard = [-1,-1,-1,-1,-1,-1,-1,-1,0,-1; -1,8,8,-1,2,-1,0,-1,-1,-1; 5,-1,8,-1,-1,-1,-1,-1,-1,-1; -1,-1,-1,-1,-1,2,-1,-1,-1,2; 1,-1,-1,-1,4,5,6,-1,-1,-1; -1,0,-1,-1,-1,7,9,-1,-1,6; -1,-1,-1,6,-1,-1,9,-1,-1,6; -1,-1,6,6,8,7,8,7,-1,5; -1,4,-1,6,6,6,-1,6,-1,4; -1,-1,-1,-1,-1,-1,3,-1,-1,-1];\r\nboard(board==-1) = NaN;\r\nsolution = [0,1,1,0,0,0,0,0,0,0; 1,1,1,1,0,0,0,0,0,0; 1,1,1,1,0,0,0,0,0,0; 0,1,1,0,0,0,0,0,0,0; 0,0,0,0,0,1,1,1,1,1; 0,0,0,1,1,1,1,1,1,1; 0,0,0,1,0,1,1,1,1,1; 0,1,1,1,1,1,1,1,1,1; 0,1,0,1,1,1,0,1,0,1; 0,0,1,0,0,0,1,0,1,0];\r\nassert(isequal(fill_a_pix_solver_basic(board),solution))\r\n\r\n%%\r\nboard = [-1,2,3,-1,-1,0,-1,-1,-1,-1; -1,-1,-1,-1,3,-1,2,-1,-1,6; -1,-1,5,-1,5,3,-1,5,7,4; -1,4,-1,5,-1,5,-1,6,-1,3; -1,-1,4,-1,5,-1,6,-1,-1,3; -1,-1,-1,2,-1,5,-1,-1,-1,-1; 4,-1,1,-1,-1,-1,1,1,-1,-1; 4,-1,1,-1,-1,-1,1,-1,4,-1; -1,-1,-1,-1,6,-1,-1,-1,-1,4; -1,4,4,-1,-1,-1,-1,4,-1,-1];\r\nboard(board==-1) = NaN;\r\nsolution = [0,1,1,0,0,0,0,0,1,1; 0,0,0,1,0,0,0,1,1,1; 0,0,1,1,1,0,0,1,1,1; 0,1,1,0,1,1,0,1,0,0; 0,1,0,0,0,1,1,1,1,0; 1,1,0,0,1,1,0,0,1,1; 1,0,0,0,1,0,0,0,0,1;  1,0,0,0,1,0,0,0,0,1; 1,1,0,0,1,1,0,0,1,1; 0,1,1,1,1,1,1,1,1,0];\r\nassert(isequal(fill_a_pix_solver_basic(board),solution))\r\n\r\n%%\r\nboard = [0,-1,-1,4,3,2,1,-1,-1,-1,-1,-1,3,-1,-1; -1,-1,5,-1,-1,4,-1,-1,4,4,-1,-1,-1,-1,3; -1,5,4,5,4,5,5,-1,5,3,-1,1,2,-1,3; 4,-1,-1,-1,4,-1,-1,4,2,-1,1,-1,-1,-1,-1; -1,-1,5,4,-1,2,2,-1,1,0,-1,-1,7,5,-1; -1,-1,-1,5,-1,-1,0,-1,-1,-1,-1,4,5,-1,2; 4,-1,-1,5,4,2,0,0,-1,-1,-1,5,6,-1,-1; 5,-1,-1,6,5,-1,-1,-1,-1,-1,3,3,3,-1,3; -1,-1,5,-1,5,3,-1,-1,-1,-1,-1,-1,3,-1,-1; 5,-1,-1,6,5,-1,3,5,-1,6,-1,-1,0,-1,0; -1,-1,5,-1,4,3,2,4,5,-1,4,-1,-1,1,-1; -1,7,-1,-1,5,-1,-1,1,-1,5,5,5,-1,-1,-1; -1,-1,6,4,4,4,3,1,2,4,-1,-1,6,4,-1; -1,5,-1,6,-1,-1,-1,-1,-1,4,6,-1,-1,-1,-1; -1,-1,-1,-1,-1,-1,3,2,0,-1,4,4,3,-1,2];\r\nboard(board==-1) = NaN;\r\nsolution = [0,0,0,1,1,0,0,0,0,0,1,1,1,1,0; 0,0,1,0,1,0,0,1,1,1,0,0,0,0,1; 1,1,1,1,0,1,1,0,1,0,0,0,0,0,1; 1,0,0,0,1,0,1,1,0,0,0,0,1,1,0; 0,1,1,1,0,0,0,0,0,0,0,1,1,0,0; 0,1,0,1,0,0,0,0,0,0,0,1,1,1,0; 1,1,1,0,1,0,0,0,0,0,0,0,0,0,1; 1,0,0,1,1,0,0,0,0,0,1,1,1,1,1; 1,1,1,1,0,1,0,0,1,1,0,0,0,0,0; 1,0,0,1,0,0,1,1,1,1,0,0,0,0,0; 1,1,1,1,1,0,0,0,1,0,1,0,0,0,0; 1,1,0,0,1,0,0,0,0,1,0,1,1,0,0; 0,1,1,1,0,1,0,0,0,1,1,0,1,1,0; 0,1,1,0,0,1,1,0,0,0,1,1,0,1,0; 0,0,1,1,1,0,1,0,0,0,1,1,0,0,1];\r\nassert(isequal(fill_a_pix_solver_basic(board),solution))\r\n\r\n%% anti-cheating test case\r\nboard = NaN(9);\r\nsolution = NaN(9);\r\nfor i = 1:3\r\n\tfor j = 1:3\r\n\t\tif randi(2) == 2\r\n\t\t\tboard(i*3-1,j*3-1) = 9;\r\n\t\t\tsolution((i*3-2):(i*3),(j*3-2):(j*3)) = 1;\r\n\t\telse\r\n\t\t\tboard(i*3-1,j*3-1) = 0;\r\n\t\t\tsolution((i*3-2):(i*3),(j*3-2):(j*3)) = 0;\r\n\t\tend\r\n\tend\r\nend\r\nassert(isequal(fill_a_pix_solver_basic(board),solution))\r\n","published":true,"deleted":false,"likes_count":2,"comments_count":11,"created_by":26769,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":10,"test_suite_updated_at":"2015-02-25T19:14:45.000Z","rescore_all_solutions":true,"group_id":1,"created_at":"2015-02-25T04:24:32.000Z","updated_at":"2026-04-01T15:40:48.000Z","published_at":"2015-02-25T04:24:32.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/image\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/media/image1.gif\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/image\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/media/image2.gif\"}],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:hyperlink w:docLocation=\\\"http://www.conceptispuzzles.com/index.aspx?uri=puzzle/fill-a-pix/rules\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eFill-a-pix\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e is a logic puzzle game similar to Pic-a-Pix (aka Logic art) and Minesweeper. An example starting board is shown below on the left with the completed board shown to its right. Each number in the board indicates how many surrounding cells, including itself, are to be filled in. There are (up to) nine total cells associated with each number: four immediately adjacent (up, down, left, and right), four diagonally adjacent (one touching each corner), and the central cell (where the number is located).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eBased on this logic, all 0's and 9's are determinant, as all nine cells are either empty or filled, respectively, for these numbers. Also, all 6's on the board edges and 4's in the corners should be completely filled in, as they only involve 6 or 4 cells, respectively.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"-1\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"-1\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"-1\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"-1\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId2\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis problem deals with basic-logic Fill-a-pix problems; a sample step-by-step solution is found\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://www.conceptispuzzles.com/index.aspx?uri=puzzle/fill-a-pix/techniques\\\"\u003e\u003cw:r\u003e\u003cw:t\u003ehere\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e. These problems are basic in that each clue can be solved independent of all other clues, though some looping or iteration over the board will be required to solve all the clues. Basic logic can be summarized in the following two cases, regarding the cells associated with each clue: (1) if the sum of filled-in cells equals the clue, all other associated cells should be marked as empty, and (2) if the sum of empty cells equals the total number of associated cells minus the clue, all other associated cells should be marked as filled in.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor this problem, you will be presented with a board full of clues. Write a function to solve the Fill-a-pix puzzle based on those clues, returning a solution of the same size as the board filled with 1's (filled) and 0's (empty).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA related problem is\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/3042-fill-a-pix-solution-checker\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eFill-a-pix - Solution Checker\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" 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Boggle","description":"Description\r\nIn the classic Parker Brothers game Boggle, players find words from a 4x4 game board of letters. This exercise is to make sure that a particular solution to a boggle board is actually available on the board.\r\nThe program does not need to check to make sure if the input word is a valid english word. Furthermore, all inputs will be in all uppercase, so the user does not need to check/convert for case differences. The game board will always be 4x4.\r\nNote: This does not perfectly align with the rules of Boggle. Specifically, all solutions in the original game must be 3 or more letters, which this problem is not asking to account for, and the atomic \"Qu\" is present (which I have avoided in the test suite).\r\nHappy MATLABing!\r\nExample\r\n    x = ['TIPE'\r\n         'YECV'\r\n         'LSRA'\r\n         'WOTU'];\r\n    y = 'RACIEST';\r\n    TF = true;","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 387.6px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 193.8px; transform-origin: 407px 193.8px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 40.5px 8px; transform-origin: 40.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eDescription\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 112px 8px; transform-origin: 112px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eIn the classic Parker Brothers game\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"/#null\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eBoggle\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 247px 8px; transform-origin: 247px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, players find words from a 4x4 game board of letters. This exercise is to make sure that a particular solution to a boggle board is actually available on the board.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 41px 8px; transform-origin: 41px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe program\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 27.5px 8px; transform-origin: 27.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003edoes not\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 311px 8px; transform-origin: 311px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e need to check to make sure if the input word is a valid english word. Furthermore, all inputs will be in all uppercase, so the user does not need to check/convert for case differences. The game board will always be 4x4.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 370px 8px; transform-origin: 370px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eNote: This does not perfectly align with the rules of Boggle. Specifically, all solutions in the original game must be 3 or more letters, which this problem is not asking to account for, and the atomic \"Qu\" is present (which I have avoided in the test suite).\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 61px 8px; transform-origin: 61px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eHappy MATLABing!\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 29.5px 8px; transform-origin: 29.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eExample\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 122.6px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 404px 61.3px; transform-origin: 404px 61.3px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 60px 8.5px; tab-size: 4; transform-origin: 60px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 36px 8.5px; transform-origin: 36px 8.5px; \"\u003e    x = [\u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); perspective-origin: 24px 8.5px; text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); transform-origin: 24px 8.5px; \"\u003e'TIPE'\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 60px 8.5px; tab-size: 4; transform-origin: 60px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 36px 8.5px; transform-origin: 36px 8.5px; \"\u003e         \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); perspective-origin: 24px 8.5px; text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); transform-origin: 24px 8.5px; \"\u003e'YECV'\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 60px 8.5px; tab-size: 4; transform-origin: 60px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 36px 8.5px; transform-origin: 36px 8.5px; \"\u003e         \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); perspective-origin: 24px 8.5px; text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); transform-origin: 24px 8.5px; \"\u003e'LSRA'\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 68px 8.5px; tab-size: 4; transform-origin: 68px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 36px 8.5px; transform-origin: 36px 8.5px; \"\u003e         \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); perspective-origin: 24px 8.5px; text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); transform-origin: 24px 8.5px; \"\u003e'WOTU'\u003c/span\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 8px 8.5px; transform-origin: 8px 8.5px; \"\u003e];\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 72px 8.5px; tab-size: 4; transform-origin: 72px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 32px 8.5px; transform-origin: 32px 8.5px; \"\u003e    y = \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); perspective-origin: 36px 8.5px; text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); transform-origin: 36px 8.5px; \"\u003e'RACIEST'\u003c/span\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 4px 8.5px; transform-origin: 4px 8.5px; \"\u003e;\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 56px 8.5px; tab-size: 4; transform-origin: 56px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e    TF = true;\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function tf = boggle_checker(x,y)\r\n  tf = true;\r\nend","test_suite":"%%\r\nx = ['TIPE'\r\n     'YECV'\r\n     'LSRA'\r\n     'WOTU'];\r\ny = 'RACIEST';\r\nassert(isequal(boggle_checker(x,y),true))\r\n\r\n%%\r\nx = ['TIPE'\r\n     'YECV'\r\n     'LSRA'\r\n     'WOTU'];\r\ny = 'RACIESTS';\r\nassert(isequal(boggle_checker(x,y),false))\r\n\r\n%%\r\nx = ['TIPE'\r\n     'YECV'\r\n     'LSRA'\r\n     'WOTU'];\r\ny = 'RACIESTW';\r\nassert(isequal(boggle_checker(x,y),false))\r\n\r\n%%\r\nx = ['TIPE'\r\n     'YECV'\r\n     'LSRA'\r\n     'WOTU'];\r\ny = 'AUTOLYTIC';\r\nassert(isequal(boggle_checker(x,y),true))\r\n\r\n%%\r\nx = ['TIPE'\r\n     'YECV'\r\n     'LSRA'\r\n     'WOTU'];\r\ny = 'RESTAR';\r\nassert(isequal(boggle_checker(x,y),false))\r\n\r\n%%\r\nx = ['OCEW'\r\n     'LRIR'\r\n     'GYSI'\r\n     'KREM'];\r\ny = 'SIRI';\r\nassert(isequal(boggle_checker(x,y),true))\r\n\r\n%%\r\nx = ['OCEW'\r\n     'LRIR'\r\n     'GYSI'\r\n     'KREM'];\r\ny = 'SIRIM';\r\nassert(isequal(boggle_checker(x,y),true))\r\n\r\n%%\r\nx = ['OCEW'\r\n     'LRIR'\r\n     'GYSI'\r\n     'KREM'];\r\ny = 'GLORY';\r\nassert(isequal(boggle_checker(x,y),true))\r\n\r\n%%\r\nx = ['OCEW'\r\n     'LRIR'\r\n     'GYSI'\r\n     'KREM'];\r\ny = 'ROME';\r\nassert(isequal(boggle_checker(x,y),false))","published":true,"deleted":false,"likes_count":3,"comments_count":2,"created_by":134,"edited_by":223089,"edited_at":"2023-02-02T11:43:47.000Z","deleted_by":null,"deleted_at":null,"solvers_count":60,"test_suite_updated_at":"2023-02-02T11:43:47.000Z","rescore_all_solutions":false,"group_id":40,"created_at":"2012-01-28T22:27:00.000Z","updated_at":"2026-04-02T08:30:49.000Z","published_at":"2012-02-01T01:02:17.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eDescription\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIn the classic Parker Brothers game\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eBoggle\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, players find words from a 4x4 game board of letters. This exercise is to make sure that a particular solution to a boggle board is actually available on the board.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe program\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003edoes not\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e need to check to make sure if the input word is a valid english word. Furthermore, all inputs will be in all uppercase, so the user does not need to check/convert for case differences. The game board will always be 4x4.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eNote: This does not perfectly align with the rules of Boggle. Specifically, all solutions in the original game must be 3 or more letters, which this problem is not asking to account for, and the atomic \\\"Qu\\\" is present (which I have avoided in the test suite).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eHappy MATLABing!\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eExample\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[    x = ['TIPE'\\n         'YECV'\\n         'LSRA'\\n         'WOTU'];\\n    y = 'RACIEST';\\n    TF = true;]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":54750,"title":"Find the length of stream affected by a spill","description":"When a contaminant is spilled into a stream, one might want to know how much of the stream is affected—e.g., the length over which the concentration exceeds a specified threshold. The concentration  is often computed as a function of time  and distance  from the spill using the advection-dispersion equation:\r\n\r\nwhere  is the mean velocity of the river and  is a dispersion coefficient, which describes spreading by several mechanisms. For an instantaneous spill of mass  mixed over the cross section (with area ) at , the concentration can be shown—using some of the math needed for Cody Problem 51625—to be\r\n\r\nWrite a function to compute the length of stream affected by the spill. In other words, find the position  (say) beyond which the concentration never exceeds a threshold . ","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 282.7px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 141.35px; transform-origin: 407px 141.35px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 378.317px 8px; transform-origin: 378.317px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWhen a contaminant is spilled into a stream, one might want to know how much of the stream is affected—e.g., the length over which the concentration exceeds a specified threshold. The concentration \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eC\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 123.675px 8px; transform-origin: 123.675px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is often computed as a function of time \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003et\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and distance \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ex\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 168.833px 8px; transform-origin: 168.833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e from the spill using the advection-dispersion equation:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 36.6px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 18.3px; text-align: left; transform-origin: 384px 18.3px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-16px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"dC/dt + U dC/dx = K d^2C/dx^2\" style=\"width: 126.5px; height: 36.5px;\" width=\"126.5\" height=\"36.5\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 21.0083px 8px; transform-origin: 21.0083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ewhere \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eU\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 113.958px 8px; transform-origin: 113.958px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the mean velocity of the river and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eK\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 202.158px 8px; transform-origin: 202.158px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is a dispersion coefficient, which describes spreading by several mechanisms. For an instantaneous spill of mass \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eM\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 125.242px 8px; transform-origin: 125.242px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e mixed over the cross section (with area \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eA\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 12.05px 8px; transform-origin: 12.05px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e) at \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAEkAAAAkCAYAAADFGRdYAAAC7UlEQVRoQ+2YPU8VQRSG4ReI2lkRPwoqKDQ0WmgBJLYmQPwBaENFTNBSMdFAQ4GY2KsBWiOaSIGFBEK0svCjtFMw/AB9X3MmOTs7s3Puyl1IdjY52Xt3vs48886Zs9vbk68kgd5kjVyhJ0MyiCBDypAMBAxVspIypCiBsyg5I6XvU5zapqQJAHkA24HtwvphfDYLW4X9DAFrE6QlALgNewi7p2BM4fcybB12MwSqLZAciG+AMBwA8RrPRgMA/7FsA6TTmOcX2MkYBNlyz0VdQ7h/0tuuDZCcijjv67BXgbjDQE6V8fK3YyuUtI2JXxQA53D/HoDER79EbYR1vo6S3JH5ObCfL+PZgS/RiCNH8fiPDLqH+6kKB1xcYpUCzKrtNojKlOqINPKlyPI1KaMDXK3YKjnfGB8GDoHUD8NYHIY+fqwBqbAtqyBRPb9FOV8FhjsdTuA/c40nsHFZoapVclyous1DgHQLfTw19KPH60RJhf6tgfsOHHokTlGKL2ELsBcGR3UVrqzrp8OmheqL+BcKwH6fGhJ9ZuIYu/Qca0HSg1FBb2A6IfufCXezrfabyeJYxWBzKLsr5bUgsa01AHZz0p323eh2o3Mu+lNJlzr19gjrWxdXn26FhNIakzhHxh8GaQbAC7Dgy2ACRtOnG91xh441cJdOaisknbVy4FjmmhJM06cb/XEvtvxdeuVQDjvFlXaKBZLLNXiqRVP3FB0pb/p047B6YSZlR/ju6nyqlF6kIHF7bMGmYTxyQ3GJKzUPSyWSRo5dqeb8jp1w7mQLfiUIQeLW4vUB9gy2Anssz/x8aQbPuYePezrAxJjbiF8C/C2nvxJcQXnpS6UPyY8ZfgKmZUluqQStK7Ko2Sl935C2V3Hn5xDC4xz4ShWNsz4kUr0vjd8pBWm/qKZrsFh5zTk00ozzuwEjpD7YvoB7i3s0XKRiUiOeH/dBMiTDCmVIGZKBgKFKVlKGZCBgqJKVlCEZCBiqZCUZIP0F1sSXJS9IuzgAAAAASUVORK5CYII=\" alt=\"x = 0\" style=\"width: 36.5px; height: 18px;\" width=\"36.5\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 59.5083px 8px; transform-origin: 59.5083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, the concentration can be shown—using some of the math needed for \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/51625\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003eCody Problem 51625\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 22.5583px 8px; transform-origin: 22.5583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e—to be\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 40.1px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 20.05px; text-align: left; transform-origin: 384px 20.05px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-17px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"C = (M/(A sqrt(4 pi K t))) exp(-(x-U t)^2/(4 K t))\" style=\"width: 204.5px; height: 40px;\" width=\"204.5\" height=\"40\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 44px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 22px; text-align: left; transform-origin: 384px 22px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 313.617px 8px; transform-origin: 313.617px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to compute the length of stream affected by the spill. In other words, find the position \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"x = L_a\" style=\"width: 42.5px; height: 20px;\" width=\"42.5\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 44.3417px 8px; transform-origin: 44.3417px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e (say) beyond which the concentration never exceeds a threshold \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAFwAAAAoCAYAAABzXJ2PAAADxUlEQVRoQ+2Zue9NQRTH/f4Ca6VQWAqJhFgbDQ2hVFiiU1iiFISIQqylwpLQaJDQSIgloaCxhigUllJlKfwBfD8yI+d3f/fOnXnunfdeMpN88+57b+acM985c+bMuRPTSsvKwERWbUXZtEJ4ZicohBfCMzOQWV3x8DEjfL7snWts/qXnd+b7Wj1/EL5nnldf6mZL8OKK8Gfm+1I9w8GXJgMG8XBI3CFsE2YKn4VPTsEGff4UXggYR1vV1+wzycWpdglbhQVmfqhf7Th4YOY/R8+NDpZCOKt3VoBU2iHhlmBXE+NuCitdn4v63JeJmK7V4DAnhL1OMPM6LdgdXO2D8y0MGRJLON58wa0mQrdUFFsdGPFcwBtYlHNdM5FBHs51280BdZuFewG9N/QfOwBP3/i/hEP2dScEstcIbTF5t/pcijA0A3fJKiD7iXMuBi8LOJcXzpi3winh6P8QTrx+agTgtY0HgunnDQjGs2Qq+h/A7vxoyN6uZ7w3pv1Qp51CaCcEb5pV5Xsk7HKMZtcHL0/pnyC6t673JdmfUcRsdndso+8jIbj7QzGcmO0PDDKPWbGax7SfDZ1MISaUJE+1iXC8+5uRluvwq8tzkyelAV+FmNBnZb/UF59dtR5+gxjFmCbC/aHn5fay2jVGV8+MQeeVGv78meP1pY6PtrOJcJ/mIChnOPG5fvQEGjqe1+/Bw6syLpuDNRHOicstkvZKGPfbYtsCWgejb2/ZVRPhv42Fqad12+RG8X+bnfS6o2MIb03mR5HBRJss4b3u6FELKcPKUoYeUqwBrDj1gbbrfKJT1XYfVpZSPTRjb9TJc27y8EEvAb4OsWjABRpWlkKVkzqRb7FpITuScHS8ISvi8kh18d+NO3TTtBcByqzHWkjEO+8I65yS5NUf8oCT0n/E2cCupvoXujz5UvQVS6gbb8u2k+4wIcJtmRU5HJ5Xa4xA8QGBXTGuZPu1tqGU2yY3bFv/ph+88ELisECtv1rcwvH2uwUj4zkjIOuvnLZ6eLXAjoCHwhthurBCoNgTswP8pEb986Aj099DIOuxM3q9PnnLQ/gJ7YBN+v+uMCXDayPck4MXo2iegFLaa+G90FohG3WGa+zD0aj7LxGWCzMEwgteynzb6jQ+PE15cRFL+BhyNlSTecdLdXVK8lAI735dfMZTW3EshHdPuE+pa0vahfDuCfcvbkgHSSgmvUQvhHdPuI/fZHPXhEll4kJ494Tj4cTx2pp8Ibx7woMSC+GF8MwMZFZXPLwQnpmBzOqKhxfCMzOQWd0fvS21Ke8sW2EAAAAASUVORK5CYII=\" alt=\"C = C_t\" style=\"width: 46px; height: 20px;\" width=\"46\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function La = affectedReach(U,K,M,A,Ct)\r\n% La = length of affected reach of stream [L]\r\n% U  = mean velocity [L/T]\r\n% K  = dispersion coefficient [L^2/T]\r\n% M  = mass of contaminant [M]\r\n% A  = cross-sectional area (L^2)\r\n% Ct = threshold concentration (M/L^3)\r\n\r\n  La = M/(Ct*A);\r\nend","test_suite":"%%\r\nM = 100;                    %  Mass (kg)\r\nA = 30;                     %  Cross-sectional area (m2)\r\nU = 0.3;                    %  Mean velocity (m/s)\r\nK = 2;                      %  Dispersion coefficient (m2/s)\r\nCt = 0.01;                  %  Target concentration (kg/m3)\r\nLa_correct = 1329.62;       %  Length of affected reach (m)\r\nassert(abs(affectedReach(U,K,M,A,Ct)-La_correct)\u003c1e-2)\r\n\r\n%%\r\nM = 50;                     %  Mass (kg)\r\nA = 15;                     %  Cross-sectional area (m2)\r\nU = 0.25;                   %  Mean velocity (m/s)\r\nK = 8.4;                    %  Dispersion coefficient (m2/s)\r\nCt = 0.001;                 %  Target concentration (kg/m3)\r\nLa_correct = 26332.1;       %  Length of affected reach (m)\r\nassert(abs(affectedReach(U,K,M,A,Ct)-La_correct)\u003c1e-2)\r\n\r\n%%\r\nM = 15;                     %  Mass (kg)\r\nA = 25;                     %  Cross-sectional area (m2)\r\nU = 0.25;                   %  Mean velocity (m/s)\r\nK = 11;                     %  Dispersion coefficient (m2/s)\r\nCt = 0.003;                 %  Target concentration (kg/m3)\r\nLa_correct = 91.59;         %  Length of affected reach (m)\r\nassert(abs(affectedReach(U,K,M,A,Ct)-La_correct)\u003c1e-2)\r\n\r\n%%\r\nM = 15;                     %  Mass (kg)\r\nA = 25;                     %  Cross-sectional area (m2)\r\nU = 0.25;                   %  Mean velocity (m/s)\r\nK = 11;                     %  Dispersion coefficient (m2/s)\r\nCt = 3e-4;                  %  Target concentration (kg/m3)\r\nLa_correct = 7256.28;       %  Length of affected reach (m)\r\nassert(abs(affectedReach(U,K,M,A,Ct)-La_correct)\u003c1e-2)\r\n\r\n%%\r\nM = 70;                     %  Mass (kg)\r\nA = 21;                     %  Cross-sectional area (m2)\r\nU = 0.15;                   %  Mean velocity (m/s)\r\nK = 1;                      %  Dispersion coefficient (m2/s)\r\nCt = 0.01;                  %  Target concentration (kg/m3)\r\nLa_correct = 1329.62;       %  Length of affected reach (m)\r\nassert(abs(affectedReach(U,K,M,A,Ct)-La_correct)\u003c1e-2)\r\n\r\n%%\r\nM = 280;                    %  Mass (kg)\r\nA = 21;                     %  Cross-sectional area (m2)\r\nU = 0.54;                   %  Mean velocity (m/s)\r\nK = 3.7;                    %  Dispersion coefficient (m2/s)\r\nCt = 0.007;                 %  Target concentration (kg/m3)\r\nLa_correct = 42140.42;      %  Length of affected reach (m)\r\nassert(abs(affectedReach(U,K,M,A,Ct)-La_correct)\u003c1e-2)\r\n\r\n%% Approximately plug flow\r\nM = 5*rand;                 %  Mass (kg)\r\nA = 40;                     %  Cross-sectional area (m2)\r\nU = 0.3*(1+rand);           %  Mean velocity (m/s)\r\nK = rand*1e-3;              %  Dispersion coefficient (m2/s)\r\nCt = 0.02*rand;             %  Target concentration (kg/m3)\r\nLa_approx = (U/(4*pi*K))*(M/(Ct*A))^2;\r\nassert(abs(affectedReach(U,K,M,A,Ct)-La_approx)/La_approx\u003c1e-3)\r\n\r\n%%\r\nfiletext = fileread('affectedReach.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'assert') || contains(filetext,'switch') || contains(filetext,'regexp') || contains(filetext,'if'); \r\nassert(~illegal)\r\n","published":true,"deleted":false,"likes_count":2,"comments_count":1,"created_by":46909,"edited_by":46909,"edited_at":"2022-06-14T05:04:44.000Z","deleted_by":null,"deleted_at":null,"solvers_count":4,"test_suite_updated_at":"2022-06-14T05:04:44.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2022-06-14T04:57:20.000Z","updated_at":"2022-06-14T05:04:44.000Z","published_at":"2022-06-14T04:59:16.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWhen a contaminant is spilled into a stream, one might want to know how much of the stream is affected—e.g., the length over which the concentration exceeds a specified threshold. The concentration \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"C\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eC\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is often computed as a function of time \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"t\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003et\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and distance \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"x\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e from the spill using the advection-dispersion equation:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"dC/dt + U dC/dx = K d^2C/dx^2\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\frac{\\\\partial C}{\\\\partial t} + U \\\\frac{\\\\partial C}{\\\\partial x} = K \\\\frac{\\\\partial^2 C}{\\\\partial x^2}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"U\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eU\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the mean velocity of the river and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"K\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eK\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is a dispersion coefficient, which describes spreading by several mechanisms. For an instantaneous spill of mass \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"M\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eM\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e mixed over the cross section (with area \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"A\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eA\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e) at \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"x = 0\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex = 0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, the concentration can be shown—using some of the math needed for \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/51625\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eCody Problem 51625\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e—to be\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"C = (M/(A sqrt(4 pi K t))) exp(-(x-U t)^2/(4 K t))\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eC = \\\\frac{M}{A\\\\sqrt{4\\\\pi K t}} \\\\exp\\\\left(-\\\\frac{(x-U t)^2}{4 K t}\\\\right)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function to compute the length of stream affected by the spill. In other words, find the position \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"x = L_a\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex = L_a\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e (say) beyond which the concentration never exceeds a threshold \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"C = C_t\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eC = C_t\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":46938,"title":"Numerical computation of the optimal shooting angle of a catapult","description":null,"description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 879.667px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 406.5px 439.833px; transform-origin: 406.5px 439.833px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 64.3333px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.5px 32.1667px; text-align: left; transform-origin: 383.5px 32.1667px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eConsider a capapult that fires a projects into the air with an initial velocity\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"56.5\" height=\"20\" style=\"width: 56.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e. The free-flying projectile is subjected to air friction and a gravitional force. Given a desired target \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAANoAAAAqCAYAAADVj0XCAAAKM0lEQVR4Xu2cd6w2VRGHH+xdEewGW4gao2Cw94IaxR5jQTQC9oZdFLuCINixiwTsJYoSomAUNWILJmCJsYsl9hIVG7Y8+ebw7bfflrO7777svfecv27uu2XOnPmdmfnNnN2FMooGigZm18Aus7+hvKBooGiAArRiBEUDa9BAAdoalFxeUTRQgFZsoGhgDRooQFuDkssrigYK0LbZwGWAA4DLN5jE54GvbFFTuSrwUODiDfP/KPD9LaoXpy127gA8Ebgl8A/gFOB1wM/qeilA26aR3YD3AJcG/l5T0puBj29Rg7ou8ErgCpX5XwjYE3g4cMYW1YvTdgN6GvAW4Fzg0cA9wlYeB/y6qpsCtO1AOxZ4CfDdLWw8OVO/JPBa4N1bGGhXA14NvBz4TijNTVq9PCaio/cWoO1sTnq0ArQcmEEBGtwWuAHwLuB/FbXdNzzaiwKE5/9UPFrxaHnw2n7VRgOaoPhixiT/ApwF/BA4Ffg08PuW+y4W//9X7ff0rscDbyserXi0DLtrvWQjAs086mDgR8AzAEO/FwaBkSbqvG4HvCzIsT8DLwU+DPw7U2F6tLcC9we+VoBWgJZpN42XbUSgvQl4SOTfAuwawNMbiK/rAx8MMF4HOAI4BPhAhsIuDLwYuHLTs0voWELHDBva4ZKtALQnAV8FDgXuCDwS+GWPom4IHA08u0KQlBytprRChuTDbZVA81m3Bx4G3BrQo/QNw7shZQXzpqEeTaD5jpuENzuop5Yq4ygDaRnIuutOo3i04tH6DLv++yqApt3dGTgSuPlAAdYJNDdgaXpLGTvQ9RWZLxKh5s+B99dYyOLRikcbaN7bL58KNEFmvqSXuWIwfK8HvhCF39GCtdw4xaP1Ac256I2vCbymizRp82jGmyaCl+qYtZ0UIn0zjNzQ0RDBHfgB0QVwJeBRwMmhhMtGjG7oIT38FOC3MynIdynLTYGbRdh1NvDkmsFqaMcB3wh5duhYGCHbVKApj97hWtEg8KoGUmKEWK23TAGatbL3RZtVvQ1P7GgHkibWYP9ZkUD83Aj4SPpfG9BsrxFIbcO2pOfMsAP1vTd3AYaGF7lAc+dynBeJ7yNisxFY/412JQ3R3rc/RBL901yhB15nyCLYLgccFh0JJux1anm/CGm81rYhWbUpYwrQ3Kg0Sjcn2T9Dx1zqfKzMY4H2pWirenALGSJJYnfIJ4G/VoSzxmYPpO1Z3+4Cmhfqzb4ZC1QtyonUZ8bCTt0ZmxS3dKBVZbafzZrJ1wEBdx+gM04faykZ9107NkaNSgM+vJIr2Jt4zwjVbA/S004ZU4C2T3h/61k2cf9kiiCZ944FmhvZO8Lr1nOvvWPt3VCbxhvCEZ3v5Zo8muGQdKZeq9pge5VYQFGc+rsy57r4y3I9WnUiyWgsftoF8LtYlLl36CZlphqOIPtUAF950nBNzSFeAJwzcTWmAC1tTvXNYKJInbc3Ac1wr16w9iECyOK2xeZbAALGzXTymuayjr305ZyaWsOzxwDt6pFr3Ak4PYz7F2uQte0VdwU+FmGM3lVPm4ZGYwhkiFnNJcaIOwVoGredF1PG0LSgCWhtMvyGbb2c5mWGtW5K1V7G0XLnAC2LvqxJ4HPNHdw5bhy53EmRx4wWdsYbxwDtEhGjex7Jrm2Lm/XetzaR59BPFfjVXju9nU2usnqf6dBhrkybAWipM8SwWjJGj6+3/VOwiJJY1s5WFrn1AS2bvmwAmmeY3EH3jyTchV7qGAM0dWMXwFEt4VrXXL131foxt3YXtrXIUDa1GFkEdjN4fg95lSvTFKCl0NF+QzendYy+HE3QyZ7bSGxa5CFXwef/dzpXNlbgPqDJrNwv4lkPtw0Z7qRWy3X1gk2ioG9sJDJESl36Vprak8YPCgq9b47p9zH66Xt20t/n4mCmoZBn7Axtu7zZEJmmAO1uwGkR4trk+8e+Ca3g9z6g+Qrt3FqefY12dshHuFn9YEXhdufn5qYyjLvHTmGc29TA2aTDjQI0F8KFkcEzxLhN02G/HiMZo58+u0sEjXSzwJfStzj83MxaVY5MU4AmcXRilD+UT9DNPXKAZnokm25um9hQN1JzNTeq1o6PXOHbPNoqGEYTcPMyO5rfuaqkMndiA68bEjq6KNYQpabtbTPcMMTwyL/JvvU0+/c8qd1VAmnTj4Zs/uf5qKFsl7mGxrFv1Ko0srcDZ2bqI2fNpgBNe3tqfFfD72t4/P9XmbKNvSwHaD5bTuGNQSa5vn+LfE2gWRZp7GHMFaoJaGMZRu9zRzAnMM61uHurKBUs/eM2XUBLJMF/Isex5cZ5JS+R8o5Eq9sRcPdg16oMX45+jCKOjx3fplbDqyGfVqgSNBavzYOk9ZW9aeTIVL9vCtB8VgrLTEk862W0Mydbmws0ZVP/npoWcHoxw/u6p8vF1g7X1YGWXKhJtccETghX35ef+bGWY4BPROFUtvFDwI9jNzBXWPLoApq1FT2zfXnfA+z0eELFWyUvYFikhzNsc3Gq3ixXP/XQeUy9ScMVXH0eI1emVQMtGXTaUNxIJJTU8Rw5m0CrH/x0vZvSmUT+6cX0tnZ2+CUw0wTlHN0NVQVaeokFOmP7NKrtVu6AMkbWFgyZLGinXdhWlNS3Zo+YQLMH0NBxaAi0blB2Ac0d2Ll6etYDgFLl1XDHHd45WuTXq/l39XNjQ/RjNGCzrTUxR5U9zNWJYPVclLnGZ1tuGiLTHEDzmZJIelz7BYeMMXW0+qcMuvSqs/FktSxtfVjC0RYG23MVaLsGQ+jiaFyPDW/kTm7fllXy61VOm9o3p8sXXHsBB8b3FhQusUsPDIZpiCIviGuH5GhD5BOEY/UjcPeotVP1vdv1dKe+aIdBTJHJ908NHatz0KhtY7KY7qfa5jiP1qeztfzeR+/bQye6pT91m9Ya3IUMi3Sv7i52I2hMqUE0tQPpAdLx8bVMZsJL5gJa6tYYqh8jh1dEvmbXfe6QKXODfBbgNy+axliZ0rNWCbTceW346/qA5gS9RmLDBF+vJ4P15eiCsCAtAHX/qU5jfmYiaUxrhb1twZekvDmApt7G6GdMJ466zGGKx8pUXasCtBGWmwO0tscmhd+lUqyVbbRzXDLAcNOjNl6XU6weIf7KbhFo5qISOnaWV4c0b/3rxTkvHqMfWUPpb09OGD1YKmgarpvsptd7rR5QFtQOh291CDdUpnQUx1alNHynjQiecRvySYEcnW3aa6YALXU2PC+ApmFYWfc7C8bc0uB6N+s6UzvG516AdJLWPKE+JBXajrF3yTWnfgSZ1LikhqG7rLDffK82EjfJNlSm9FUoc/D6GEpKzL2Gi37+FKA5MSliqeR7R+honuaOZ5FUBs4u6XWcOVqqkufSTzr2cq/I4/TEuYXfuWRa6hosQq6pQFvEJIoQRQNL10AB2tJXqMi3KTRQgLYplrFMYukaKEBb+goV+TaFBgrQNsUylkksXQMFaEtfoSLfptDA/wF1oOpJsndYXQAAAABJRU5ErkJggg==\" width=\"109\" height=\"21\" style=\"width: 109px; height: 21px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e and an initial velocity \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"56.5\" height=\"20\" style=\"width: 56.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e, find the optimal shooting angle \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"16\" height=\"18.5\" style=\"width: 16px; height: 18.5px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eof the catapult that minimizes the distance between the target and the trajectory of the fired projectile. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42.5px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.5px 21.25px; text-align: left; transform-origin: 383.5px 21.25px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003etip 1:\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e Consider the states \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"14.5\" height=\"20\" style=\"width: 14.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"14.5\" height=\"20\" style=\"width: 14.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e as the x- and y-position of the projectile, and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAB0AAAAoCAYAAAACJPERAAACPklEQVRYR+3VS6iNcRQF8N+lKGJAJkpJSh5T5VVIJEURRZ6lPAoloUgpz0wklIGJgUchUiJCkUwYUAbKQJSIUh6FvNq3ffX5Oufee65z3IFz6nTqfP9vr73XXmv9W3TDp6UbMDVBG8p6k94mvXVhoCmkutBYrcj/TW8PDMEszMFEXMJ6vKP1khiP/RiNNThbyz4q0dsbw/ASk3Aa/TAD1zEZG/EVM7ENR/4WtPj+YJzElCx+EZuwHa9rASqe7UhIvZLGmOxyTrcTj7oKGO91BBpnVuNYgqzCcfxsNOg4XMNHzMaDKoADEE2twAjcwF7cKjfZmUlDVGcwFktyx2Xc/tiXDcUaRmEXopEFeFzLTkPJe1I88V4U3oHvJdS5+Iyrhanm4XylRtubNJ4twgS8QQgoii7F2wJo+HoonuNb4f/w9xVEQ0H17097oCOxNb/Ds8ArzE/1DspwuI0fpcmjboTGGGzBp2qgYY+++ICBOITDuIuiX2Ov4dfY2SncrwA4NQMkUuxZWQBtkwZgFImunmTnuzONwh6x2wPYgId4kc8irYr2CdWuw/JMsTi7FvcqTRrgobIo/D73F9MUaYu8PYg+aYVzpR221W3bcYBHqFzAyszt1jOdsUxXcyBsFOuZXvZ3I0Gj2WU4kRdHaKPhkwbA4qR4IZ7+C9CeKc4QadxKX+oJGsVDodNwFDdT0WGbyOHN5WuwHjuNGhEYYbmwzJ20VfxGDv8RDI1Wb1XV12PSmi3VBK2Zslpe6BZ6fwFJmW0pj/+3QwAAAABJRU5ErkJggg==\" width=\"14.5\" height=\"20\" style=\"width: 14.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"14.5\" height=\"20\" style=\"width: 14.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e as the x- and y-velocity. Then, the trajectory of the projectile can be found by solving the following ordinary differential equation (ODE):\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 22px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.5px 11px; text-align: left; transform-origin: 383.5px 11px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e        \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"45\" height=\"22\" style=\"width: 45px; height: 22px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e,     \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 22px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.5px 11px; text-align: left; transform-origin: 383.5px 11px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e        \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"45.5\" height=\"22\" style=\"width: 45.5px; height: 22px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e      \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 22px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.5px 11px; text-align: left; transform-origin: 383.5px 11px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; 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height: 19.5px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e, and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"47.5\" height=\"17.5\" style=\"width: 47.5px; height: 17.5px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eis the friction coefficient between the air and the projectile. Use the ode45.m function to compute the trajectory of the projectile with initial conditions \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" 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Plotting \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAB0AAAAoCAYAAAACJPERAAABwElEQVRYR+3VS6hNcRTH8c9VKDKSiTKRiYzlGUaSYsRAMbkD14SSooiUt4nEwMDUoxhI6d6ukRtKMWBmrESUwkheLa20O23249zTGdy964zO/7++a/1+a63/iCF8I0Ng6qADVb2Tt5N3WhToGmlaZPxXkJkt7ywswVZsxzrcx3584s8jsQbnsQL7cKeJH2XyzsVSvMV63MICbMZDbMRBfMMWHMXVfqHF+4txA5sy+D0cwjG8bwIqnq1qpDkpY1T2IKs7iVdtgXGvChpnxnAtIXtxHb8GDV2NSXzFNryoAC7KRCOxM2Vn61QaTXUbK7E7PS6LNR978kx0/AmcagONTo5so3niO4fj+FESbHbKvgqP20JDhV1Yiw+IBprIaj7+R+KosjV0OY7kbxnG8Q47snvDu1gOU/hZSKIRNMYjfPmChbiMK3iC4ryGrzGv4ddNPO+pujY0gBHkMF5n5qdzG0UXhrcXcQAv8Sb/i23VOz61oeHfzgz8Of2Laoqyxb69hHk4i7v4XuJtbWg/s957t4P+VaTORmoq/VDk3YBHbTdS0wrjoY8qR3MSnuECnva+vYOQtzLZDlopUT8HZo68vwGa/l8pXtmErgAAAABJRU5ErkJggg==\" width=\"14.5\" height=\"20\" style=\"width: 14.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e vs. \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"14.5\" height=\"20\" style=\"width: 14.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e will result in the x-y trajectory of the projectile, as shown in the figure below.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21.8333px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.5px 10.9167px; text-align: left; transform-origin: 383.5px 10.9167px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003etip 2: \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eUse the following update law, to incrementally update the shooting angle \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"15\" height=\"20\" style=\"width: 15px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21.8333px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.5px 10.9167px; text-align: left; transform-origin: 383.5px 10.9167px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e        \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" 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width=\"44\" height=\"20\" style=\"width: 44px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e the smallest Euclidean distance between the trajectory of the projectile and the target \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg 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\" width=\"298\" height=\"20\" style=\"width: 298px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eis a difference angle, and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"55.5\" height=\"17.5\" style=\"width: 55.5px; height: 17.5px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003ean update parameter.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.6667px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.5px 10.3333px; text-align: left; transform-origin: 383.5px 10.3333px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.6667px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.5px 10.3333px; text-align: left; transform-origin: 383.5px 10.3333px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.6667px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.5px 10.3333px; text-align: left; transform-origin: 383.5px 10.3333px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eExample of algorithm's numerical result:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 80px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 403.5px 40px; transform-origin: 403.5px 40px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 403.5px 10px; transform-origin: 403.5px 10px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003etheta = catapult(25,3,25)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 403.5px 10px; transform-origin: 403.5px 10px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003etheta = \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 403.5px 10px; transform-origin: 403.5px 10px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e    0.8431\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 403.5px 10px; transform-origin: 403.5px 10px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e    \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 264.333px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 10px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 10px; perspective-origin: 383.5px 132.167px; text-align: left; transform-origin: 383.5px 132.167px; white-space: pre-wrap; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cimg class=\"imageNode\" width=\"570\" height=\"259\" style=\"vertical-align: baseline;width: 570px;height: 259px\" 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\" data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function theta = catapult(xd,yd,v0) \r\n  \r\n    global g nu;\r\n    \r\n    g   = -9.81;  % grav. acceleration\r\n    nu  = 0.5;    % air friction coeff.\r\n    k   = 0;      % solver increments\r\n    dt  = 1e-2;   % timesteps\r\n    T   = 10;     % simulation time\r\n    TOL = 1e-2;   % absolute tolerance\r\n    \r\n    [~,y] = ode45(@ODECatapult,0:dt:T,[v0,0,0]); \r\n    \r\n    % solver for optimal angle\r\n    while (e \u003e= TOL) \u0026\u0026 (k \u003e 150)        \r\n        \r\n        %theta = theta + beta;\r\n        \r\n        k = k+1;    % add increment\r\n    end\r\n  \r\n    function dx = ODECatapult(t,x)\r\n        global g nu;\r\n        %% fill in ordinary differential equation %%\r\n    end\r\n    \r\n    function e = EuclideanDistance(y,xd,yd)\r\n        %% fill in computation of smallest euclidean distance %%\r\n    end\r\n    \r\n    function beta = UpdateLaw(y,e,lambda)\r\n        %% fill in update law to update the shooting angle %%\r\n    end\r\nend","test_suite":"xd = 8;\r\nyd = 2;\r\nv0 = 35;\r\ny_correct = 1.446;\r\n\r\nassert(isequal(round(catapult(xd,yd,v0),3),y_correct))\r\n\r\n%%\r\nxd = 15;\r\nyd = 5;\r\nv0 = 35;\r\ny_correct = 1.33;\r\n\r\nassert(isequal(round(catapult(xd,yd,v0),2),y_correct))\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":2,"created_by":636373,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":7,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2020-10-19T12:41:43.000Z","updated_at":"2025-01-02T11:31:42.000Z","published_at":"2020-10-19T13:39:36.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eConsider a capapult that fires a projects into the air with an initial velocity\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ev_0 \\\\in \\\\mathbb{R}_{\\\\ge 0}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. The free-flying projectile is subjected to air friction and a gravitional force. Given a desired target \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e$z_d = [x_d, y_d] \\\\in \\\\mathbb{R}^2$\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and an initial velocity \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ev_0 \\\\in \\\\mathbb{R}_{\\\\ge 0}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, find the optimal shooting angle \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\theta^*\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003eof the catapult that minimizes the distance between the target and the trajectory of the fired projectile. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003etip 1:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e Consider the states \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex_1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex_2\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e as the x- and y-position of the projectile, and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex_3\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex_4\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e as the x- and y-velocity. Then, the trajectory of the projectile can be found by solving the following ordinary differential equation (ODE):\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e        \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\dot{x_1} = x_3\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e,     \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e        \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\dot{x}_2 = x_4\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e      \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e        \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\dot{x}_3 = -\\\\nu x_3\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e,  \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e    \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e        \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\dot{x}_4 = -g - \\\\nu x_4\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e.   \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eg = 9.81\\\\; (\\\\text{m/s}^2)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\nu = 0.5\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003eis the friction coefficient between the air and the projectile. Use the ode45.m function to compute the trajectory of the projectile with initial conditions \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex(t = 0) = (0,0,v_0 \\\\cos(\\\\theta_k), v_0 \\\\sin(\\\\theta_k))\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. Plotting \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex_1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e vs. \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex_2\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e will result in the x-y trajectory of the projectile, as shown in the figure below.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003etip 2: \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eUse the following update law, to incrementally update the shooting angle \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\theta_k\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e        \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\theta_{k+1} = \\\\theta_k + \\\\lambda \\\\, \\\\text{sign}(\\\\theta_{e,k})\\\\,e_k\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ee_k \\\\in \\\\mathbb{R}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e the smallest Euclidean distance between the trajectory of the projectile and the target \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ez_d\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\theta_{e,k} = \\\\text{atan2}(d_y,d_x) - \\\\text{atan2}(v_0\\\\sin(\\\\theta_k),v_0\\\\cos(\\\\theta_k))\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003eis a difference angle, and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e$\\\\lambda = 0.01$\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003ean update parameter.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eExample of algorithm's numerical result:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[theta = catapult(25,3,25)\\ntheta = \\n    0.8431\\n    ]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"259\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"570\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" 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