Problem 56040. A Binary Search

Created by Renee Coetsee

Solve Later

{"parts":[{"partUri":"/matlab/document.xml","contentType":"application/vnd.mathworks.matlab.code.document+xml","content":"<?xml version=\"1.0\" encoding=\"UTF-8\"?><w:document xmlns:w=\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\"><w:body><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>One way to locate a target value in a sorted array, is to use a binary search algorithm. Here, you test if the midpoint in the array is the target value. If it is, great! You're done. If not, then you continually narrow your search area depending on whether the target is less than or greater than the midpoint. The algorithm is as follows:</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>Given an array of sorted values (</w:t></w:r><w:r><w:rPr><w:rFonts w:cs=\"monospace\"/></w:rPr><w:t>X</w:t></w:r><w:r><w:t>), and a target value you wish to locate (</w:t></w:r><w:r><w:rPr><w:rFonts w:cs=\"monospace\"/></w:rPr><w:t>target</w:t></w:r><w:r><w:t>)</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"ListParagraph\"/><w:numPr><w:numId w:val=\"2\"/></w:numPr><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>Calculate the index of the midpoint of the array </w:t></w:r><w:r><w:rPr><w:rFonts w:cs=\"monospace\"/></w:rPr><w:t>X</w:t></w:r><w:r><w:t> by taking the average of the largest and smallest indices and rounding to the nearest integer. </w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"ListParagraph\"/><w:numPr><w:numId w:val=\"2\"/></w:numPr><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>If the value located at the midpoint matches your target, set found to true.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"ListParagraph\"/><w:numPr><w:numId w:val=\"2\"/></w:numPr><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>If the target is less than the value located at the midpoint of </w:t></w:r><w:r><w:rPr><w:rFonts w:cs=\"monospace\"/></w:rPr><w:t>X</w:t></w:r><w:r><w:t>, narrow your search to the lower half of </w:t></w:r><w:r><w:rPr><w:rFonts w:cs=\"monospace\"/></w:rPr><w:t>X</w:t></w:r><w:r><w:t> by setting the largest index in the array to the midpoint - 1. </w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"ListParagraph\"/><w:numPr><w:numId w:val=\"2\"/></w:numPr><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>If the target is greater than the value located at the midpoint of </w:t></w:r><w:r><w:rPr><w:rFonts w:cs=\"monospace\"/></w:rPr><w:t>X</w:t></w:r><w:r><w:t>, narrow your search to the upper half of </w:t></w:r><w:r><w:rPr><w:rFonts w:cs=\"monospace\"/></w:rPr><w:t>X</w:t></w:r><w:r><w:t> by setting the smallest index in the array to the midpoint + 1. </w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"ListParagraph\"/><w:numPr><w:numId w:val=\"2\"/></w:numPr><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>Repeat the steps above until found is true.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:customXml w:element=\"image\"><w:customXmlPr><w:attr w:name=\"height\" w:val=\"551\"/><w:attr w:name=\"width\" w:val=\"610\"/><w:attr w:name=\"verticalAlign\" w:val=\"baseline\"/><w:attr w:name=\"altText\" w:val=\"\"/><w:attr w:name=\"relationshipId\" w:val=\"rId1\"/></w:customXmlPr></w:customXml></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>Write a function that takes </w:t></w:r><w:r><w:rPr><w:rFonts w:cs=\"monospace\"/></w:rPr><w:t>X</w:t></w:r><w:r><w:t> and </w:t></w:r><w:r><w:rPr><w:rFonts w:cs=\"monospace\"/></w:rPr><w:t>target</w:t></w:r><w:r><w:t> as inputs, performs a binary search and outputs the index of target value as well as the number of iterations it took to 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<div 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; "><div style="block-size: 926.467px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 463.233px; transform-origin: 407px 463.233px; vertical-align: baseline; "><div 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; "><span 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: 383.5px 8px; transform-origin: 383.5px 8px; unicode-bidi: normal; ">One way to locate a target value in a sorted array, is to use a binary search algorithm. Here, you test if the midpoint in the array is the target value. If it is, great! You're done. If not, then you continually narrow your search area depending on whether the target is less than or greater than the midpoint. The algorithm is as follows:</div><div style="block-size: 21.5px; 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: 384px 10.75px; text-align: left; transform-origin: 384px 10.75px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span 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: 104px 8px; transform-origin: 104px 8px; unicode-bidi: normal; ">Given an array of sorted values (<span 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: 4px 8px; transform-origin: 4px 8px; unicode-bidi: normal; ">X<span 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: 126.5px 8px; transform-origin: 126.5px 8px; unicode-bidi: normal; ">), and a target value you wish to locate (<span 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: 24px 8px; transform-origin: 24px 8px; unicode-bidi: normal; ">target<span 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: 2.5px 8px; transform-origin: 2.5px 8px; unicode-bidi: normal; ">)</div><ol style="block-size: 164.967px; counter-reset: list-item 0; font-family: Helvetica, Arial, sans-serif; list-style-type: decimal; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; perspective-origin: 391px 82.4833px; transform-origin: 391px 82.4833px; margin-top: 10px; margin-bottom: 20px; "><li style="block-size: 41.3667px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 20.6833px; text-align: left; transform-origin: 363px 20.6833px; white-space: pre-wrap; margin-left: 56px; ">Calculate the index of the midpoint of the array X by taking the average of the largest and smallest indices and rounding to the nearest integer. </li><li style="block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2167px; text-align: left; transform-origin: 363px 10.2167px; white-space: pre-wrap; margin-left: 56px; ">If the value located at the midpoint matches your target, set found to true.</li><li style="block-size: 41.3667px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 20.6833px; text-align: left; transform-origin: 363px 20.6833px; white-space: pre-wrap; margin-left: 56px; ">If the target is less than the value located at the midpoint of X, narrow your search to the lower half of X by setting the largest index in the array to the midpoint - 1. </li><li style="block-size: 41.3667px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 20.6833px; text-align: left; transform-origin: 363px 20.6833px; white-space: pre-wrap; margin-left: 56px; ">If the target is greater than the value located at the midpoint of X, narrow your search to the upper half of X by setting the smallest index in the array to the midpoint + 1. </li><li style="block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2167px; text-align: left; transform-origin: 363px 10.2167px; white-space: pre-wrap; margin-left: 56px; ">Repeat the steps above until found is true.</li></ol><div style="block-size: 556.5px; 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: 384px 278.25px; text-align: left; transform-origin: 384px 278.25px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><img class="imageNode" style="vertical-align: baseline;width: 610px;height: 551px" 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data-image-state="image-loaded" width="610" height="551"></div><div 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: 384px 21.25px; text-align: left; transform-origin: 384px 21.25px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span 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: 84.5px 8px; transform-origin: 84.5px 8px; unicode-bidi: normal; ">Write a function that takes <span 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: 4px 8px; transform-origin: 4px 8px; unicode-bidi: normal; ">X<span 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: 16px 8px; transform-origin: 16px 8px; unicode-bidi: normal; "> and <span 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: 24px 8px; transform-origin: 24px 8px; unicode-bidi: normal; ">target<span 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: 255.5px 8px; transform-origin: 255.5px 8px; unicode-bidi: normal; "> as inputs, performs a binary search and outputs the index of target value as well as the number of iterations it took to find the target.</div><div 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; "><span 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 8px; transform-origin: 0px 8px; unicode-bidi: normal; "></div></div></div>

One way to locate a target value in a sorted array, is to use a binary search algorithm. Here, you test if the midpoint in the array is the target value. If it is, great! You're done. If not, then you continually narrow your search area depending on whether the target is less than or greater than the midpoint. The algorithm is as follows:
Given an array of sorted values (X), and a target value you wish to locate (target)
Calculate the index of the midpoint of the array X by taking the average of the largest and smallest indices and rounding to the nearest integer.  
If the value located at the midpoint matches your target, set found to true.
If the target is less than the value located at the midpoint of X, narrow your search to the lower half of X by setting the largest index in the array to the midpoint - 1. 
If the target is greater than the value located at the midpoint of X, narrow your search to the upper half of X by setting the smallest index in the array to the midpoint + 1. 
Repeat the steps above until found is true.

Write a function that takes X and target as inputs, performs a binary search and outputs the index of target value as well as the number of iterations it took to find the target.

Solve

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Last Solution submitted on Jan 27, 2023

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Rafael S.T. Vieira on 30 Oct 2022

This is a good exercise, but you can't enforce people to do a binary search in a programming competition unless you can find a way to identify a search done with a binary search uniquely.

Rafael S.T. Vieira on 30 Oct 2022

Maybe requiring that the sequence of midpoints until a key is retrieved is returned as part of the solution. It would make it harder to "cheat".

Jean-Marie Sainthillier on 5 Jan 2023 at 16:24

You can add the incrementation of the number of iterations in your algorithm's description and test its exact value in the test suite.

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Solution 9465668

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1 Comment

Marco Fuscà on 18 Oct 2022

uh.. oh well

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Problem 56040. A Binary Search

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Problem 56040. A Binary Search

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