{"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":45415,"title":"Find an optimal placement of coolers on a grid","description":"In a certain chemical plant, 6 new pieces of cooling equipment (coolers) are to be installed in a vacant space. This vacant space was divided into a grid of 6 cells by 6 cells. Your task is to assign the 6 coolers to 6 cells in this grid with the following requirements:\r\n\r\n# There must be one cooler for every column in the grid.\r\n# If you decide to install a cooler at row R, column C, then the cooler at column C+1 must be installed either on row R-1, R, or R+1 only. This is done to ease the connection of coolers by piping.\r\n# The total installation cost for the 6 coolers must be minimum.\r\n\r\nFor this problem, you are given a cost matrix (COST) in relation to the third requirement above. COST is a 6 x 6 matrix where the _r,c_-th element is the cost of assigning any cooler to row _r_, column _c_ (All the coolers are identical). Write a function that accepts the matrix COST, and output the value of the minimum cost of installation. You are ensured that all elements of COST are integers in the range [1,1000].\r\n\r\nIn the sample test case below, the optimal placement is at the following rows: 4,3,3,2,2,2.\r\n\r\n \u003e\u003e COST = [695 766 710 119 752 548;\r\n 318 796 755 499 256 139;\r\n 951 187 277 960 506 150;\r\n 35 490 680 341 700 258;\r\n 439 446 656 586 891 841;\r\n 382 647 163 224 960 255];\r\n \u003e\u003e coolers(COST)\r\n ans = \r\n 1393\r\n \r\nMeanwhile, the optimal placement for the case below is at rows: 5,6,5,6,5,6\r\n\r\n \u003e\u003e COST = [815 617 918 76 569 312;\r\n 244 474 286 54 470 529;\r\n 930 352 758 531 455 988;\r\n 350 831 754 780 12 602;\r\n 197 586 381 935 163 263;\r\n 252 550 568 130 795 100];\r\n \u003e\u003e coolers(COST)\r\n ans = \r\n 1521\r\n","description_html":"\u003cp\u003eIn a certain chemical plant, 6 new pieces of cooling equipment (coolers) are to be installed in a vacant space. This vacant space was divided into a grid of 6 cells by 6 cells. Your task is to assign the 6 coolers to 6 cells in this grid with the following requirements:\u003c/p\u003e\u003col\u003e\u003cli\u003eThere must be one cooler for every column in the grid.\u003c/li\u003e\u003cli\u003eIf you decide to install a cooler at row R, column C, then the cooler at column C+1 must be installed either on row R-1, R, or R+1 only. This is done to ease the connection of coolers by piping.\u003c/li\u003e\u003cli\u003eThe total installation cost for the 6 coolers must be minimum.\u003c/li\u003e\u003c/ol\u003e\u003cp\u003eFor this problem, you are given a cost matrix (COST) in relation to the third requirement above. COST is a 6 x 6 matrix where the \u003ci\u003er,c\u003c/i\u003e-th element is the cost of assigning any cooler to row \u003ci\u003er\u003c/i\u003e, column \u003ci\u003ec\u003c/i\u003e (All the coolers are identical). Write a function that accepts the matrix COST, and output the value of the minimum cost of installation. You are ensured that all elements of COST are integers in the range [1,1000].\u003c/p\u003e\u003cp\u003eIn the sample test case below, the optimal placement is at the following rows: 4,3,3,2,2,2.\u003c/p\u003e\u003cpre class=\"language-matlab\"\u003e\u0026gt;\u0026gt; COST = [695 766 710 119 752 548;\r\n 318 796 755 499 256 139;\r\n 951 187 277 960 506 150;\r\n 35 490 680 341 700 258;\r\n 439 446 656 586 891 841;\r\n 382 647 163 224 960 255];\r\n\u0026gt;\u0026gt; coolers(COST)\r\nans = \r\n 1393\r\n\u003c/pre\u003e\u003cp\u003eMeanwhile, the optimal placement for the case below is at rows: 5,6,5,6,5,6\u003c/p\u003e\u003cpre class=\"language-matlab\"\u003e\u0026gt;\u0026gt; COST = [815 617 918 76 569 312;\r\n 244 474 286 54 470 529;\r\n 930 352 758 531 455 988;\r\n 350 831 754 780 12 602;\r\n 197 586 381 935 163 263;\r\n 252 550 568 130 795 100];\r\n\u0026gt;\u0026gt; coolers(COST)\r\nans = \r\n 1521\r\n\u003c/pre\u003e","function_template":"function y = coolers(COST)\r\n y = x;\r\nend","test_suite":"%%\r\nfiletext = fileread('coolers.m')\r\nassert(isempty(strfind(filetext, 'rand')))\r\n%%\r\nCOST = [815 617 918 76 569 312;\r\n 244 474 286 54 470 529;\r\n 930 352 758 531 455 988;\r\n 350 831 754 780 12 602;\r\n 197 586 381 935 163 263;\r\n 252 550 568 130 795 100];\r\nassert(isequal(coolers(COST),1521))\r\n%%\r\nCOST = [690 153 107 85 182 550;\r\n 749 826 962 400 264 145;\r\n 451 539 5 260 146 854;\r\n 84 997 775 801 137 623;\r\n 229 79 818 432 870 351;\r\n 914 443 869 911 580 514];\r\nassert(isequal(coolers(COST),1179))\r\n%%\r\nCOST = [402 418 338 242 576 44;\r\n 76 50 901 404 60 169;\r\n 240 903 370 97 235 650;\r\n 124 945 112 132 354 732;\r\n 184 491 781 943 822 648;\r\n 240 490 390 957 16 451];\r\nassert(isequal(coolers(COST),697))\r\n%%\r\nCOST = [1 1 1000 1000 1000 1;\r\n 1 1000 1 1000 1000 1000;\r\n 1 1000 1000 1000 1 1000;\r\n 1 1000 1000 1 1000 1000;\r\n 1 1000 1000 1000 1000 1000;\r\n 1 1000 1000 1000 1000 1000];\r\nassert(isequal(coolers(COST),2004))\r\n%%\r\nCOST = [548 369 487 818 351 208;\r\n 297 626 436 795 940 302;\r\n 745 781 447 645 876 471;\r\n 189 82 307 379 551 231;\r\n 687 930 509 812 623 845;\r\n 184 776 511 533 588 195];\r\nassert(isequal(coolers(COST),1739))\r\n%%\r\nCOST = [226 431 259 222 86 489;\r\n 171 185 409 118 263 579;\r\n 228 905 595 297 802 238;\r\n 436 980 263 319 30 459;\r\n 312 439 603 425 929 964;\r\n 924 112 712 508 731 547];\r\nassert(isequal(coolers(COST),1234))\r\n%%\r\nCOST = [522 368 99 107 891 501;\r\n 232 988 262 654 335 480;\r\n 489 38 336 495 699 905;\r\n 625 886 680 780 198 610;\r\n 680 914 137 716 31 618;\r\n 396 797 722 904 745 860];\r\nassert(isequal(coolers(COST),1454))\r\n%%\r\nCOST = [806 490 60 819 973 84;\r\n 577 168 682 818 649 134;\r\n 183 979 43 723 801 174;\r\n 240 713 72 150 454 391;\r\n 887 501 522 660 433 832;\r\n 29 472 97 519 826 804];\r\nassert(isequal(coolers(COST),1172))\r\n%%\r\nCOST = [61 292 373 53 418 699;\r\n 400 432 199 738 984 667;\r\n 527 16 490 270 302 179;\r\n 417 985 340 423 702 129;\r\n 657 168 952 548 667 1000;\r\n 628 107 921 943 540 172];\r\nassert(isequal(coolers(COST),1253))\r\n%%\r\nCOST = [33 461 191 385 825 907;\r\n 562 982 429 583 983 880;\r\n 882 157 483 252 731 818;\r\n 670 856 121 291 344 261;\r\n 191 645 590 618 585 595;\r\n 369 377 227 266 108 23];\r\nassert(isequal(coolers(COST),1192))\r\n%%\r\nCOST = [426 599 69 719 779 441;\r\n 313 471 320 969 424 528;\r\n 162 696 531 532 91 458;\r\n 179 700 655 326 267 876;\r\n 423 639 408 106 154 519;\r\n 95 34 820 611 282 944];\r\nassert(isequal(coolers(COST),1316))\r\n%%\r\nCOST = [638 696 345 916 323 474;\r\n 958 68 781 2 785 153;\r\n 241 255 676 463 472 342;\r\n 677 225 7 425 36 608;\r\n 290 668 603 461 176 192;\r\n 672 845 387 771 722 739];\r\nassert(isequal(coolers(COST),1126))\r\n%%\r\nCOST = [243 92 648 237 771 257;\r\n 918 577 680 120 351 614;\r\n 270 684 636 608 663 583;\r\n 766 547 946 451 417 541;\r\n 189 426 209 459 842 870;\r\n 288 645 710 662 833 265];\r\nassert(isequal(coolers(COST),1711))\r\n%%\r\nCOST = [319 545 219 366 193 862;\r\n 120 648 106 764 139 485;\r\n 940 544 110 628 697 394;\r\n 646 722 64 772 94 672;\r\n 480 523 405 933 526 742;\r\n 640 994 449 973 531 521];\r\nassert(isequal(coolers(COST),1669))\r\n%%\r\nCOST = [674 622 842 636 885 896;\r\n 575 722 853 599 699 975;\r\n 794 844 722 911 905 664;\r\n 632 680 510 715 878 836;\r\n 523 869 667 944 689 720;\r\n 878 698 713 696 609 917];\r\nassert(isequal(coolers(COST),3837))\r\n%%\r\nCOST = [82 122 681 602 355 371;...\r\n 483 544 417 347 776 384;...\r\n 129 315 643 365 237 862;...\r\n 253 383 215 172 845 464;...\r\n 884 792 618 796 817 571;...\r\n 197 840 676 493 847 696];\r\nassert(isequal(coolers(COST),1452))\r\n%%\r\nCOST = [961 170 710 563 536 327;...\r\n 547 179 176 177 199 603;...\r\n 637 244 859 514 624 362;...\r\n 571 752 910 549 27 135;...\r\n 928 200 962 166 319 914;...\r\n 864 983 571 494 533 641];\r\nassert(isequal(coolers(COST),1569))\r\n%%\r\nCOST = [659 381 223 112 267 869;...\r\n 676 822 1000 425 292 529;...\r\n 745 172 64 614 189 915;...\r\n 843 330 426 989 23 974;...\r\n 517 967 405 220 450 586;...\r\n 152 807 401 355 244 119];\r\nassert(isequal(coolers(COST),1835))\r\n%%\r\nCOST = [927 925 215 554 571 679;...\r\n 594 643 249 631 336 213;...\r\n 884 105 227 986 958 82;...\r\n 425 701 704 635 440 275;...\r\n 608 396 755 601 602 868;...\r\n 71 85 548 910 721 560];\r\nassert(isequal(coolers(COST),1751))\r\n%%\r\nCOST = [465 433 384 904 809 299;...\r\n 431 506 712 219 180 769;...\r\n 774 376 481 874 166 502;...\r\n 654 481 730 83 182 910;...\r\n 658 343 938 466 692 58;...\r\n 162 778 518 22 214 437];\r\nassert(isequal(coolers(COST),1317))\r\n%%\r\nCOST = [573 952 497 860 78 228;...\r\n 566 767 809 627 339 710;...\r\n 824 752 633 181 581 149;...\r\n 127 139 689 574 476 659;...\r\n 301 350 640 164 806 634;...\r\n 3 152 730 907 531 230];\r\nassert(isequal(coolers(COST),1568))\r\n%%\r\nCOST = [183 958 897 179 998 879;...\r\n 167 26 190 747 5 747;...\r\n 150 972 661 50 543 118;...\r\n 203 298 942 72 862 510;...\r\n 955 526 976 490 910 169;...\r\n 16 863 108 850 846 832];\r\nassert(isequal(coolers(COST),539))\r\n%%\r\nCOST = [929 868 245 81 27 760;...\r\n 170 742 641 361 786 926;...\r\n 884 448 809 829 923 833;...\r\n 388 710 854 215 493 260;...\r\n 383 945 399 792 835 214;...\r\n 272 175 116 655 132 523];\r\nassert(isequal(coolers(COST),1564))\r\n%%\r\nCOST = [398 438 798 217 378 972;...\r\n 480 773 656 812 168 361;...\r\n 994 745 33 139 541 645;...\r\n 605 443 558 882 102 68;...\r\n 945 54 720 924 40 208;...\r\n 491 88 111 13 934 40];\r\nassert(isequal(coolers(COST),749))\r\n%%\r\nCOST = [470 581 9 642 470 879;...\r\n 151 541 825 106 220 189;...\r\n 992 706 768 269 923 760;...\r\n 428 6 998 764 321 32;...\r\n 956 783 228 806 858 643;...\r\n 725 927 920 105 260 567];\r\nassert(isequal(coolers(COST),1216))\r\n%%\r\nCOST = [377 187 35 595 562 603;...\r\n 213 486 489 499 634 474;...\r\n 793 839 972 568 931 357;...\r\n 146 142 113 427 978 476;...\r\n 490 733 744 77 94 672;...\r\n 13 692 639 291 662 960];\r\nassert(isequal(coolers(COST),1048))\r\n%%\r\nCOST = [90 52 454 629 707 46;...\r\n 798 505 738 133 536 886;...\r\n 591 769 510 619 194 840;...\r\n 913 283 383 384 690 119;...\r\n 102 226 906 992 51 411;...\r\n 294 332 966 287 185 121];\r\nassert(isequal(coolers(COST),1042))\r\n%%\r\nCOST = [573 666 232 754 549 464;...\r\n 950 974 53 622 461 590;...\r\n 257 623 902 395 646 188;...\r\n 990 64 794 360 514 612;...\r\n 350 374 374 89 815 52;...\r\n 209 167 833 342 98 576];\r\nassert(isequal(coolers(COST),934))\r\n%%\r\nCOST = [843 797 666 67 652 382;...\r\n 500 294 961 898 134 301;...\r\n 440 116 944 498 639 341;...\r\n 150 376 113 772 385 919;...\r\n 29 829 649 61 766 457;...\r\n 757 842 481 263 653 443];\r\nassert(isequal(coolers(COST),1166))\r\n%%\r\nCOST = [455 767 602 56 365 673;...\r\n 946 343 650 99 677 203;...\r\n 220 619 343 650 376 869;...\r\n 883 454 494 765 864 752;...\r\n 20 11 702 988 292 420;...\r\n 342 600 888 126 134 1];\r\nassert(isequal(coolers(COST),994))\r\n%%\r\nCOST = [150 436 24 66 150 132;...\r\n 274 904 575 924 351 887;...\r\n 873 926 47 535 336 675;...\r\n 602 506 423 367 785 836;...\r\n 322 628 468 364 487 657;...\r\n 285 720 23 152 465 984];\r\nassert(isequal(coolers(COST),958))\r\n%%\r\nCOST = [980 191 386 245 842 952;...\r\n 251 125 311 804 79 966;...\r\n 625 3 4 824 238 766;...\r\n 729 153 816 853 818 575;...\r\n 499 535 639 468 406 916;...\r\n 850 511 449 971 467 496];\r\nassert(isequal(coolers(COST),1655))\r\n%%\r\nCOST = [167 167 988 896 65 887;...\r\n 326 948 151 835 264 421;...\r\n 297 812 959 3 103 284;...\r\n 559 711 531 641 484 49;...\r\n 68 971 75 804 419 220;...\r\n 69 999 312 246 382 240];\r\nassert(isequal(coolers(COST),640))\r\n%%\r\nCOST = [30 653 667 689 433 469;...\r\n 703 321 848 321 905 546;...\r\n 8 104 763 532 631 180;...\r\n 611 536 808 874 984 635;...\r\n 409 165 633 55 586 963;...\r\n 249 884 711 501 841 535];\r\nassert(isequal(coolers(COST),2007))\r\n%%\r\nCOST = [480 679 683 689 62 13;...\r\n 794 566 947 148 220 217;...\r\n 93 479 100 778 83 12;...\r\n 881 321 512 400 951 643;...\r\n 4 602 111 899 17 517;...\r\n 512 914 546 308 115 246];\r\nassert(isequal(coolers(COST),648))\r\n%%\r\nCOST = [194 309 342 580 56 396;...\r\n 91 745 840 329 35 170;...\r\n 369 840 983 269 287 431;...\r\n 8 263 627 551 78 417;...\r\n 603 515 182 181 901 729;...\r\n 479 447 124 679 847 407];\r\nassert(isequal(coolers(COST),1129))\r\n%%\r\nCOST = [952 211 79 334 443 924;...\r\n 912 131 934 693 633 153;...\r\n 952 521 603 204 930 406;...\r\n 347 906 378 959 530 313;...\r\n 291 403 665 712 627 694;...\r\n 887 216 793 167 681 891];\r\nassert(isequal(coolers(COST),2052))\r\n%%\r\nCOST = [491 677 35 27 661 34;...\r\n 806 829 437 501 330 407;...\r\n 327 111 937 828 660 717;...\r\n 550 280 263 259 14 922;...\r\n 389 768 570 46 719 985;...\r\n 897 217 360 247 392 984];\r\nassert(isequal(coolers(COST),1266))\r\n%%\r\nCOST = [897 655 269 739 879 390;...\r\n 866 864 153 13 903 300;...\r\n 801 275 631 606 153 735;...\r\n 555 841 317 577 193 105;...\r\n 419 71 960 808 791 793;...\r\n 128 379 499 655 61 783];\r\nassert(isequal(coolers(COST),1254))\r\n%%\r\nCOST = [533 130 314 596 463 399;...\r\n 254 451 642 537 368 478;...\r\n 71 673 787 331 680 67;...\r\n 626 857 290 412 568 412;...\r\n 25 499 498 795 652 970;...\r\n 63 49 819 344 492 781];\r\nassert(isequal(coolers(COST),1580))\r\n%%\r\nCOST = [730 112 727 411 679 798;...\r\n 766 397 148 143 254 712;...\r\n 757 493 148 799 844 784;...\r\n 844 259 705 931 294 624;...\r\n 771 37 381 5 27 826;...\r\n 979 975 77 651 94 36];\r\nassert(isequal(coolers(COST),953))\r\n%%\r\nCOST = [406 27 672 377 507 436;...\r\n 250 156 53 114 329 158;...\r\n 481 834 735 965 754 601;...\r\n 881 195 500 433 837 938;...\r\n 281 830 944 85 254 108;...\r\n 600 339 290 717 535 900];\r\nassert(isequal(coolers(COST),931))\r\n%%\r\nCOST = [551 355 642 427 787 943;...\r\n 428 774 128 34 512 97;...\r\n 153 882 497 930 563 846;...\r\n 248 735 311 925 685 910;...\r\n 448 407 579 359 93 12;...\r\n 533 605 944 260 873 524];\r\nassert(isequal(coolers(COST),1430))\r\n%%\r\nCOST = [651 279 401 430 885 568;...\r\n 386 840 555 38 256 895;...\r\n 650 427 444 976 910 215;...\r\n 763 632 91 523 895 4;...\r\n 576 834 745 910 399 881;...\r\n 632 271 33 384 626 236];\r\nassert(isequal(coolers(COST),1575))\r\n%%\r\nCOST = [245 391 532 153 716 903;...\r\n 641 802 889 231 281 290;...\r\n 305 158 264 658 413 500;...\r\n 826 626 235 563 363 784;...\r\n 884 699 840 292 782 678;...\r\n 946 86 496 623 136 150];\r\nassert(isequal(coolers(COST),1276))\r\n%%\r\nCOST = [697 977 429 793 902 349;...\r\n 130 126 15 420 52 166;...\r\n 946 753 326 533 809 29;...\r\n 887 828 135 926 335 956;...\r\n 516 782 451 900 229 681;...\r\n 680 191 573 545 823 861];\r\nassert(isequal(coolers(COST),772))\r\n%%\r\nCOST = [940 301 652 887 695 895;...\r\n 681 74 170 115 207 842;...\r\n 918 768 532 443 555 131;...\r\n 257 85 634 660 880 190;...\r\n 886 729 15 295 558 154;...\r\n 921 448 471 951 753 29];\r\nassert(isequal(coolers(COST),1239))\r\n%%\r\nCOST = [10 496 746 686 237 463;...\r\n 597 259 338 268 196 926;...\r\n 610 733 585 970 706 216;...\r\n 919 117 469 184 181 2;...\r\n 734 747 88 300 523 907;...\r\n 302 810 829 412 297 681];\r\nassert(isequal(coolers(COST),1182))\r\n%%\r\nCOST = [515 394 842 779 399 396;...\r\n 523 8 49 728 671 399;...\r\n 103 546 317 651 441 752;...\r\n 997 510 784 665 133 523;...\r\n 359 247 973 939 440 491;...\r\n 626 46 587 536 548 89];\r\nassert(isequal(coolers(COST),1435))\r\n%%\r\nCOST = [251 93 71 159 652 1;...\r\n 448 954 301 63 499 641;...\r\n 638 163 814 702 285 8;...\r\n 710 971 77 87 831 107;...\r\n 993 598 355 617 819 107;...\r\n 933 241 133 174 939 368];\r\nassert(isequal(coolers(COST),771))\r\n%%\r\nCOST = [240 788 66 813 71 954;...\r\n 347 270 611 815 242 209;...\r\n 250 844 702 90 732 117;...\r\n 388 741 112 732 41 647;...\r\n 422 827 96 904 425 109;...\r\n 641 183 598 453 541 984];\r\nassert(isequal(coolers(COST),1343))\r\n%%\r\nCOST = [249 916 747 918 880 282;...\r\n 607 901 476 471 799 169;...\r\n 817 215 584 270 325 746;...\r\n 831 548 261 763 670 478;...\r\n 490 785 85 773 297 654;...\r\n 761 195 299 22 930 967];\r\nassert(isequal(coolers(COST),1567))\r\n%%\r\nCOST = [314 77 818 283 736 557;...\r\n 77 154 767 639 157 274;...\r\n 792 827 375 593 435 133;...\r\n 366 301 190 326 833 700;...\r\n 586 384 647 989 360 486;...\r\n 184 651 4 124 77 183];\r\nassert(isequal(coolers(COST),956))\r\n%%\r\nCOST = [102 248 381 378 851 968;...\r\n 202 438 749 973 257 477;...\r\n 135 670 157 606 286 995;...\r\n 324 548 59 339 780 491;...\r\n 951 610 340 928 702 504;...\r\n 533 864 818 899 493 769];\r\nassert(isequal(coolers(COST),1799))\r\n%%\r\nCOST = [389 799 340 268 52 543;...\r\n 454 221 273 177 628 809;...\r\n 133 858 171 432 30 794;...\r\n 759 905 665 476 137 502;...\r\n 566 293 536 786 695 277;...\r\n 649 726 830 131 516 120];\r\nassert(isequal(coolers(COST),1234))\r\n%%\r\nCOST = [887 183 567 504 84 962;...\r\n 971 32 378 261 74 467;...\r\n 943 725 822 733 770 787;...\r\n 639 145 305 163 818 423;...\r\n 91 636 320 922 741 944;...\r\n 75 790 785 223 759 2];\r\nassert(isequal(coolers(COST),1447))\r\n%%\r\nCOST = [982 666 329 847 415 7;...\r\n 571 685 928 902 662 767;...\r\n 347 793 757 596 784 22;...\r\n 558 349 289 69 248 394;...\r\n 300 251 607 219 555 253;...\r\n 160 346 767 870 230 205];\r\nassert(isequal(coolers(COST),1039))\r\n%%\r\nCOST = [663 975 947 135 372 260;...\r\n 915 120 967 806 227 134;...\r\n 7 519 68 525 447 420;...\r\n 747 822 438 945 267 507;...\r\n 800 638 321 989 460 325;...\r\n 908 954 135 410 433 685];\r\nassert(isequal(coolers(COST),1081))\r\n%%\r\nCOST = [444 502 305 970 394 701;...\r\n 436 556 767 690 459 110;...\r\n 794 631 268 718 209 7;...\r\n 816 98 40 560 758 598;...\r\n 753 246 297 534 547 660;...\r\n 790 616 557 876 358 581];\r\nassert(isequal(coolers(COST),1667))\r\n%%\r\nCOST = [910 165 870 241 503 143;...\r\n 637 281 788 9 568 381;...\r\n 526 260 970 672 189 397;...\r\n 260 548 181 905 325 577;...\r\n 52 542 931 573 717 20;...\r\n 732 789 46 156 553 578];\r\nassert(isequal(coolers(COST),1369))\r\n%%\r\nCOST = [933 303 817 55 540 946;...\r\n 107 460 451 638 938 377;...\r\n 733 49 807 425 661 68;...\r\n 971 386 791 906 395 182;...\r\n 609 362 283 418 259 576;...\r\n 720 288 69 155 848 186];\r\nassert(isequal(coolers(COST),1495))\r\n%%\r\nCOST = [292 28 747 842 871 890;...\r\n 462 659 747 511 212 66;...\r\n 347 159 174 166 837 510;...\r\n 319 803 118 715 860 621;...\r\n 460 409 175 908 524 734;...\r\n 236 328 628 219 478 230];\r\nassert(isequal(coolers(COST),1040))\r\n%%\r\nCOST = [22 327 315 114 208 74;...\r\n 139 138 160 701 785 595;...\r\n 770 385 153 180 527 862;...\r\n 970 563 137 804 572 449;...\r\n 387 634 710 514 423 653;...\r\n 994 542 465 549 722 304];\r\nassert(isequal(coolers(COST),716))\r\n%%\r\nCOST = [608 457 948 406 340 75;...\r\n 279 600 453 439 896 664;...\r\n 800 843 811 679 546 704;...\r\n 797 32 929 466 750 919;...\r\n 955 188 673 954 125 661;...\r\n 445 944 373 355 454 691];\r\nassert(isequal(coolers(COST),2010))\r\n%%\r\nCOST = [854 26 473 324 731 29;...\r\n 468 57 679 802 774 128;...\r\n 459 143 115 300 901 134;...\r\n 807 172 237 776 139 129;...\r\n 825 626 290 553 795 936;...\r\n 191 30 173 555 190 274];\r\nassert(isequal(coolers(COST),1199))\r\n%%\r\nCOST = [943 546 850 417 382 152;...\r\n 639 256 8 518 723 437;...\r\n 873 306 635 887 96 13;...\r\n 368 16 360 150 668 230;...\r\n 237 588 115 435 297 264;...\r\n 188 963 541 60 599 512];\r\nassert(isequal(coolers(COST),627))\r\n%%\r\nCOST = [216 475 261 618 402 95;...\r\n 347 826 590 145 15 376;...\r\n 748 304 480 717 75 546;...\r\n 414 822 199 402 592 112;...\r\n 56 566 240 463 447 905;...\r\n 391 55 781 708 927 634];\r\nassert(isequal(coolers(COST),940))\r\n%%\r\nCOST = [906 61 814 762 771 880;...\r\n 631 674 316 876 876 374;...\r\n 15 478 312 872 68 767;...\r\n 317 306 345 173 647 169;...\r\n 112 517 667 851 325 520;...\r\n 630 708 862 960 641 628];\r\nassert(isequal(coolers(COST),1043))\r\n%%\r\nCOST = [714 628 766 404 544 135;...\r\n 307 193 319 751 411 541;...\r\n 264 777 253 488 901 858;...\r\n 917 865 201 385 57 199;...\r\n 616 334 70 62 444 156;...\r\n 94 136 552 214 538 62];\r\nassert(isequal(coolers(COST),575))\r\n%%\r\nCOST = [662 683 487 77 915 603;...\r\n 19 138 680 445 92 466;...\r\n 292 630 705 166 994 299;...\r\n 974 858 461 399 97 134;...\r\n 765 900 365 921 314 296;...\r\n 244 349 281 512 786 167];\r\nassert(isequal(coolers(COST),1112))\r\n%%\r\nCOST = [318 40 863 414 595 658;...\r\n 110 617 277 415 310 685;...\r\n 833 670 532 984 902 474;...\r\n 972 38 523 58 94 142;...\r\n 219 4 568 397 320 951;...\r\n 707 143 334 792 887 883];\r\nassert(isequal(coolers(COST),1040))\r\n%%\r\nCOST = [438 952 914 477 226 187;...\r\n 835 2 534 251 568 647;...\r\n 326 296 805 308 999 129;...\r\n 368 49 563 967 132 82;...\r\n 795 443 751 209 955 660;...\r\n 100 790 10 521 124 28];\r\nassert(isequal(coolers(COST),914))\r\n%%\r\nCOST = [986 693 226 415 41 625;...\r\n 540 603 797 499 583 296;...\r\n 374 776 997 950 565 75;...\r\n 707 592 282 954 356 294;...\r\n 948 377 711 733 881 235;...\r\n 383 851 665 385 625 346];\r\nassert(isequal(coolers(COST),1955))\r\n%%\r\nCOST = [849 636 448 593 844 465;...\r\n 161 844 327 69 424 31;...\r\n 158 783 280 206 545 435;...\r\n 509 265 932 724 528 558;...\r\n 604 315 400 576 186 639;...\r\n 162 184 380 201 82 35];\r\nassert(isequal(coolers(COST),1044))\r\n%%\r\nCOST = [710 855 367 351 91 968;...\r\n 170 385 350 193 258 434;...\r\n 594 400 631 920 428 785;...\r\n 609 326 665 289 578 526;...\r\n 773 556 993 551 900 332;...\r\n 57 296 945 920 219 432];\r\nassert(isequal(coolers(COST),1623))\r\n%%\r\nCOST = [718 654 235 805 97 557;...\r\n 917 41 201 104 600 840;...\r\n 891 505 381 730 234 205;...\r\n 135 895 595 649 33 622;...\r\n 120 386 269 475 580 175;...\r\n 894 293 623 933 843 290];\r\nassert(isequal(coolers(COST),1365))\r\n%%\r\nCOST = [19 283 206 904 234 347;...\r\n 702 245 435 541 247 298;...\r\n 953 287 143 818 171 405;...\r\n 750 964 376 709 236 303;...\r\n 757 231 794 44 276 758;...\r\n 543 538 813 146 952 360];\r\nassert(isequal(coolers(COST),1417))\r\n%%\r\nCOST = [125 458 201 22 719 780;...\r\n 618 78 960 483 450 568;...\r\n 356 905 666 808 660 77;...\r\n 363 282 542 737 754 252;...\r\n 69 614 869 573 805 134;...\r\n 868 662 558 9 30 565];\r\nassert(isequal(coolers(COST),953))\r\n%%\r\nCOST = [541 43 122 494 863 421;...\r\n 69 528 592 856 685 488;...\r\n 989 257 360 725 635 461;...\r\n 252 409 720 200 142 516;...\r\n 316 948 524 158 80 272;...\r\n 301 920 261 371 877 232];\r\nassert(isequal(coolers(COST),1198))\r\n%%\r\nCOST = [900 895 226 336 740 434;...\r\n 909 88 105 620 889 290;...\r\n 604 540 10 993 860 632;...\r\n 366 429 60 649 598 296;...\r\n 599 618 323 540 655 623;...\r\n 669 559 780 233 916 48];\r\nassert(isequal(coolers(COST),2054))\r\n%%\r\nCOST = [995 67 543 281 171 63;...\r\n 207 928 781 599 372 407;...\r\n 608 88 522 37 40 464;...\r\n 348 333 932 64 710 203;...\r\n 718 527 148 323 642 870;...\r\n 28 247 417 99 175 598];\r\nassert(isequal(coolers(COST),730))\r\n%%\r\nCOST = [24 867 571 301 445 250;...\r\n 900 616 326 522 983 956;...\r\n 453 27 451 562 579 143;...\r\n 59 323 578 242 235 513;...\r\n 107 464 75 913 811 972;...\r\n 999 100 58 826 452 649];\r\nassert(isequal(coolers(COST),902))\r\n%%\r\nCOST = [615 424 874 119 114 462;...\r\n 470 274 301 99 491 864;...\r\n 578 445 401 891 600 263;...\r\n 912 628 518 34 91 824;...\r\n 377 535 62 840 979 329;...\r\n 229 386 232 508 654 942];\r\nassert(isequal(coolers(COST),1065))\r\n%%\r\nCOST = [245 314 524 145 800 565;...\r\n 958 58 893 245 209 218;...\r\n 511 45 406 379 897 858;...\r\n 565 813 605 271 746 862;...\r\n 994 413 95 216 537 314;...\r\n 771 385 336 634 970 327];\r\nassert(isequal(coolers(COST),1381))\r\n%%\r\nCOST = [841 334 286 610 505 816;...\r\n 493 367 657 384 8 910;...\r\n 52 795 232 31 920 778;...\r\n 779 39 622 858 411 758;...\r\n 427 727 76 604 733 406;...\r\n 280 873 967 848 152 702];\r\nassert(isequal(coolers(COST),1140))\r\n%%\r\nCOST = [566 563 904 539 781 176;...\r\n 585 547 605 738 537 417;...\r\n 345 551 927 182 770 740;...\r\n 705 695 117 427 639 893;...\r\n 161 928 341 99 894 26;...\r\n 2 945 37 304 61 138];\r\nassert(isequal(coolers(COST),1153))\r\n%%\r\nCOST = [425 619 192 805 191 892;...\r\n 765 7 715 860 504 674;...\r\n 525 741 178 567 51 686;...\r\n 755 992 987 755 57 696;...\r\n 170 129 17 520 336 800;...\r\n 673 361 40 586 631 661];\r\nassert(isequal(coolers(COST),1579))\r\n%%\r\nCOST = [520 255 928 227 995 523;...\r\n 332 846 588 2 984 274;...\r\n 935 539 102 894 965 719;...\r\n 247 911 367 454 667 779;...\r\n 512 351 276 579 727 82;...\r\n 741 936 267 316 335 222];\r\nassert(isequal(coolers(COST),1598))\r\n%%\r\nCOST = [204 470 675 379 889 587;...\r\n 625 379 552 618 563 969;...\r\n 726 341 52 563 195 582;...\r\n 835 64 308 831 222 100;...\r\n 19 762 966 958 706 167;...\r\n 203 403 932 76 597 103];\r\nassert(isequal(coolers(COST),993))\r\n%%\r\nCOST = [147 800 210 627 782 774;...\r\n 672 400 481 412 936 748;...\r\n 640 756 113 639 740 319;...\r\n 373 296 133 857 254 511;...\r\n 163 641 65 764 720 774;...\r\n 390 886 80 977 694 573];\r\nassert(isequal(coolers(COST),1784))\r\n%%\r\nCOST = [954 463 111 359 365 588;...\r\n 172 130 200 135 400 778;...\r\n 908 550 163 999 927 658;...\r\n 753 970 37 514 496 529;...\r\n 287 443 273 388 610 826;...\r\n 628 591 231 250 5 963];\r\nassert(isequal(coolers(COST),1501))\r\n%%\r\nCOST = [314 306 715 905 664 101;...\r\n 798 19 460 387 603 287;...\r\n 286 163 920 604 657 355;...\r\n 15 444 989 561 310 536;...\r\n 95 767 933 846 332 991;...\r\n 329 682 462 285 189 29];\r\nassert(isequal(coolers(COST),1729))\r\n%%\r\nCOST = [710 876 77 818 359 455;...\r\n 906 865 377 174 364 30;...\r\n 866 356 150 677 268 638;...\r\n 120 632 35 876 338 60;...\r\n 956 865 783 758 87 170;...\r\n 441 21 328 230 452 685];\r\nassert(isequal(coolers(COST),1098))\r\n%%\r\nCOST = [555 461 15 279 896 625;...\r\n 7 371 5 645 888 207;...\r\n 289 825 167 288 394 110;...\r\n 377 538 366 322 676 566;...\r\n 147 818 719 156 253 275;...\r\n 75 461 160 388 950 72];\r\nassert(isequal(coolers(COST),1175))\r\n%%\r\nCOST = [159 896 447 617 948 551;...\r\n 50 608 812 304 334 161;...\r\n 681 15 145 90 390 118;...\r\n 782 345 975 522 151 399;...\r\n 808 534 834 826 334 832;...\r\n 266 628 341 764 554 186];\r\nassert(isequal(coolers(COST),569))\r\n%%\r\nCOST = [501 491 579 185 613 662;...\r\n 127 887 776 198 738 896;...\r\n 865 906 662 862 304 275;...\r\n 767 499 470 126 43 998;...\r\n 565 530 220 646 836 835;...\r\n 390 910 603 438 370 792];\r\nassert(isequal(coolers(COST),1584))\r\n%%\r\nCOST = [657 988 206 794 242 185;...\r\n 544 789 495 682 210 88;...\r\n 387 853 32 651 273 309;...\r\n 823 486 828 238 776 231;...\r\n 596 874 265 478 332 910;...\r\n 782 334 678 937 604 937];\r\nassert(isequal(coolers(COST),1504))\r\n%%\r\nCOST = [32 626 369 811 16 974;...\r\n 594 256 338 724 95 373;...\r\n 44 905 619 675 515 321;...\r\n 425 768 87 914 953 784;...\r\n 522 563 376 821 844 213;...\r\n 841 898 188 549 936 960];\r\nassert(isequal(coolers(COST),1717))\r\n%%\r\nCOST = [931 594 600 844 914 151;...\r\n 366 98 227 771 577 947;...\r\n 345 560 714 510 288 651;...\r\n 693 44 725 707 267 983;...\r\n 717 758 345 792 891 194;...\r\n 801 660 33 331 367 829];\r\nassert(isequal(coolers(COST),1626))\r\n%%\r\nCOST = [494 60 648 497 429 28;...\r\n 591 516 624 763 42 906;...\r\n 45 54 954 180 226 472;...\r\n 565 844 177 692 667 911;...\r\n 634 595 475 915 872 328;...\r\n 499 692 843 163 345 692];\r\nassert(isequal(coolers(COST),526))\r\n%%\r\nCOST = [18 334 151 424 616 681;...\r\n 513 633 839 529 102 394;...\r\n 332 416 727 276 670 392;...\r\n 337 577 109 828 348 207;...\r\n 954 960 162 793 670 725;...\r\n 751 616 298 274 296 820];\r\nassert(isequal(coolers(COST),1421))\r\n%%\r\nCOST = [927 854 101 228 459 109;...\r\n 515 430 413 358 952 652;...\r\n 194 926 925 925 133 147;...\r\n 603 374 56 503 71 694;...\r\n 199 699 385 804 707 626;...\r\n 411 589 241 351 932 44];\r\nassert(isequal(coolers(COST),1345))\r\n%%\r\nCOST = [798 582 93 769 788 680;...\r\n 987 602 334 283 125 10;...\r\n 437 253 652 650 158 129;...\r\n 345 655 504 923 415 764;...\r\n 49 61 531 331 688 842;...\r\n 226 941 380 814 658 747];\r\nassert(isequal(coolers(COST),1350))\r\n%%\r\nCOST = [945 618 338 215 587 443;...\r\n 920 559 552 293 939 692;...\r\n 224 731 744 450 619 760;...\r\n 510 64 413 241 251 400;...\r\n 788 493 508 264 103 568;...\r\n 523 230 129 892 547 206];\r\nassert(isequal(coolers(COST),1251))\r\n%%\r\nCOST = [944 708 393 379 767 434;...\r\n 513 657 243 634 337 103;...\r\n 277 779 282 32 626 237;...\r\n 230 581 905 921 327 972;...\r\n 953 504 703 470 312 699;...\r\n 690 879 854 520 647 660];\r\nassert(isequal(coolers(COST),1565))\r\n%%\r\nCOST = [327 450 172 573 377 40;...\r\n 20 769 722 832 394 565;...\r\n 571 628 90 348 429 50;...\r\n 37 315 918 780 424 873;...\r\n 265 293 430 709 219 861;...\r\n 191 79 80 591 497 339];\r\nassert(isequal(coolers(COST),1224))\r\n%%\r\nCOST = [975 347 346 214 761 636;...\r\n 955 234 903 936 580 803;...\r\n 989 756 13 970 622 670;...\r\n 158 226 133 376 490 472;...\r\n 3 449 389 985 221 945;...\r\n 249 260 841 123 145 592];\r\nassert(isequal(coolers(COST),1311))\r\n%%\r\nCOST = [227 932 883 581 327 592;...\r\n 684 697 780 627 288 1;...\r\n 321 96 19 112 497 904;...\r\n 749 246 771 214 182 683;...\r\n 999 935 686 37 934 74;...\r\n 270 480 868 445 941 997];\r\nassert(isequal(coolers(COST),804))\r\n%%\r\nCOST = [315 176 835 189 254 788;...\r\n 810 588 997 578 287 438;...\r\n 462 155 973 629 126 551;...\r\n 588 446 746 365 529 987;...\r\n 478 538 200 637 821 690;...\r\n 553 462 37 892 300 971];\r\nassert(isequal(coolers(COST),2037))\r\n%%\r\nCOST = [96 320 833 203 939 1;...\r\n 899 796 571 493 975 484;...\r\n 59 302 71 730 608 148;...\r\n 124 608 267 955 958 315;...\r\n 631 462 171 763 331 172;...\r\n 371 293 561 81 902 593];\r\nassert(isequal(coolers(COST),1341))\r\n%%\r\nCOST = [658 16 262 188 656 56;...\r\n 349 974 894 744 782 820;...\r\n 54 735 973 719 863 107;...\r\n 48 753 995 189 786 7;...\r\n 56 34 347 434 434 276;...\r\n 72 118 293 46 348 943];\r\nassert(isequal(coolers(COST),862))\r\n%%\r\nCOST = [675 962 293 837 855 788;...\r\n 386 823 439 42 174 175;...\r\n 857 11 399 424 536 720;...\r\n 675 142 138 76 295 233;...\r\n 609 483 953 314 903 208;...\r\n 440 581 361 946 82 217];\r\nassert(isequal(coolers(COST),1114))\r\n%%\r\nCOST = [977 461 237 907 842 269;...\r\n 382 4 832 993 684 981;...\r\n 636 465 438 391 172 313;...\r\n 47 825 508 827 238 572;...\r\n 233 872 186 955 435 612;...\r\n 875 302 152 894 26 902];\r\nassert(isequal(coolers(COST),1700))\r\n%%\r\nCOST = [397 297 634 847 995 269;...\r\n 693 572 965 41 429 758;...\r\n 205 317 201 330 268 610;...\r\n 63 810 599 710 473 967;...\r\n 623 366 84 861 161 774;...\r\n 689 699 545 501 159 573];\r\nassert(isequal(coolers(COST),1320))\r\n%%\r\nCOST = [451 355 996 87 199 597;...\r\n 288 581 84 520 657 323;...\r\n 753 299 469 553 699 831;...\r\n 95 714 94 686 460 123;...\r\n 107 361 726 300 158 252;...\r\n 735 719 913 602 422 938];\r\nassert(isequal(coolers(COST),1069))\r\n\r\n","published":true,"deleted":false,"likes_count":7,"comments_count":2,"created_by":255320,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":56,"test_suite_updated_at":"2020-04-03T23:22:52.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2020-04-01T22:04:29.000Z","updated_at":"2026-02-26T16:11:43.000Z","published_at":"2020-04-01T22:55:22.000Z","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\":[],\"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:r\u003e\u003cw:t\u003eIn a certain chemical plant, 6 new pieces of cooling equipment (coolers) are to be installed in a vacant space. This vacant space was divided into a grid of 6 cells by 6 cells. Your task is to assign the 6 coolers to 6 cells in this grid with the following requirements:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"2\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThere must be one cooler for every column in the grid.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"2\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIf you decide to install a cooler at row R, column C, then the cooler at column C+1 must be installed either on row R-1, R, or R+1 only. This is done to ease the connection of coolers by piping.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"2\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe total installation cost for the 6 coolers must be minimum.\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 are given a cost matrix (COST) in relation to the third requirement above. COST is a 6 x 6 matrix where the\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\u003er,c\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e-th element is the cost of assigning any cooler to row\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\u003er\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, column\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\u003ec\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e (All the coolers are identical). Write a function that accepts the matrix COST, and output the value of the minimum cost of installation. You are ensured that all elements of COST are integers in the range [1,1000].\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\u003eIn the sample test case below, the optimal placement is at the following rows: 4,3,3,2,2,2.\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[\u003e\u003e COST = [695 766 710 119 752 548;\\n 318 796 755 499 256 139;\\n 951 187 277 960 506 150;\\n 35 490 680 341 700 258;\\n 439 446 656 586 891 841;\\n 382 647 163 224 960 255];\\n\u003e\u003e coolers(COST)\\nans = \\n 1393]]\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\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eMeanwhile, the optimal placement for the case below is at rows: 5,6,5,6,5,6\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[\u003e\u003e COST = [815 617 918 76 569 312;\\n 244 474 286 54 470 529;\\n 930 352 758 531 455 988;\\n 350 831 754 780 12 602;\\n 197 586 381 935 163 263;\\n 252 550 568 130 795 100];\\n\u003e\u003e coolers(COST)\\nans = \\n 1521]]\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\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"}],"problem_search":{"errors":[],"problems":[{"id":45415,"title":"Find an optimal placement of coolers on a grid","description":"In a certain chemical plant, 6 new pieces of cooling equipment (coolers) are to be installed in a vacant space. This vacant space was divided into a grid of 6 cells by 6 cells. Your task is to assign the 6 coolers to 6 cells in this grid with the following requirements:\r\n\r\n# There must be one cooler for every column in the grid.\r\n# If you decide to install a cooler at row R, column C, then the cooler at column C+1 must be installed either on row R-1, R, or R+1 only. This is done to ease the connection of coolers by piping.\r\n# The total installation cost for the 6 coolers must be minimum.\r\n\r\nFor this problem, you are given a cost matrix (COST) in relation to the third requirement above. COST is a 6 x 6 matrix where the _r,c_-th element is the cost of assigning any cooler to row _r_, column _c_ (All the coolers are identical). Write a function that accepts the matrix COST, and output the value of the minimum cost of installation. You are ensured that all elements of COST are integers in the range [1,1000].\r\n\r\nIn the sample test case below, the optimal placement is at the following rows: 4,3,3,2,2,2.\r\n\r\n \u003e\u003e COST = [695 766 710 119 752 548;\r\n 318 796 755 499 256 139;\r\n 951 187 277 960 506 150;\r\n 35 490 680 341 700 258;\r\n 439 446 656 586 891 841;\r\n 382 647 163 224 960 255];\r\n \u003e\u003e coolers(COST)\r\n ans = \r\n 1393\r\n \r\nMeanwhile, the optimal placement for the case below is at rows: 5,6,5,6,5,6\r\n\r\n \u003e\u003e COST = [815 617 918 76 569 312;\r\n 244 474 286 54 470 529;\r\n 930 352 758 531 455 988;\r\n 350 831 754 780 12 602;\r\n 197 586 381 935 163 263;\r\n 252 550 568 130 795 100];\r\n \u003e\u003e coolers(COST)\r\n ans = \r\n 1521\r\n","description_html":"\u003cp\u003eIn a certain chemical plant, 6 new pieces of cooling equipment (coolers) are to be installed in a vacant space. This vacant space was divided into a grid of 6 cells by 6 cells. Your task is to assign the 6 coolers to 6 cells in this grid with the following requirements:\u003c/p\u003e\u003col\u003e\u003cli\u003eThere must be one cooler for every column in the grid.\u003c/li\u003e\u003cli\u003eIf you decide to install a cooler at row R, column C, then the cooler at column C+1 must be installed either on row R-1, R, or R+1 only. This is done to ease the connection of coolers by piping.\u003c/li\u003e\u003cli\u003eThe total installation cost for the 6 coolers must be minimum.\u003c/li\u003e\u003c/ol\u003e\u003cp\u003eFor this problem, you are given a cost matrix (COST) in relation to the third requirement above. COST is a 6 x 6 matrix where the \u003ci\u003er,c\u003c/i\u003e-th element is the cost of assigning any cooler to row \u003ci\u003er\u003c/i\u003e, column \u003ci\u003ec\u003c/i\u003e (All the coolers are identical). Write a function that accepts the matrix COST, and output the value of the minimum cost of installation. You are ensured that all elements of COST are integers in the range [1,1000].\u003c/p\u003e\u003cp\u003eIn the sample test case below, the optimal placement is at the following rows: 4,3,3,2,2,2.\u003c/p\u003e\u003cpre class=\"language-matlab\"\u003e\u0026gt;\u0026gt; COST = [695 766 710 119 752 548;\r\n 318 796 755 499 256 139;\r\n 951 187 277 960 506 150;\r\n 35 490 680 341 700 258;\r\n 439 446 656 586 891 841;\r\n 382 647 163 224 960 255];\r\n\u0026gt;\u0026gt; coolers(COST)\r\nans = \r\n 1393\r\n\u003c/pre\u003e\u003cp\u003eMeanwhile, the optimal placement for the case below is at rows: 5,6,5,6,5,6\u003c/p\u003e\u003cpre class=\"language-matlab\"\u003e\u0026gt;\u0026gt; COST = [815 617 918 76 569 312;\r\n 244 474 286 54 470 529;\r\n 930 352 758 531 455 988;\r\n 350 831 754 780 12 602;\r\n 197 586 381 935 163 263;\r\n 252 550 568 130 795 100];\r\n\u0026gt;\u0026gt; coolers(COST)\r\nans = \r\n 1521\r\n\u003c/pre\u003e","function_template":"function y = coolers(COST)\r\n y = x;\r\nend","test_suite":"%%\r\nfiletext = fileread('coolers.m')\r\nassert(isempty(strfind(filetext, 'rand')))\r\n%%\r\nCOST = [815 617 918 76 569 312;\r\n 244 474 286 54 470 529;\r\n 930 352 758 531 455 988;\r\n 350 831 754 780 12 602;\r\n 197 586 381 935 163 263;\r\n 252 550 568 130 795 100];\r\nassert(isequal(coolers(COST),1521))\r\n%%\r\nCOST = [690 153 107 85 182 550;\r\n 749 826 962 400 264 145;\r\n 451 539 5 260 146 854;\r\n 84 997 775 801 137 623;\r\n 229 79 818 432 870 351;\r\n 914 443 869 911 580 514];\r\nassert(isequal(coolers(COST),1179))\r\n%%\r\nCOST = [402 418 338 242 576 44;\r\n 76 50 901 404 60 169;\r\n 240 903 370 97 235 650;\r\n 124 945 112 132 354 732;\r\n 184 491 781 943 822 648;\r\n 240 490 390 957 16 451];\r\nassert(isequal(coolers(COST),697))\r\n%%\r\nCOST = [1 1 1000 1000 1000 1;\r\n 1 1000 1 1000 1000 1000;\r\n 1 1000 1000 1000 1 1000;\r\n 1 1000 1000 1 1000 1000;\r\n 1 1000 1000 1000 1000 1000;\r\n 1 1000 1000 1000 1000 1000];\r\nassert(isequal(coolers(COST),2004))\r\n%%\r\nCOST = [548 369 487 818 351 208;\r\n 297 626 436 795 940 302;\r\n 745 781 447 645 876 471;\r\n 189 82 307 379 551 231;\r\n 687 930 509 812 623 845;\r\n 184 776 511 533 588 195];\r\nassert(isequal(coolers(COST),1739))\r\n%%\r\nCOST = [226 431 259 222 86 489;\r\n 171 185 409 118 263 579;\r\n 228 905 595 297 802 238;\r\n 436 980 263 319 30 459;\r\n 312 439 603 425 929 964;\r\n 924 112 712 508 731 547];\r\nassert(isequal(coolers(COST),1234))\r\n%%\r\nCOST = [522 368 99 107 891 501;\r\n 232 988 262 654 335 480;\r\n 489 38 336 495 699 905;\r\n 625 886 680 780 198 610;\r\n 680 914 137 716 31 618;\r\n 396 797 722 904 745 860];\r\nassert(isequal(coolers(COST),1454))\r\n%%\r\nCOST = [806 490 60 819 973 84;\r\n 577 168 682 818 649 134;\r\n 183 979 43 723 801 174;\r\n 240 713 72 150 454 391;\r\n 887 501 522 660 433 832;\r\n 29 472 97 519 826 804];\r\nassert(isequal(coolers(COST),1172))\r\n%%\r\nCOST = [61 292 373 53 418 699;\r\n 400 432 199 738 984 667;\r\n 527 16 490 270 302 179;\r\n 417 985 340 423 702 129;\r\n 657 168 952 548 667 1000;\r\n 628 107 921 943 540 172];\r\nassert(isequal(coolers(COST),1253))\r\n%%\r\nCOST = [33 461 191 385 825 907;\r\n 562 982 429 583 983 880;\r\n 882 157 483 252 731 818;\r\n 670 856 121 291 344 261;\r\n 191 645 590 618 585 595;\r\n 369 377 227 266 108 23];\r\nassert(isequal(coolers(COST),1192))\r\n%%\r\nCOST = [426 599 69 719 779 441;\r\n 313 471 320 969 424 528;\r\n 162 696 531 532 91 458;\r\n 179 700 655 326 267 876;\r\n 423 639 408 106 154 519;\r\n 95 34 820 611 282 944];\r\nassert(isequal(coolers(COST),1316))\r\n%%\r\nCOST = [638 696 345 916 323 474;\r\n 958 68 781 2 785 153;\r\n 241 255 676 463 472 342;\r\n 677 225 7 425 36 608;\r\n 290 668 603 461 176 192;\r\n 672 845 387 771 722 739];\r\nassert(isequal(coolers(COST),1126))\r\n%%\r\nCOST = [243 92 648 237 771 257;\r\n 918 577 680 120 351 614;\r\n 270 684 636 608 663 583;\r\n 766 547 946 451 417 541;\r\n 189 426 209 459 842 870;\r\n 288 645 710 662 833 265];\r\nassert(isequal(coolers(COST),1711))\r\n%%\r\nCOST = [319 545 219 366 193 862;\r\n 120 648 106 764 139 485;\r\n 940 544 110 628 697 394;\r\n 646 722 64 772 94 672;\r\n 480 523 405 933 526 742;\r\n 640 994 449 973 531 521];\r\nassert(isequal(coolers(COST),1669))\r\n%%\r\nCOST = [674 622 842 636 885 896;\r\n 575 722 853 599 699 975;\r\n 794 844 722 911 905 664;\r\n 632 680 510 715 878 836;\r\n 523 869 667 944 689 720;\r\n 878 698 713 696 609 917];\r\nassert(isequal(coolers(COST),3837))\r\n%%\r\nCOST = [82 122 681 602 355 371;...\r\n 483 544 417 347 776 384;...\r\n 129 315 643 365 237 862;...\r\n 253 383 215 172 845 464;...\r\n 884 792 618 796 817 571;...\r\n 197 840 676 493 847 696];\r\nassert(isequal(coolers(COST),1452))\r\n%%\r\nCOST = [961 170 710 563 536 327;...\r\n 547 179 176 177 199 603;...\r\n 637 244 859 514 624 362;...\r\n 571 752 910 549 27 135;...\r\n 928 200 962 166 319 914;...\r\n 864 983 571 494 533 641];\r\nassert(isequal(coolers(COST),1569))\r\n%%\r\nCOST = [659 381 223 112 267 869;...\r\n 676 822 1000 425 292 529;...\r\n 745 172 64 614 189 915;...\r\n 843 330 426 989 23 974;...\r\n 517 967 405 220 450 586;...\r\n 152 807 401 355 244 119];\r\nassert(isequal(coolers(COST),1835))\r\n%%\r\nCOST = [927 925 215 554 571 679;...\r\n 594 643 249 631 336 213;...\r\n 884 105 227 986 958 82;...\r\n 425 701 704 635 440 275;...\r\n 608 396 755 601 602 868;...\r\n 71 85 548 910 721 560];\r\nassert(isequal(coolers(COST),1751))\r\n%%\r\nCOST = [465 433 384 904 809 299;...\r\n 431 506 712 219 180 769;...\r\n 774 376 481 874 166 502;...\r\n 654 481 730 83 182 910;...\r\n 658 343 938 466 692 58;...\r\n 162 778 518 22 214 437];\r\nassert(isequal(coolers(COST),1317))\r\n%%\r\nCOST = [573 952 497 860 78 228;...\r\n 566 767 809 627 339 710;...\r\n 824 752 633 181 581 149;...\r\n 127 139 689 574 476 659;...\r\n 301 350 640 164 806 634;...\r\n 3 152 730 907 531 230];\r\nassert(isequal(coolers(COST),1568))\r\n%%\r\nCOST = [183 958 897 179 998 879;...\r\n 167 26 190 747 5 747;...\r\n 150 972 661 50 543 118;...\r\n 203 298 942 72 862 510;...\r\n 955 526 976 490 910 169;...\r\n 16 863 108 850 846 832];\r\nassert(isequal(coolers(COST),539))\r\n%%\r\nCOST = [929 868 245 81 27 760;...\r\n 170 742 641 361 786 926;...\r\n 884 448 809 829 923 833;...\r\n 388 710 854 215 493 260;...\r\n 383 945 399 792 835 214;...\r\n 272 175 116 655 132 523];\r\nassert(isequal(coolers(COST),1564))\r\n%%\r\nCOST = [398 438 798 217 378 972;...\r\n 480 773 656 812 168 361;...\r\n 994 745 33 139 541 645;...\r\n 605 443 558 882 102 68;...\r\n 945 54 720 924 40 208;...\r\n 491 88 111 13 934 40];\r\nassert(isequal(coolers(COST),749))\r\n%%\r\nCOST = [470 581 9 642 470 879;...\r\n 151 541 825 106 220 189;...\r\n 992 706 768 269 923 760;...\r\n 428 6 998 764 321 32;...\r\n 956 783 228 806 858 643;...\r\n 725 927 920 105 260 567];\r\nassert(isequal(coolers(COST),1216))\r\n%%\r\nCOST = [377 187 35 595 562 603;...\r\n 213 486 489 499 634 474;...\r\n 793 839 972 568 931 357;...\r\n 146 142 113 427 978 476;...\r\n 490 733 744 77 94 672;...\r\n 13 692 639 291 662 960];\r\nassert(isequal(coolers(COST),1048))\r\n%%\r\nCOST = [90 52 454 629 707 46;...\r\n 798 505 738 133 536 886;...\r\n 591 769 510 619 194 840;...\r\n 913 283 383 384 690 119;...\r\n 102 226 906 992 51 411;...\r\n 294 332 966 287 185 121];\r\nassert(isequal(coolers(COST),1042))\r\n%%\r\nCOST = [573 666 232 754 549 464;...\r\n 950 974 53 622 461 590;...\r\n 257 623 902 395 646 188;...\r\n 990 64 794 360 514 612;...\r\n 350 374 374 89 815 52;...\r\n 209 167 833 342 98 576];\r\nassert(isequal(coolers(COST),934))\r\n%%\r\nCOST = [843 797 666 67 652 382;...\r\n 500 294 961 898 134 301;...\r\n 440 116 944 498 639 341;...\r\n 150 376 113 772 385 919;...\r\n 29 829 649 61 766 457;...\r\n 757 842 481 263 653 443];\r\nassert(isequal(coolers(COST),1166))\r\n%%\r\nCOST = [455 767 602 56 365 673;...\r\n 946 343 650 99 677 203;...\r\n 220 619 343 650 376 869;...\r\n 883 454 494 765 864 752;...\r\n 20 11 702 988 292 420;...\r\n 342 600 888 126 134 1];\r\nassert(isequal(coolers(COST),994))\r\n%%\r\nCOST = [150 436 24 66 150 132;...\r\n 274 904 575 924 351 887;...\r\n 873 926 47 535 336 675;...\r\n 602 506 423 367 785 836;...\r\n 322 628 468 364 487 657;...\r\n 285 720 23 152 465 984];\r\nassert(isequal(coolers(COST),958))\r\n%%\r\nCOST = [980 191 386 245 842 952;...\r\n 251 125 311 804 79 966;...\r\n 625 3 4 824 238 766;...\r\n 729 153 816 853 818 575;...\r\n 499 535 639 468 406 916;...\r\n 850 511 449 971 467 496];\r\nassert(isequal(coolers(COST),1655))\r\n%%\r\nCOST = [167 167 988 896 65 887;...\r\n 326 948 151 835 264 421;...\r\n 297 812 959 3 103 284;...\r\n 559 711 531 641 484 49;...\r\n 68 971 75 804 419 220;...\r\n 69 999 312 246 382 240];\r\nassert(isequal(coolers(COST),640))\r\n%%\r\nCOST = [30 653 667 689 433 469;...\r\n 703 321 848 321 905 546;...\r\n 8 104 763 532 631 180;...\r\n 611 536 808 874 984 635;...\r\n 409 165 633 55 586 963;...\r\n 249 884 711 501 841 535];\r\nassert(isequal(coolers(COST),2007))\r\n%%\r\nCOST = [480 679 683 689 62 13;...\r\n 794 566 947 148 220 217;...\r\n 93 479 100 778 83 12;...\r\n 881 321 512 400 951 643;...\r\n 4 602 111 899 17 517;...\r\n 512 914 546 308 115 246];\r\nassert(isequal(coolers(COST),648))\r\n%%\r\nCOST = [194 309 342 580 56 396;...\r\n 91 745 840 329 35 170;...\r\n 369 840 983 269 287 431;...\r\n 8 263 627 551 78 417;...\r\n 603 515 182 181 901 729;...\r\n 479 447 124 679 847 407];\r\nassert(isequal(coolers(COST),1129))\r\n%%\r\nCOST = [952 211 79 334 443 924;...\r\n 912 131 934 693 633 153;...\r\n 952 521 603 204 930 406;...\r\n 347 906 378 959 530 313;...\r\n 291 403 665 712 627 694;...\r\n 887 216 793 167 681 891];\r\nassert(isequal(coolers(COST),2052))\r\n%%\r\nCOST = [491 677 35 27 661 34;...\r\n 806 829 437 501 330 407;...\r\n 327 111 937 828 660 717;...\r\n 550 280 263 259 14 922;...\r\n 389 768 570 46 719 985;...\r\n 897 217 360 247 392 984];\r\nassert(isequal(coolers(COST),1266))\r\n%%\r\nCOST = [897 655 269 739 879 390;...\r\n 866 864 153 13 903 300;...\r\n 801 275 631 606 153 735;...\r\n 555 841 317 577 193 105;...\r\n 419 71 960 808 791 793;...\r\n 128 379 499 655 61 783];\r\nassert(isequal(coolers(COST),1254))\r\n%%\r\nCOST = [533 130 314 596 463 399;...\r\n 254 451 642 537 368 478;...\r\n 71 673 787 331 680 67;...\r\n 626 857 290 412 568 412;...\r\n 25 499 498 795 652 970;...\r\n 63 49 819 344 492 781];\r\nassert(isequal(coolers(COST),1580))\r\n%%\r\nCOST = [730 112 727 411 679 798;...\r\n 766 397 148 143 254 712;...\r\n 757 493 148 799 844 784;...\r\n 844 259 705 931 294 624;...\r\n 771 37 381 5 27 826;...\r\n 979 975 77 651 94 36];\r\nassert(isequal(coolers(COST),953))\r\n%%\r\nCOST = [406 27 672 377 507 436;...\r\n 250 156 53 114 329 158;...\r\n 481 834 735 965 754 601;...\r\n 881 195 500 433 837 938;...\r\n 281 830 944 85 254 108;...\r\n 600 339 290 717 535 900];\r\nassert(isequal(coolers(COST),931))\r\n%%\r\nCOST = [551 355 642 427 787 943;...\r\n 428 774 128 34 512 97;...\r\n 153 882 497 930 563 846;...\r\n 248 735 311 925 685 910;...\r\n 448 407 579 359 93 12;...\r\n 533 605 944 260 873 524];\r\nassert(isequal(coolers(COST),1430))\r\n%%\r\nCOST = [651 279 401 430 885 568;...\r\n 386 840 555 38 256 895;...\r\n 650 427 444 976 910 215;...\r\n 763 632 91 523 895 4;...\r\n 576 834 745 910 399 881;...\r\n 632 271 33 384 626 236];\r\nassert(isequal(coolers(COST),1575))\r\n%%\r\nCOST = [245 391 532 153 716 903;...\r\n 641 802 889 231 281 290;...\r\n 305 158 264 658 413 500;...\r\n 826 626 235 563 363 784;...\r\n 884 699 840 292 782 678;...\r\n 946 86 496 623 136 150];\r\nassert(isequal(coolers(COST),1276))\r\n%%\r\nCOST = [697 977 429 793 902 349;...\r\n 130 126 15 420 52 166;...\r\n 946 753 326 533 809 29;...\r\n 887 828 135 926 335 956;...\r\n 516 782 451 900 229 681;...\r\n 680 191 573 545 823 861];\r\nassert(isequal(coolers(COST),772))\r\n%%\r\nCOST = [940 301 652 887 695 895;...\r\n 681 74 170 115 207 842;...\r\n 918 768 532 443 555 131;...\r\n 257 85 634 660 880 190;...\r\n 886 729 15 295 558 154;...\r\n 921 448 471 951 753 29];\r\nassert(isequal(coolers(COST),1239))\r\n%%\r\nCOST = [10 496 746 686 237 463;...\r\n 597 259 338 268 196 926;...\r\n 610 733 585 970 706 216;...\r\n 919 117 469 184 181 2;...\r\n 734 747 88 300 523 907;...\r\n 302 810 829 412 297 681];\r\nassert(isequal(coolers(COST),1182))\r\n%%\r\nCOST = [515 394 842 779 399 396;...\r\n 523 8 49 728 671 399;...\r\n 103 546 317 651 441 752;...\r\n 997 510 784 665 133 523;...\r\n 359 247 973 939 440 491;...\r\n 626 46 587 536 548 89];\r\nassert(isequal(coolers(COST),1435))\r\n%%\r\nCOST = [251 93 71 159 652 1;...\r\n 448 954 301 63 499 641;...\r\n 638 163 814 702 285 8;...\r\n 710 971 77 87 831 107;...\r\n 993 598 355 617 819 107;...\r\n 933 241 133 174 939 368];\r\nassert(isequal(coolers(COST),771))\r\n%%\r\nCOST = [240 788 66 813 71 954;...\r\n 347 270 611 815 242 209;...\r\n 250 844 702 90 732 117;...\r\n 388 741 112 732 41 647;...\r\n 422 827 96 904 425 109;...\r\n 641 183 598 453 541 984];\r\nassert(isequal(coolers(COST),1343))\r\n%%\r\nCOST = [249 916 747 918 880 282;...\r\n 607 901 476 471 799 169;...\r\n 817 215 584 270 325 746;...\r\n 831 548 261 763 670 478;...\r\n 490 785 85 773 297 654;...\r\n 761 195 299 22 930 967];\r\nassert(isequal(coolers(COST),1567))\r\n%%\r\nCOST = [314 77 818 283 736 557;...\r\n 77 154 767 639 157 274;...\r\n 792 827 375 593 435 133;...\r\n 366 301 190 326 833 700;...\r\n 586 384 647 989 360 486;...\r\n 184 651 4 124 77 183];\r\nassert(isequal(coolers(COST),956))\r\n%%\r\nCOST = [102 248 381 378 851 968;...\r\n 202 438 749 973 257 477;...\r\n 135 670 157 606 286 995;...\r\n 324 548 59 339 780 491;...\r\n 951 610 340 928 702 504;...\r\n 533 864 818 899 493 769];\r\nassert(isequal(coolers(COST),1799))\r\n%%\r\nCOST = [389 799 340 268 52 543;...\r\n 454 221 273 177 628 809;...\r\n 133 858 171 432 30 794;...\r\n 759 905 665 476 137 502;...\r\n 566 293 536 786 695 277;...\r\n 649 726 830 131 516 120];\r\nassert(isequal(coolers(COST),1234))\r\n%%\r\nCOST = [887 183 567 504 84 962;...\r\n 971 32 378 261 74 467;...\r\n 943 725 822 733 770 787;...\r\n 639 145 305 163 818 423;...\r\n 91 636 320 922 741 944;...\r\n 75 790 785 223 759 2];\r\nassert(isequal(coolers(COST),1447))\r\n%%\r\nCOST = [982 666 329 847 415 7;...\r\n 571 685 928 902 662 767;...\r\n 347 793 757 596 784 22;...\r\n 558 349 289 69 248 394;...\r\n 300 251 607 219 555 253;...\r\n 160 346 767 870 230 205];\r\nassert(isequal(coolers(COST),1039))\r\n%%\r\nCOST = [663 975 947 135 372 260;...\r\n 915 120 967 806 227 134;...\r\n 7 519 68 525 447 420;...\r\n 747 822 438 945 267 507;...\r\n 800 638 321 989 460 325;...\r\n 908 954 135 410 433 685];\r\nassert(isequal(coolers(COST),1081))\r\n%%\r\nCOST = [444 502 305 970 394 701;...\r\n 436 556 767 690 459 110;...\r\n 794 631 268 718 209 7;...\r\n 816 98 40 560 758 598;...\r\n 753 246 297 534 547 660;...\r\n 790 616 557 876 358 581];\r\nassert(isequal(coolers(COST),1667))\r\n%%\r\nCOST = [910 165 870 241 503 143;...\r\n 637 281 788 9 568 381;...\r\n 526 260 970 672 189 397;...\r\n 260 548 181 905 325 577;...\r\n 52 542 931 573 717 20;...\r\n 732 789 46 156 553 578];\r\nassert(isequal(coolers(COST),1369))\r\n%%\r\nCOST = [933 303 817 55 540 946;...\r\n 107 460 451 638 938 377;...\r\n 733 49 807 425 661 68;...\r\n 971 386 791 906 395 182;...\r\n 609 362 283 418 259 576;...\r\n 720 288 69 155 848 186];\r\nassert(isequal(coolers(COST),1495))\r\n%%\r\nCOST = [292 28 747 842 871 890;...\r\n 462 659 747 511 212 66;...\r\n 347 159 174 166 837 510;...\r\n 319 803 118 715 860 621;...\r\n 460 409 175 908 524 734;...\r\n 236 328 628 219 478 230];\r\nassert(isequal(coolers(COST),1040))\r\n%%\r\nCOST = [22 327 315 114 208 74;...\r\n 139 138 160 701 785 595;...\r\n 770 385 153 180 527 862;...\r\n 970 563 137 804 572 449;...\r\n 387 634 710 514 423 653;...\r\n 994 542 465 549 722 304];\r\nassert(isequal(coolers(COST),716))\r\n%%\r\nCOST = [608 457 948 406 340 75;...\r\n 279 600 453 439 896 664;...\r\n 800 843 811 679 546 704;...\r\n 797 32 929 466 750 919;...\r\n 955 188 673 954 125 661;...\r\n 445 944 373 355 454 691];\r\nassert(isequal(coolers(COST),2010))\r\n%%\r\nCOST = [854 26 473 324 731 29;...\r\n 468 57 679 802 774 128;...\r\n 459 143 115 300 901 134;...\r\n 807 172 237 776 139 129;...\r\n 825 626 290 553 795 936;...\r\n 191 30 173 555 190 274];\r\nassert(isequal(coolers(COST),1199))\r\n%%\r\nCOST = [943 546 850 417 382 152;...\r\n 639 256 8 518 723 437;...\r\n 873 306 635 887 96 13;...\r\n 368 16 360 150 668 230;...\r\n 237 588 115 435 297 264;...\r\n 188 963 541 60 599 512];\r\nassert(isequal(coolers(COST),627))\r\n%%\r\nCOST = [216 475 261 618 402 95;...\r\n 347 826 590 145 15 376;...\r\n 748 304 480 717 75 546;...\r\n 414 822 199 402 592 112;...\r\n 56 566 240 463 447 905;...\r\n 391 55 781 708 927 634];\r\nassert(isequal(coolers(COST),940))\r\n%%\r\nCOST = [906 61 814 762 771 880;...\r\n 631 674 316 876 876 374;...\r\n 15 478 312 872 68 767;...\r\n 317 306 345 173 647 169;...\r\n 112 517 667 851 325 520;...\r\n 630 708 862 960 641 628];\r\nassert(isequal(coolers(COST),1043))\r\n%%\r\nCOST = [714 628 766 404 544 135;...\r\n 307 193 319 751 411 541;...\r\n 264 777 253 488 901 858;...\r\n 917 865 201 385 57 199;...\r\n 616 334 70 62 444 156;...\r\n 94 136 552 214 538 62];\r\nassert(isequal(coolers(COST),575))\r\n%%\r\nCOST = [662 683 487 77 915 603;...\r\n 19 138 680 445 92 466;...\r\n 292 630 705 166 994 299;...\r\n 974 858 461 399 97 134;...\r\n 765 900 365 921 314 296;...\r\n 244 349 281 512 786 167];\r\nassert(isequal(coolers(COST),1112))\r\n%%\r\nCOST = [318 40 863 414 595 658;...\r\n 110 617 277 415 310 685;...\r\n 833 670 532 984 902 474;...\r\n 972 38 523 58 94 142;...\r\n 219 4 568 397 320 951;...\r\n 707 143 334 792 887 883];\r\nassert(isequal(coolers(COST),1040))\r\n%%\r\nCOST = [438 952 914 477 226 187;...\r\n 835 2 534 251 568 647;...\r\n 326 296 805 308 999 129;...\r\n 368 49 563 967 132 82;...\r\n 795 443 751 209 955 660;...\r\n 100 790 10 521 124 28];\r\nassert(isequal(coolers(COST),914))\r\n%%\r\nCOST = [986 693 226 415 41 625;...\r\n 540 603 797 499 583 296;...\r\n 374 776 997 950 565 75;...\r\n 707 592 282 954 356 294;...\r\n 948 377 711 733 881 235;...\r\n 383 851 665 385 625 346];\r\nassert(isequal(coolers(COST),1955))\r\n%%\r\nCOST = [849 636 448 593 844 465;...\r\n 161 844 327 69 424 31;...\r\n 158 783 280 206 545 435;...\r\n 509 265 932 724 528 558;...\r\n 604 315 400 576 186 639;...\r\n 162 184 380 201 82 35];\r\nassert(isequal(coolers(COST),1044))\r\n%%\r\nCOST = [710 855 367 351 91 968;...\r\n 170 385 350 193 258 434;...\r\n 594 400 631 920 428 785;...\r\n 609 326 665 289 578 526;...\r\n 773 556 993 551 900 332;...\r\n 57 296 945 920 219 432];\r\nassert(isequal(coolers(COST),1623))\r\n%%\r\nCOST = [718 654 235 805 97 557;...\r\n 917 41 201 104 600 840;...\r\n 891 505 381 730 234 205;...\r\n 135 895 595 649 33 622;...\r\n 120 386 269 475 580 175;...\r\n 894 293 623 933 843 290];\r\nassert(isequal(coolers(COST),1365))\r\n%%\r\nCOST = [19 283 206 904 234 347;...\r\n 702 245 435 541 247 298;...\r\n 953 287 143 818 171 405;...\r\n 750 964 376 709 236 303;...\r\n 757 231 794 44 276 758;...\r\n 543 538 813 146 952 360];\r\nassert(isequal(coolers(COST),1417))\r\n%%\r\nCOST = [125 458 201 22 719 780;...\r\n 618 78 960 483 450 568;...\r\n 356 905 666 808 660 77;...\r\n 363 282 542 737 754 252;...\r\n 69 614 869 573 805 134;...\r\n 868 662 558 9 30 565];\r\nassert(isequal(coolers(COST),953))\r\n%%\r\nCOST = [541 43 122 494 863 421;...\r\n 69 528 592 856 685 488;...\r\n 989 257 360 725 635 461;...\r\n 252 409 720 200 142 516;...\r\n 316 948 524 158 80 272;...\r\n 301 920 261 371 877 232];\r\nassert(isequal(coolers(COST),1198))\r\n%%\r\nCOST = [900 895 226 336 740 434;...\r\n 909 88 105 620 889 290;...\r\n 604 540 10 993 860 632;...\r\n 366 429 60 649 598 296;...\r\n 599 618 323 540 655 623;...\r\n 669 559 780 233 916 48];\r\nassert(isequal(coolers(COST),2054))\r\n%%\r\nCOST = [995 67 543 281 171 63;...\r\n 207 928 781 599 372 407;...\r\n 608 88 522 37 40 464;...\r\n 348 333 932 64 710 203;...\r\n 718 527 148 323 642 870;...\r\n 28 247 417 99 175 598];\r\nassert(isequal(coolers(COST),730))\r\n%%\r\nCOST = [24 867 571 301 445 250;...\r\n 900 616 326 522 983 956;...\r\n 453 27 451 562 579 143;...\r\n 59 323 578 242 235 513;...\r\n 107 464 75 913 811 972;...\r\n 999 100 58 826 452 649];\r\nassert(isequal(coolers(COST),902))\r\n%%\r\nCOST = [615 424 874 119 114 462;...\r\n 470 274 301 99 491 864;...\r\n 578 445 401 891 600 263;...\r\n 912 628 518 34 91 824;...\r\n 377 535 62 840 979 329;...\r\n 229 386 232 508 654 942];\r\nassert(isequal(coolers(COST),1065))\r\n%%\r\nCOST = [245 314 524 145 800 565;...\r\n 958 58 893 245 209 218;...\r\n 511 45 406 379 897 858;...\r\n 565 813 605 271 746 862;...\r\n 994 413 95 216 537 314;...\r\n 771 385 336 634 970 327];\r\nassert(isequal(coolers(COST),1381))\r\n%%\r\nCOST = [841 334 286 610 505 816;...\r\n 493 367 657 384 8 910;...\r\n 52 795 232 31 920 778;...\r\n 779 39 622 858 411 758;...\r\n 427 727 76 604 733 406;...\r\n 280 873 967 848 152 702];\r\nassert(isequal(coolers(COST),1140))\r\n%%\r\nCOST = [566 563 904 539 781 176;...\r\n 585 547 605 738 537 417;...\r\n 345 551 927 182 770 740;...\r\n 705 695 117 427 639 893;...\r\n 161 928 341 99 894 26;...\r\n 2 945 37 304 61 138];\r\nassert(isequal(coolers(COST),1153))\r\n%%\r\nCOST = [425 619 192 805 191 892;...\r\n 765 7 715 860 504 674;...\r\n 525 741 178 567 51 686;...\r\n 755 992 987 755 57 696;...\r\n 170 129 17 520 336 800;...\r\n 673 361 40 586 631 661];\r\nassert(isequal(coolers(COST),1579))\r\n%%\r\nCOST = [520 255 928 227 995 523;...\r\n 332 846 588 2 984 274;...\r\n 935 539 102 894 965 719;...\r\n 247 911 367 454 667 779;...\r\n 512 351 276 579 727 82;...\r\n 741 936 267 316 335 222];\r\nassert(isequal(coolers(COST),1598))\r\n%%\r\nCOST = [204 470 675 379 889 587;...\r\n 625 379 552 618 563 969;...\r\n 726 341 52 563 195 582;...\r\n 835 64 308 831 222 100;...\r\n 19 762 966 958 706 167;...\r\n 203 403 932 76 597 103];\r\nassert(isequal(coolers(COST),993))\r\n%%\r\nCOST = [147 800 210 627 782 774;...\r\n 672 400 481 412 936 748;...\r\n 640 756 113 639 740 319;...\r\n 373 296 133 857 254 511;...\r\n 163 641 65 764 720 774;...\r\n 390 886 80 977 694 573];\r\nassert(isequal(coolers(COST),1784))\r\n%%\r\nCOST = [954 463 111 359 365 588;...\r\n 172 130 200 135 400 778;...\r\n 908 550 163 999 927 658;...\r\n 753 970 37 514 496 529;...\r\n 287 443 273 388 610 826;...\r\n 628 591 231 250 5 963];\r\nassert(isequal(coolers(COST),1501))\r\n%%\r\nCOST = [314 306 715 905 664 101;...\r\n 798 19 460 387 603 287;...\r\n 286 163 920 604 657 355;...\r\n 15 444 989 561 310 536;...\r\n 95 767 933 846 332 991;...\r\n 329 682 462 285 189 29];\r\nassert(isequal(coolers(COST),1729))\r\n%%\r\nCOST = [710 876 77 818 359 455;...\r\n 906 865 377 174 364 30;...\r\n 866 356 150 677 268 638;...\r\n 120 632 35 876 338 60;...\r\n 956 865 783 758 87 170;...\r\n 441 21 328 230 452 685];\r\nassert(isequal(coolers(COST),1098))\r\n%%\r\nCOST = [555 461 15 279 896 625;...\r\n 7 371 5 645 888 207;...\r\n 289 825 167 288 394 110;...\r\n 377 538 366 322 676 566;...\r\n 147 818 719 156 253 275;...\r\n 75 461 160 388 950 72];\r\nassert(isequal(coolers(COST),1175))\r\n%%\r\nCOST = [159 896 447 617 948 551;...\r\n 50 608 812 304 334 161;...\r\n 681 15 145 90 390 118;...\r\n 782 345 975 522 151 399;...\r\n 808 534 834 826 334 832;...\r\n 266 628 341 764 554 186];\r\nassert(isequal(coolers(COST),569))\r\n%%\r\nCOST = [501 491 579 185 613 662;...\r\n 127 887 776 198 738 896;...\r\n 865 906 662 862 304 275;...\r\n 767 499 470 126 43 998;...\r\n 565 530 220 646 836 835;...\r\n 390 910 603 438 370 792];\r\nassert(isequal(coolers(COST),1584))\r\n%%\r\nCOST = [657 988 206 794 242 185;...\r\n 544 789 495 682 210 88;...\r\n 387 853 32 651 273 309;...\r\n 823 486 828 238 776 231;...\r\n 596 874 265 478 332 910;...\r\n 782 334 678 937 604 937];\r\nassert(isequal(coolers(COST),1504))\r\n%%\r\nCOST = [32 626 369 811 16 974;...\r\n 594 256 338 724 95 373;...\r\n 44 905 619 675 515 321;...\r\n 425 768 87 914 953 784;...\r\n 522 563 376 821 844 213;...\r\n 841 898 188 549 936 960];\r\nassert(isequal(coolers(COST),1717))\r\n%%\r\nCOST = [931 594 600 844 914 151;...\r\n 366 98 227 771 577 947;...\r\n 345 560 714 510 288 651;...\r\n 693 44 725 707 267 983;...\r\n 717 758 345 792 891 194;...\r\n 801 660 33 331 367 829];\r\nassert(isequal(coolers(COST),1626))\r\n%%\r\nCOST = [494 60 648 497 429 28;...\r\n 591 516 624 763 42 906;...\r\n 45 54 954 180 226 472;...\r\n 565 844 177 692 667 911;...\r\n 634 595 475 915 872 328;...\r\n 499 692 843 163 345 692];\r\nassert(isequal(coolers(COST),526))\r\n%%\r\nCOST = [18 334 151 424 616 681;...\r\n 513 633 839 529 102 394;...\r\n 332 416 727 276 670 392;...\r\n 337 577 109 828 348 207;...\r\n 954 960 162 793 670 725;...\r\n 751 616 298 274 296 820];\r\nassert(isequal(coolers(COST),1421))\r\n%%\r\nCOST = [927 854 101 228 459 109;...\r\n 515 430 413 358 952 652;...\r\n 194 926 925 925 133 147;...\r\n 603 374 56 503 71 694;...\r\n 199 699 385 804 707 626;...\r\n 411 589 241 351 932 44];\r\nassert(isequal(coolers(COST),1345))\r\n%%\r\nCOST = [798 582 93 769 788 680;...\r\n 987 602 334 283 125 10;...\r\n 437 253 652 650 158 129;...\r\n 345 655 504 923 415 764;...\r\n 49 61 531 331 688 842;...\r\n 226 941 380 814 658 747];\r\nassert(isequal(coolers(COST),1350))\r\n%%\r\nCOST = [945 618 338 215 587 443;...\r\n 920 559 552 293 939 692;...\r\n 224 731 744 450 619 760;...\r\n 510 64 413 241 251 400;...\r\n 788 493 508 264 103 568;...\r\n 523 230 129 892 547 206];\r\nassert(isequal(coolers(COST),1251))\r\n%%\r\nCOST = [944 708 393 379 767 434;...\r\n 513 657 243 634 337 103;...\r\n 277 779 282 32 626 237;...\r\n 230 581 905 921 327 972;...\r\n 953 504 703 470 312 699;...\r\n 690 879 854 520 647 660];\r\nassert(isequal(coolers(COST),1565))\r\n%%\r\nCOST = [327 450 172 573 377 40;...\r\n 20 769 722 832 394 565;...\r\n 571 628 90 348 429 50;...\r\n 37 315 918 780 424 873;...\r\n 265 293 430 709 219 861;...\r\n 191 79 80 591 497 339];\r\nassert(isequal(coolers(COST),1224))\r\n%%\r\nCOST = [975 347 346 214 761 636;...\r\n 955 234 903 936 580 803;...\r\n 989 756 13 970 622 670;...\r\n 158 226 133 376 490 472;...\r\n 3 449 389 985 221 945;...\r\n 249 260 841 123 145 592];\r\nassert(isequal(coolers(COST),1311))\r\n%%\r\nCOST = [227 932 883 581 327 592;...\r\n 684 697 780 627 288 1;...\r\n 321 96 19 112 497 904;...\r\n 749 246 771 214 182 683;...\r\n 999 935 686 37 934 74;...\r\n 270 480 868 445 941 997];\r\nassert(isequal(coolers(COST),804))\r\n%%\r\nCOST = [315 176 835 189 254 788;...\r\n 810 588 997 578 287 438;...\r\n 462 155 973 629 126 551;...\r\n 588 446 746 365 529 987;...\r\n 478 538 200 637 821 690;...\r\n 553 462 37 892 300 971];\r\nassert(isequal(coolers(COST),2037))\r\n%%\r\nCOST = [96 320 833 203 939 1;...\r\n 899 796 571 493 975 484;...\r\n 59 302 71 730 608 148;...\r\n 124 608 267 955 958 315;...\r\n 631 462 171 763 331 172;...\r\n 371 293 561 81 902 593];\r\nassert(isequal(coolers(COST),1341))\r\n%%\r\nCOST = [658 16 262 188 656 56;...\r\n 349 974 894 744 782 820;...\r\n 54 735 973 719 863 107;...\r\n 48 753 995 189 786 7;...\r\n 56 34 347 434 434 276;...\r\n 72 118 293 46 348 943];\r\nassert(isequal(coolers(COST),862))\r\n%%\r\nCOST = [675 962 293 837 855 788;...\r\n 386 823 439 42 174 175;...\r\n 857 11 399 424 536 720;...\r\n 675 142 138 76 295 233;...\r\n 609 483 953 314 903 208;...\r\n 440 581 361 946 82 217];\r\nassert(isequal(coolers(COST),1114))\r\n%%\r\nCOST = [977 461 237 907 842 269;...\r\n 382 4 832 993 684 981;...\r\n 636 465 438 391 172 313;...\r\n 47 825 508 827 238 572;...\r\n 233 872 186 955 435 612;...\r\n 875 302 152 894 26 902];\r\nassert(isequal(coolers(COST),1700))\r\n%%\r\nCOST = [397 297 634 847 995 269;...\r\n 693 572 965 41 429 758;...\r\n 205 317 201 330 268 610;...\r\n 63 810 599 710 473 967;...\r\n 623 366 84 861 161 774;...\r\n 689 699 545 501 159 573];\r\nassert(isequal(coolers(COST),1320))\r\n%%\r\nCOST = [451 355 996 87 199 597;...\r\n 288 581 84 520 657 323;...\r\n 753 299 469 553 699 831;...\r\n 95 714 94 686 460 123;...\r\n 107 361 726 300 158 252;...\r\n 735 719 913 602 422 938];\r\nassert(isequal(coolers(COST),1069))\r\n\r\n","published":true,"deleted":false,"likes_count":7,"comments_count":2,"created_by":255320,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":56,"test_suite_updated_at":"2020-04-03T23:22:52.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2020-04-01T22:04:29.000Z","updated_at":"2026-02-26T16:11:43.000Z","published_at":"2020-04-01T22:55:22.000Z","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\":[],\"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:r\u003e\u003cw:t\u003eIn a certain chemical plant, 6 new pieces of cooling equipment (coolers) are to be installed in a vacant space. This vacant space was divided into a grid of 6 cells by 6 cells. Your task is to assign the 6 coolers to 6 cells in this grid with the following requirements:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"2\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThere must be one cooler for every column in the grid.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"2\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIf you decide to install a cooler at row R, column C, then the cooler at column C+1 must be installed either on row R-1, R, or R+1 only. This is done to ease the connection of coolers by piping.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"2\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe total installation cost for the 6 coolers must be minimum.\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 are given a cost matrix (COST) in relation to the third requirement above. COST is a 6 x 6 matrix where the\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\u003er,c\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e-th element is the cost of assigning any cooler to row\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\u003er\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, column\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\u003ec\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e (All the coolers are identical). Write a function that accepts the matrix COST, and output the value of the minimum cost of installation. You are ensured that all elements of COST are integers in the range [1,1000].\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\u003eIn the sample test case below, the optimal placement is at the following rows: 4,3,3,2,2,2.\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[\u003e\u003e COST = [695 766 710 119 752 548;\\n 318 796 755 499 256 139;\\n 951 187 277 960 506 150;\\n 35 490 680 341 700 258;\\n 439 446 656 586 891 841;\\n 382 647 163 224 960 255];\\n\u003e\u003e coolers(COST)\\nans = \\n 1393]]\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\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eMeanwhile, the optimal placement for the case below is at rows: 5,6,5,6,5,6\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[\u003e\u003e COST = [815 617 918 76 569 312;\\n 244 474 286 54 470 529;\\n 930 352 758 531 455 988;\\n 350 831 754 780 12 602;\\n 197 586 381 935 163 263;\\n 252 550 568 130 795 100];\\n\u003e\u003e coolers(COST)\\nans = \\n 1521]]\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\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray 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