2018-09-30 23:01:58 +01:00
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---
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id: 5900f4c81000cf542c50ffda
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title: 'Problem 345: Matrix Sum'
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2020-11-27 19:02:05 +01:00
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challengeType: 5
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2019-08-05 09:17:33 -07:00
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forumTopicId: 302004
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2021-01-13 03:31:00 +01:00
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dashedName: problem-345-matrix-sum
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2018-09-30 23:01:58 +01:00
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---
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2020-11-27 19:02:05 +01:00
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# --description--
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2018-09-30 23:01:58 +01:00
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2021-07-29 19:14:22 +02:00
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We define the Matrix Sum of a matrix as the maximum sum of matrix elements with each element being the only one in his row and column.
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2018-09-30 23:01:58 +01:00
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2021-07-29 19:14:22 +02:00
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For example, the Matrix Sum of the matrix below equals $3315 ( = 863 + 383 + 343 + 959 + 767)$:
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$$\begin{array}{rrrrr}
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7 & 53 & 183 & 439 & \color{lime}{863} \\\\
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497 & \color{lime}{383} & 563 & 79 & 973 \\\\
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287 & 63 & \color{lime}{343} & 169 & 583 \\\\
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627 & 343 & 773 & \color{lime}{959} & 943 \\\\
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\color{lime}{767} & 473 & 103 & 699 & 303
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\end{array}$$
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2018-09-30 23:01:58 +01:00
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Find the Matrix Sum of:
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2021-07-29 19:14:22 +02:00
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$$\\begin{array}{r}
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7 & 53 & 183 & 439 & 863 & 497 & 383 & 563 & 79 & 973 & 287 & 63 & 343 & 169 & 583 \\\\
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627 & 343 & 773 & 959 & 943 & 767 & 473 & 103 & 699 & 303 & 957 & 703 & 583 & 639 & 913 \\\\
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447 & 283 & 463 & 29 & 23 & 487 & 463 & 993 & 119 & 883 & 327 & 493 & 423 & 159 & 743 \\\\
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217 & 623 & 3 & 399 & 853 & 407 & 103 & 983 & 89 & 463 & 290 & 516 & 212 & 462 & 350 \\\\
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960 & 376 & 682 & 962 & 300 & 780 & 486 & 502 & 912 & 800 & 250 & 346 & 172 & 812 & 350 \\\\
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870 & 456 & 192 & 162 & 593 & 473 & 915 & 45 & 989 & 873 & 823 & 965 & 425 & 329 & 803 \\\\
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973 & 965 & 905 & 919 & 133 & 673 & 665 & 235 & 509 & 613 & 673 & 815 & 165 & 992 & 326 \\\\
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322 & 148 & 972 & 962 & 286 & 255 & 941 & 541 & 265 & 323 & 925 & 281 & 601 & 95 & 973 \\\\
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445 & 721 & 11 & 525 & 473 & 65 & 511 & 164 & 138 & 672 & 18 & 428 & 154 & 448 & 848 \\\\
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414 & 456 & 310 & 312 & 798 & 104 & 566 & 520 & 302 & 248 & 694 & 976 & 430 & 392 & 198 \\\\
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184 & 829 & 373 & 181 & 631 & 101 & 969 & 613 & 840 & 740 & 778 & 458 & 284 & 760 & 390 \\\\
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821 & 461 & 843 & 513 & 17 & 901 & 711 & 993 & 293 & 157 & 274 & 94 & 192 & 156 & 574 \\\\
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34 & 124 & 4 & 878 & 450 & 476 & 712 & 914 & 838 & 669 & 875 & 299 & 823 & 329 & 699 \\\\
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815 & 559 & 813 & 459 & 522 & 788 & 168 & 586 & 966 & 232 & 308 & 833 & 251 & 631 & 107 \\\\
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813 & 883 & 451 & 509 & 615 & 77 & 281 & 613 & 459 & 205 & 380 & 274 & 302 & 35 & 805
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\end{array}$$
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2018-09-30 23:01:58 +01:00
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2020-11-27 19:02:05 +01:00
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# --hints--
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2018-09-30 23:01:58 +01:00
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2021-07-29 19:14:22 +02:00
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`matrixSum()` should return `13938`.
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2018-09-30 23:01:58 +01:00
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2020-11-27 19:02:05 +01:00
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```js
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2021-07-29 19:14:22 +02:00
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assert.strictEqual(matrixSum(), 13938);
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2018-09-30 23:01:58 +01:00
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```
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2020-11-27 19:02:05 +01:00
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# --seed--
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2018-09-30 23:01:58 +01:00
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2020-11-27 19:02:05 +01:00
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## --seed-contents--
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2018-09-30 23:01:58 +01:00
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```js
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2021-07-29 19:14:22 +02:00
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function matrixSum() {
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2020-09-15 09:57:40 -07:00
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2018-09-30 23:01:58 +01:00
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return true;
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}
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2021-07-29 19:14:22 +02:00
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matrixSum();
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2018-09-30 23:01:58 +01:00
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```
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2020-11-27 19:02:05 +01:00
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# --solutions--
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2018-09-30 23:01:58 +01:00
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```js
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// solution required
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```
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