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5 | 5 |
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6 | 6 | We define the Matrix Sum of a matrix as the maximum possible sum of
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7 | 7 | matrix elements such that none of the selected elements share the same row or column.
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8 |
| -Find the Matrix Sum of the following matrix. |
9 | 8 |
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10 |
| -Brute force solution, with caching intermediate steps to speed up the calculation. |
| 9 | +For example, the Matrix Sum of the matrix below equals 3315 ( = 863 + 383 + 343 + 959 + 767): |
| 10 | + 7 53 183 439 863 |
| 11 | + 497 383 563 79 973 |
| 12 | + 287 63 343 169 583 |
| 13 | + 627 343 773 959 943 |
| 14 | + 767 473 103 699 303 |
| 15 | +
|
| 16 | +Find the Matrix Sum of: |
| 17 | + 7 53 183 439 863 497 383 563 79 973 287 63 343 169 583 |
| 18 | + 627 343 773 959 943 767 473 103 699 303 957 703 583 639 913 |
| 19 | + 447 283 463 29 23 487 463 993 119 883 327 493 423 159 743 |
| 20 | + 217 623 3 399 853 407 103 983 89 463 290 516 212 462 350 |
| 21 | + 960 376 682 962 300 780 486 502 912 800 250 346 172 812 350 |
| 22 | + 870 456 192 162 593 473 915 45 989 873 823 965 425 329 803 |
| 23 | + 973 965 905 919 133 673 665 235 509 613 673 815 165 992 326 |
| 24 | + 322 148 972 962 286 255 941 541 265 323 925 281 601 95 973 |
| 25 | + 445 721 11 525 473 65 511 164 138 672 18 428 154 448 848 |
| 26 | + 414 456 310 312 798 104 566 520 302 248 694 976 430 392 198 |
| 27 | + 184 829 373 181 631 101 969 613 840 740 778 458 284 760 390 |
| 28 | + 821 461 843 513 17 901 711 993 293 157 274 94 192 156 574 |
| 29 | + 34 124 4 878 450 476 712 914 838 669 875 299 823 329 699 |
| 30 | + 815 559 813 459 522 788 168 586 966 232 308 833 251 631 107 |
| 31 | + 813 883 451 509 615 77 281 613 459 205 380 274 302 35 805 |
11 | 32 |
|
12 |
| ->>> solution(MATRIX_1) |
13 |
| -3315 |
| 33 | +Brute force solution, with caching intermediate steps to speed up the calculation. |
14 | 34 | """
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15 | 35 |
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16 | 36 | import numpy as np
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@@ -75,6 +95,8 @@ def solution(matrix_str: list[str] = MATRIX_2) -> int:
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75 | 95 |
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76 | 96 | >>> solution(["1 2", "3 4"])
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77 | 97 | 5
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| 98 | + >>> solution(MATRIX_1) |
| 99 | + 3315 |
78 | 100 | """
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79 | 101 |
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80 | 102 | n = len(matrix_str)
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|
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