Add solution for the Euler project problem 345 (#12666)

* Add solution for the Euler project problem 345. * Update sol1.py * Update sol1.py * Update sol1.py * Update sol1.py * [pre-commit.ci] auto fixes from pre-commit.com hooks for more information, see https://pre-commit.ci * Update sol1.py * Update sol1.py * Update sol1.py * [pre-commit.ci] auto fixes from pre-commit.com hooks for more information, see https://pre-commit.ci --------- Co-authored-by: Maxim Smolskiy <mithridatus@mail.ru> Co-authored-by: pre-commit-ci[bot] <66853113+pre-commit-ci[bot]@users.noreply.github.com>

Author: 3 people

project_euler/problem_345/__init__.py

@@ -0,0 +1,117 @@
+"""
+Project Euler Problem 345: https://projecteuler.net/problem=345
+
+Matrix Sum
+
+We define the Matrix Sum of a matrix as the maximum possible sum of
+matrix elements such that none of the selected elements share the same row or column.
+
+For example, the Matrix Sum of the matrix below equals
+3315 ( = 863 + 383 + 343 + 959 + 767):
+ 7 53 183 439 863
+ 497 383 563 79 973
+ 287 63 343 169 583
+ 627 343 773 959 943
+ 767 473 103 699 303
+
+Find the Matrix Sum of:
+ 7 53 183 439 863 497 383 563 79 973 287 63 343 169 583
+ 627 343 773 959 943 767 473 103 699 303 957 703 583 639 913
+ 447 283 463 29 23 487 463 993 119 883 327 493 423 159 743
+ 217 623 3 399 853 407 103 983 89 463 290 516 212 462 350
+ 960 376 682 962 300 780 486 502 912 800 250 346 172 812 350
+ 870 456 192 162 593 473 915 45 989 873 823 965 425 329 803
+ 973 965 905 919 133 673 665 235 509 613 673 815 165 992 326
+ 322 148 972 962 286 255 941 541 265 323 925 281 601 95 973
+ 445 721 11 525 473 65 511 164 138 672 18 428 154 448 848
+ 414 456 310 312 798 104 566 520 302 248 694 976 430 392 198
+ 184 829 373 181 631 101 969 613 840 740 778 458 284 760 390
+ 821 461 843 513 17 901 711 993 293 157 274 94 192 156 574
+ 34 124 4 878 450 476 712 914 838 669 875 299 823 329 699
+ 815 559 813 459 522 788 168 586 966 232 308 833 251 631 107
+ 813 883 451 509 615 77 281 613 459 205 380 274 302 35 805
+
+Brute force solution, with caching intermediate steps to speed up the calculation.
+"""
+
+import numpy as np
+from numpy.typing import NDArray
+
+MATRIX_1 = [
+ "7 53 183 439 863",
+ "497 383 563 79 973",
+ "287 63 343 169 583",
+ "627 343 773 959 943",
+ "767 473 103 699 303",
+]
+
+MATRIX_2 = [
+ "7 53 183 439 863 497 383 563 79 973 287 63 343 169 583",
+ "627 343 773 959 943 767 473 103 699 303 957 703 583 639 913",
+ "447 283 463 29 23 487 463 993 119 883 327 493 423 159 743",
+ "217 623 3 399 853 407 103 983 89 463 290 516 212 462 350",
+ "960 376 682 962 300 780 486 502 912 800 250 346 172 812 350",
+ "870 456 192 162 593 473 915 45 989 873 823 965 425 329 803",
+ "973 965 905 919 133 673 665 235 509 613 673 815 165 992 326",
+ "322 148 972 962 286 255 941 541 265 323 925 281 601 95 973",
+ "445 721 11 525 473 65 511 164 138 672 18 428 154 448 848",
+ "414 456 310 312 798 104 566 520 302 248 694 976 430 392 198",
+ "184 829 373 181 631 101 969 613 840 740 778 458 284 760 390",
+ "821 461 843 513 17 901 711 993 293 157 274 94 192 156 574",
+ "34 124 4 878 450 476 712 914 838 669 875 299 823 329 699",
+ "815 559 813 459 522 788 168 586 966 232 308 833 251 631 107",
+ "813 883 451 509 615 77 281 613 459 205 380 274 302 35 805",
+]
+
+
+def solve(arr: NDArray, row: int, cols: set[int], cache: dict[str, int]) -> int:
+ """
+ Finds the max sum for array `arr` starting with row index `row`, and with columns
+ included in `cols`. `cache` is used for caching intermediate results.
+
+ >>> solve(arr=np.array([[1, 2], [3, 4]]), row=0, cols={0, 1}, cache={})
+ 5
+ """
+
+ cache_id = f"{row}, {sorted(cols)}"
+ if cache_id in cache:
+ return cache[cache_id]
+
+ if row == len(arr):
+ return 0
+
+ max_sum = 0
+ for col in cols:
+ new_cols = cols - {col}
+ max_sum = max(
+ max_sum,
+ int(arr[row, col])
+ + solve(arr=arr, row=row + 1, cols=new_cols, cache=cache),
+ )
+ cache[cache_id] = max_sum
+ return max_sum
+
+
+def solution(matrix_str: list[str] = MATRIX_2) -> int:
+ """
+ Takes list of strings `matrix_str` to parse the matrix and calculates the max sum.
+
+ >>> solution(["1 2", "3 4"])
+ 5
+ >>> solution(MATRIX_1)
+ 3315
+ """
+
+ n = len(matrix_str)
+ arr = np.empty(shape=(n, n), dtype=int)
+ for row, matrix_row_str in enumerate(matrix_str):
+ matrix_row_list_str = matrix_row_str.split()
+ for col, elem_str in enumerate(matrix_row_list_str):
+ arr[row, col] = int(elem_str)
+
+ cache: dict[str, int] = {}
+ return solve(arr=arr, row=0, cols=set(range(n)), cache=cache)
+
+
+if __name__ == "__main__":
+ print(f"{solution() = }")