Add solution for the Euler project problem 345.

Author: mindaugl

Diff for: project_euler/problem_345/__init__.py

@@ -0,0 +1,93 @@
+"""
+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.
+Find the Matrix Sum of the following matrix.
+
+Brute force solution, with caching intermediate steps to speed up the calculation.
+
+>>> solution(MATRIX_1)
+3315
+"""
+
+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_ind: int, include_set: set[int], cache: dict[str, int]
+) -> int:
+    """
+    finds the max sum for array arr starting with row number row_ind, and with columns
+    included in include_set. cache is used for caching intermediate results.
+
+    >>> solve(np.array([[1, 2], [3,4]]), 0, {0, 1}, {})
+    np.int64(5)
+    """
+
+    cache_id = f"{row_ind}, {sorted(include_set)}"
+    if cache_id in cache:
+        return cache[cache_id]
+    if row_ind == len(arr):
+        return 0
+    sub_max = 0
+    for i in include_set:
+        new_set = include_set - {i}
+        sub_max = max(
+            sub_max, arr[row_ind, i] + solve(arr, row_ind + 1, new_set, cache)
+        )
+    cache[cache_id] = sub_max
+    return sub_max
+
+
+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
+    """
+
+    n = len(matrix_str)
+    arr = np.empty((n, n), dtype=np.int64)
+    for i in range(n):
+        els = matrix_str[i].strip().split(" ")
+        for j in range(len(els)):
+            arr[i, j] = int(els[j])
+
+    cache: dict[str, int] = {}
+    ans = solve(arr, 0, set(range(n)), cache)
+    return int(ans)
+
+
+if __name__ == "__main__":
+    print(f"{solution() = }")