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* 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>
118 lines
4.1 KiB
Python
118 lines
4.1 KiB
Python
"""
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Project Euler Problem 345: https://projecteuler.net/problem=345
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Matrix Sum
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We define the Matrix Sum of a matrix as the maximum possible sum of
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matrix elements such that none of the selected elements share the same row or column.
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For example, the Matrix Sum of the matrix below equals
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3315 ( = 863 + 383 + 343 + 959 + 767):
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7 53 183 439 863
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497 383 563 79 973
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287 63 343 169 583
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627 343 773 959 943
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767 473 103 699 303
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Find the Matrix Sum of:
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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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Brute force solution, with caching intermediate steps to speed up the calculation.
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"""
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import numpy as np
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from numpy.typing import NDArray
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MATRIX_1 = [
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"7 53 183 439 863",
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"497 383 563 79 973",
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"287 63 343 169 583",
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"627 343 773 959 943",
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"767 473 103 699 303",
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]
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MATRIX_2 = [
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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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]
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def solve(arr: NDArray, row: int, cols: set[int], cache: dict[str, int]) -> int:
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"""
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Finds the max sum for array `arr` starting with row index `row`, and with columns
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included in `cols`. `cache` is used for caching intermediate results.
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>>> solve(arr=np.array([[1, 2], [3, 4]]), row=0, cols={0, 1}, cache={})
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5
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"""
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cache_id = f"{row}, {sorted(cols)}"
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if cache_id in cache:
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return cache[cache_id]
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if row == len(arr):
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return 0
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max_sum = 0
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for col in cols:
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new_cols = cols - {col}
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max_sum = max(
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max_sum,
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int(arr[row, col])
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+ solve(arr=arr, row=row + 1, cols=new_cols, cache=cache),
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)
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cache[cache_id] = max_sum
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return max_sum
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def solution(matrix_str: list[str] = MATRIX_2) -> int:
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"""
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Takes list of strings `matrix_str` to parse the matrix and calculates the max sum.
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>>> solution(["1 2", "3 4"])
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5
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>>> solution(MATRIX_1)
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3315
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"""
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n = len(matrix_str)
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arr = np.empty(shape=(n, n), dtype=int)
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for row, matrix_row_str in enumerate(matrix_str):
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matrix_row_list_str = matrix_row_str.split()
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for col, elem_str in enumerate(matrix_row_list_str):
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arr[row, col] = int(elem_str)
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cache: dict[str, int] = {}
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return solve(arr=arr, row=0, cols=set(range(n)), cache=cache)
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if __name__ == "__main__":
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print(f"{solution() = }")
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