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48 lines
1.5 KiB
Python
48 lines
1.5 KiB
Python
"""
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Problem 81: https://projecteuler.net/problem=81
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In the 5 by 5 matrix below, the minimal path sum from the top left to the bottom right,
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by only moving to the right and down, is indicated in bold red and is equal to 2427.
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[131] 673 234 103 18
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[201] [96] [342] 965 150
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630 803 [746] [422] 111
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537 699 497 [121] 956
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805 732 524 [37] [331]
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Find the minimal path sum from the top left to the bottom right by only moving right
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and down in matrix.txt (https://projecteuler.net/project/resources/p081_matrix.txt),
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a 31K text file containing an 80 by 80 matrix.
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"""
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import os
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def solution(filename: str = "matrix.txt") -> int:
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"""
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Returns the minimal path sum from the top left to the bottom right of the matrix.
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>>> solution()
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427337
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"""
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with open(os.path.join(os.path.dirname(__file__), filename)) as in_file:
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data = in_file.read()
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grid = [[int(cell) for cell in row.split(",")] for row in data.strip().splitlines()]
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dp = [[0 for cell in row] for row in grid]
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n = len(grid[0])
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dp = [[0 for i in range(n)] for j in range(n)]
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dp[0][0] = grid[0][0]
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for i in range(1, n):
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dp[0][i] = grid[0][i] + dp[0][i - 1]
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for i in range(1, n):
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dp[i][0] = grid[i][0] + dp[i - 1][0]
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for i in range(1, n):
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for j in range(1, n):
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dp[i][j] = grid[i][j] + min(dp[i - 1][j], dp[i][j - 1])
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return dp[-1][-1]
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if __name__ == "__main__":
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print(f"{solution() = }")
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