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66 lines
2.1 KiB
Python
66 lines
2.1 KiB
Python
"""
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Project Euler Problem 82: https://projecteuler.net/problem=82
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The minimal path sum in the 5 by 5 matrix below, by starting in any cell
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in the left column and finishing in any cell in the right column,
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and only moving up, down, and right, is indicated in red and bold;
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the sum is equal to 994.
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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 left column to the right column in matrix.txt
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(https://projecteuler.net/project/resources/p082_matrix.txt)
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(right click and "Save Link/Target As..."),
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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 = "input.txt") -> int:
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"""
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Returns the minimal path sum in the matrix from the file, by starting in any cell
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in the left column and finishing in any cell in the right column,
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and only moving up, down, and right
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>>> solution("test_matrix.txt")
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994
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"""
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with open(os.path.join(os.path.dirname(__file__), filename)) as input_file:
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matrix = [
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[int(element) for element in line.split(",")]
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for line in input_file.readlines()
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]
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rows = len(matrix)
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cols = len(matrix[0])
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minimal_path_sums = [[-1 for _ in range(cols)] for _ in range(rows)]
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for i in range(rows):
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minimal_path_sums[i][0] = matrix[i][0]
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for j in range(1, cols):
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for i in range(rows):
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minimal_path_sums[i][j] = minimal_path_sums[i][j - 1] + matrix[i][j]
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for i in range(1, rows):
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minimal_path_sums[i][j] = min(
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minimal_path_sums[i][j], minimal_path_sums[i - 1][j] + matrix[i][j]
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)
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for i in range(rows - 2, -1, -1):
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minimal_path_sums[i][j] = min(
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minimal_path_sums[i][j], minimal_path_sums[i + 1][j] + matrix[i][j]
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)
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return min(minimal_path_sums_row[-1] for minimal_path_sums_row in minimal_path_sums)
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if __name__ == "__main__":
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print(f"{solution() = }")
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