Sidney Zhang
9a43e5e68b
✨ feat(solutions)：新增欧拉问题17、18和67的解决方案 📝 docs(solutions/0018.MaxPathSum1)：添加说明文档指出初始解法存在局部最优问题 ✨ feat(solutions/0067.MaxPathSum2)：实现基于最大加代数的优化解法
47 lines
1.1 KiB
Python
47 lines
1.1 KiB
Python
"""
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By starting at the top of the triangle below and moving to adjacent numbers on the row below,
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the maximum total from top to bottom is 23.
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3
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7 4
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2 4 6
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8 5 9 3
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That is, 3 + 7 + 4 + 9 = 23 .
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Find the maximum total from top to bottom of the triangle in the file 0067_trangle.txt.
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"""
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from pathlib import Path
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import numpy as np
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from mplusa import maxplus as mp
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def triangle_best(triangle: list[list[int]]) -> int:
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levels = len(triangle)
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current = np.array(triangle[-1], dtype=float).reshape(-1, 1)
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for i in range(levels - 2, -1, -1):
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selector = np.full((i + 1, i + 2), -np.inf)
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np.fill_diagonal(selector, triangle[i])
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np.fill_diagonal(selector[:, 1:], triangle[i])
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current = mp.mult_matrices(selector, current)
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print(current)
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return int(current[0][0])
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def main() -> None:
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with open(Path(__file__).parent / "0067_triangle.txt", "r") as file:
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data = file.read().split("\n")[:100]
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triangle = [list(map(int, row.split())) for row in data]
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res = triangle_best(triangle)
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print(res)
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if __name__ == "__main__":
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main()
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