✨ feat(pyproject.toml)：添加mplusa依赖用于最大路径和计算

✨ 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

solutions/0067.MaxPathSum2/eular_67.py

@@ -0,0 +1,46 @@
+"""
+By starting at the top of the triangle below and moving to adjacent numbers on the row below,
+the maximum total from top to bottom is 23.
+
+3
+7 4
+2 4 6
+8 5 9 3
+
+That is, 3 + 7 + 4 + 9 = 23 .
+
+Find the maximum total from top to bottom of the triangle in the file 0067_trangle.txt.
+"""
+
+from pathlib import Path
+
+import numpy as np
+from mplusa import maxplus as mp
+
+
+def triangle_best(triangle: list[list[int]]) -> int:
+    levels = len(triangle)
+
+    current = np.array(triangle[-1], dtype=float).reshape(-1, 1)
+
+    for i in range(levels - 2, -1, -1):
+        selector = np.full((i + 1, i + 2), -np.inf)
+        np.fill_diagonal(selector, triangle[i])
+        np.fill_diagonal(selector[:, 1:], triangle[i])
+        current = mp.mult_matrices(selector, current)
+
+    print(current)
+
+    return int(current[0][0])
+
+
+def main() -> None:
+    with open(Path(__file__).parent / "0067_triangle.txt", "r") as file:
+        data = file.read().split("\n")[:100]
+    triangle = [list(map(int, row.split())) for row in data]
+    res = triangle_best(triangle)
+    print(res)
+
+
+if __name__ == "__main__":
+    main()