[leetcode] Minimum Path Sum

最新推荐文章于 2026-01-05 22:36:07 发布

原创最新推荐文章于 2026-01-05 22:36:07 发布 · 303 阅读

0 ·

CC 4.0 BY-SA版权

文章标签：

#leetcode #dp

本文介绍如何使用动态规划解决最小路径和问题，通过构建二维数组并利用递推公式，实现从起点到终点的最优路径查找。

Given a m x n grid filled with non-negative numbers, find a path from top left to bottom right which minimizes the sum of all numbers along its path.

Note: You can only move either down or right at any point in time.

思路很简单，DP，f[i][j] = min(f[i][j-1], f[i-1][j]) + grid[i][j]

class Solution:
    # @param grid, a list of lists of integers
    # @return an integer
    def minPathSum(self, grid):
        m = len(grid)
        n = len(grid[0])
        f = [[0 for col in range(n)] for row in range(m)]
        f[0][0] = grid[0][0]
        for i in range(1,n):
            f[0][i] = f[0][i - 1] + grid[0][i]
        for i in range(1,m):
            f[i][0] = f[i - 1][0] + grid[i][0]
        for i in range(1,m):
            for j in range(1,n):
                f[i][j] = min(f[i][j-1], f[i-1][j]) + grid[i][j]
        return f[m-1][n-1]