68 leetcode - Minimum Path Sum

忧桑的小兔子

于 2017-01-01 09:10:59 发布

阅读量416

点赞数

CC 4.0 BY-SA版权

文章标签： leetcode Minimum Path Sum Python

本文链接：https://blog.youkuaiyun.com/lis_12/article/details/53964659

算法专栏收录该内容

84 篇文章

订阅专栏

本文介绍了一个算法问题：在一个非负数构成的mxn网格中寻找从左上角到右下角路径上的最小数字和。提供了Python实现的解决方案，通过动态规划的方法递推计算每个格子的最小路径和。

摘要生成于 C知道，由 DeepSeek-R1 满血版支持，前往体验 >

#!/usr/bin/python
# -*- coding: utf-8 -*-
'''
Minimum Path Sum
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.
'''
class Solution(object):
    def minPathSum(self, grid):
        """
        :type grid: List[List[int]]
        :rtype: int
        """
        m = len(grid)
        if 0 == m:
            return 0

        n = len(grid[0])
        if 0 == n:
            return 0

        dp = [[0] * n for i in  range(m)]  #a = [[0] * n] * m,不能使用这个,因为引用,id(a[m])相同
        dp[0][0] = grid[0][0]

        for i in range(1,m):
            dp[i][0] = dp[i - 1][0] + grid [i][0]

        for i in range(1,n):
            dp[0][i] = dp[0][i - 1] + grid[0][i]

        for row in range(1,m):
            for col in range(1,n):
                dp[row][col] = grid[row][col] + min(dp[row - 1][col], dp[row][col - 1])

        return dp[m - 1][n - 1]

if __name__ == "__main__":
    s = Solution()
    print s.minPathSum([[1,3,1],[1,5,1],[4,2,1]])