[LeetCode]题解（python）：064-Minimum Path Sum

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题目来源

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https://leetcode.com/problems/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.

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题意分析

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Input:a matrix with weight

Output:the minimum sum of the path from top-left to down-right

Conditions:经过路径和最小，只能向右或向下

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题目思路

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和上题一样采用动态规划，动态方程几乎没变，dp[i][j] = min(dp[i-1][j],dp[i][j-1]) + grid[i][j]

初始化第一行和第一列直接用grid和前一个位置的值即可

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AC代码（Python）

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 class Solution(object):
     def minPathSum(self, grid):
         """
         :type grid: List[List[int]]
         :rtype: int
         """
         m = len(grid)
         n = len(grid[0])

         dp = [[i for i in range(n)] for j in range(m)]

         dp[0][0] = grid[0][0]

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

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

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

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