题目链接

描述

解题思路

考点：动态规划

1. dp[i][j]表示当前坐标的最小路径和
2. dp初始化
3. 状态转移：
   dp[i][j] = matrix[i][j] + min(dp[i-1][j],dp[i][j-1]) 比较正上方和正左方的路径和哪个小。取小的那条路

代码

import copy
class Solution:
    def minPathSum(self , matrix: List[List[int]]) -> int:
        m = len(matrix)
        n = len(matrix[-1])
        dp = copy.deepcopy(matrix)
        # 初始化
        for i in range(1,m):
            dp[i][0] = dp[i-1][0]+matrix[i][0]
        for j in range(1,n):
            dp[0][j] = dp[0][j-1]+matrix[0][j]
        
        for i in range(1,m):
            for j in range(1,n):
                dp[i][j] = matrix[i][j] + min(dp[i-1][j],dp[i][j-1])

        return dp[-1][-1]