64 Minimum Path Sum

https://leetcode.com/problems/minimum-path-sum/

solution

# 原grid直接作为dp可以进一步优化空间

class Solution:
    def minPathSum(self, grid: List[List[int]]) -> int:
        m = len(grid)
        n = len(grid[0])
        dp = [[0] * n for _ in range(m)]
        dp[0][0] = grid[0][0]

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

        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[-1][-1]

时间复杂度：O(mn) 空间复杂度：O(mn)