64.最小路径和

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

给定一个包含非负整数的 *m* x *n* 网格 grid ，请找出一条从左上角到右下角的路径，使得路径上的数字总和为最小。

说明：每次只能向下或者向右移动一步。

示例 1：

输入：grid = [[1,3,1],[1,5,1],[4,2,1]]
输出：7
解释：因为路径 1→3→1→1→1 的总和最小。

示例 2：

输入：grid = [[1,2,3],[4,5,6]]
输出：12

提示：

m == grid.length
n == grid[i].length
1 <= m, n <= 200
0 <= grid[i][j] <= 200

python

from typing import List

class Solution:
    def minPathSum(self, grid: List[List[int]]) -> int:
        m = len(grid)
        n = len(grid[0])
        
        # Initialize the dp array with the same dimensions as grid
        dp = [[0] * n for _ in range(m)]
        
        # Set the starting point
        dp[0][0] = grid[0][0]
        
        # Fill the first row (can only come from the left)
        for j in range(1, n):
            dp[0][j] = dp[0][j - 1] + grid[0][j]
        
        # Fill the first column (can only come from above)
        for i in range(1, m):
            dp[i][0] = dp[i - 1][0] + grid[i][0]
        
        # Fill the rest of the dp array
        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]
        
        # The bottom-right corner contains the minimum path sum
        return dp[m - 1][n - 1]

if __name__ == "__main__":
    sol = Solution()
    print(sol.minPathSum([[1,3,1],[1,5,1],[4,2,1]]))  # Output: 7
    print(sol.minPathSum([[1,2,3],[4,5,6]]))  # Output: 12

64.最小路径和 ​

64.最小路径和