#Leetcode# 64. Minimum Path Sum

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.

Example:

Input:
[
  [1,3,1],
  [1,5,1],
  [4,2,1]
]
Output: 7
Explanation: Because the path 1→3→1→1→1 minimizes the sum.

代码：

class Solution {
public:
    int minPathSum(vector<vector<int>>& grid) {
        int n = grid.size(), m = grid[0].size();
        int dp[n][m];
        dp[0][0] = grid[0][0];
        for(int i = 1; i < n; i ++) dp[i][0] = grid[i][0] + dp[i - 1][0];
        for(int i = 1; i < m; i ++) dp[0][i] = grid[0][i] + dp[0][i - 1];
        
        for(int i = 1; i < n; i ++) {
            for(int j = 1; j < m; j ++)
                dp[i][j] = min(dp[i - 1][j], dp[i][j - 1]) + grid[i][j];
        }
        
        return dp[n - 1][m - 1];
    }
};

　　第一个自己想的比较明白的 $dp$ 刚开始很久都没维护好初始的状态 以后要注意辣！