64. Minimum Path Sum 动态规划

Given a m x n grid filled with non-negative numbers, find a path from top left to bottom right whichminimizes 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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分析：与前面的机器人问题类似，解法也相同。

代码：

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