Minimum Path Sum

Minimum Path Sum

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.

一道简单题，同时也是一道典型的动态规划题：

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