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.

public class Solution {
    public int minPathSum(int[][] grid) {
        int m = grid.length,n = grid[0].length;
        if(m==0||n==0)
          return 0;
        int[][] f = new int[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] = Math.min(f[i-1][j],f[i][j-1]) + grid[i][j];
        return f[m-1][n-1];
    }
}