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) {
        if(grid==null) return 0;
        return dp(grid);
    }
    public int dp(int[][] grid){
        int m=grid.length;
        int n=grid[0].length;
        int [][]path=new int[m][n];
        path[0][0]=grid[0][0];
        for(int i=1;i<m;i++) 
            path[i][0]=path[i-1][0]+grid[i][0];
        for(int j=1;j<n;j++) 
            path[0][j]=path[0][j-1]+grid[0][j];
        for(int i=1;i<m;i++){
            for(int j=1;j<n;j++){
                path[i][j]=Math.min(path[i-1][j],path[i][j-1])+grid[i][j];
            }
        }
        return path[m-1][n-1];
    }
}