Minimum Path Sum

题目：

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

reference： http://www.jiuzhang.com/solutions/minimum-path-sum/