LeetCode Minimum Path Sum

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