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.

Code

public class Solution {
    public int minPathSum(int[][] grid) {
        if (grid==null || grid.length==0 || grid[0].length==0) return 0;
        int m = grid.length;
        int n = grid[0].length;
        int[][] dp = new int[m][n];

        //dp[i][j] stands for the minimum sum from grid[0][0] to grid[i][j]

        for (int i=0; i<m; i++){
            for (int j=0; j<n; j++){
                if (i==0 && j==0) {dp[i][j] = grid[i][j];}
                else if (i==0) {dp[i][j] = dp[i][j-1] + grid[i][j];}
                else if (j==0) {dp[i][j] = dp[i-1][j] + grid[i][j];}
                else {dp[i][j] = Math.min(dp[i-1][j], dp[i][j-1]) + grid[i][j];}
            }
        }


        return dp[m-1][n-1];

    }
}