# Leetcode 64. Minimum Path Sum # Question Description

Original Question: Leetcode 64. 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.

### Example:​

``Input:[  [1,3,1],  [1,5,1],  [4,2,1]]Output: 7Explanation: Because the path 1→3→1→1→1 minimizes the sum.``

# Solution

``class Solution {    public int minPathSum(int[][] grid) {        if(grid.length == 0 || grid.length == 0) return 0;        int[][] dp = new int [grid.length][grid.length];        for(int i = 0; i<grid.length; i++){            for(int j = 0; j < grid.length; j++){                if(i==0 && j==0) dp[i][j] = grid;                else if(i==0) {                    dp[i][j] = grid[i][j] + dp[i][j-1];                } else if (j == 0){                    dp[i][j] = grid[i][j] + dp[i-1][j];                } else {                    dp[i][j] = grid[i][j] + Math.min(dp[i-1][j], dp[i][j-1]);                }            }        }        return dp[grid.length-1][grid.length-1];    }}``