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.

Solution:

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