Unique Paths

A robot is located at the top-left corner of a m x n grid (marked 'Start' in the diagram below).

The robot can only move either down or right at any point in time. The robot is trying to reach the bottom-right corner of the grid (marked 'Finish' in the diagram below).

How many possible unique paths are there?

Above is a 3 x 7 grid. How many possible unique paths are there?

Note: m and n will be at most 100.

Solution: Very basic 2-d dynamic programming.

public class Solution {
    public int uniquePaths(int m, int n) {
        int[][] ways = new int[m][n];
        for(int i = 0; i < m; i++){
            for(int j = 0; j < n; j++){
                if(i == 0 || j == 0) ways[i][j] = 1;
                else ways[i][j] = ways[i-1][j] + ways[i][j-1];
            }
        }
        return ways[m-1][n-1];
    }
}