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.

 1 public class Solution {

 2     public int uniquePaths(int m, int n) {

 3         // Note: The Solution object is instantiated only once and is reused by each test case.

 4         int[][] map = new int[m][n];

 5         map[0][0] = 1;

 6         for(int i = 0; i < m; i ++)

 7             for(int j = 0; j < n; j ++){

 8                 if(i > 0) map[i][j] += map[i -1][j];

 9                 if(j > 0) map[i][j] += map[i][j - 1];

10             }

11         return map[m - 1][n - 1];

12     }

13 }