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.

public class Solution {
    public int uniquePaths(int m, int n) {
        // Note: The Solution object is instantiated only once and is reused by each test case.
        int[][] map = new int[m][n];
        map[0][0] = 1;
        for(int i = 0; i < m; i ++)
            for(int j = 0; j < n; j ++){
                if(i > 0) map[i][j] += map[i -1][j];
                if(j > 0) map[i][j] += map[i][j - 1];
            }
        return map[m - 1][n - 1];
    }
}