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) {
        Integer[][] map = new Integer[m][n];
        for(int i = 0; i<m;i++){
            map[i][0] = 1;
        }
        for(int j= 0;j<n;j++){
            map[0][j]=1;
        }
        for(int i = 1;i<m;i++){
            for(int j = 1;j<n;j++){
                map[i][j] = map[i-1][j]+map[i][j-1];
            }
        }
        return map[m-1][n-1];
    }
}

62. Unique Paths