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:
1. public class Solution {
2. public int uniquePaths(int m, int n) {
3. int[][] dp = new int[m][n];
4. 5. // first row
6. for (int j = 0; j < n; j++) {
7. dp[0][j] = 1;
8. }
9. 10. // first col
11. for (int i = 0; i < m; i++) {
12. dp[i][0] = 1;
13. }
14. 15. // others
16. for (int i = 1; i < m; i++) {
17. for (int j = 1; j < n; j++) {
18. dp[i][j] = dp[i-1][j] + dp[i][j-1];
19. }
20. }
21. 22. return dp[m-1][n-1];
23. }
24. }