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