leetcode--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 {
    /**
	 * This is an implementation of dynamic programming
	 * Using a 2-dimensional array paths to denote the number of paths, we have
	 * paths[i][j] = paths[i-1][j] + paths[i][j-1].<br>
	 * Notice the initial condition paths[i][0] = 1, paths[0][j] = 1.<br>
	 * @param m --integer, the number of rows of a grid
	 * @param n --integer, the number of columns of a grid
	 * @return Integer, the number of paths from top-left corner to bottom-right corner
	 * @author Averill Zheng
	 * @version 2014-06-05
	 * @since JDK 1.7 
	 */ 
    public int uniquePaths(int m, int n) {
        int path = 0;
		if(m > 0 && n > 0){
			int[][] paths = new int[m][n];
			for(int i = 0; i < m; ++i)
				paths[i][0] = 1;
			for(int i = 0; i < n; ++i)
				paths[0][i] = 1;
			for(int i = 1; i < m; ++i)
				for(int j = 1; j < n; ++j)
					paths[i][j] = paths[i - 1][j] + paths[i][j - 1];
			path = paths[m - 1][n - 1];
		}
		return path;   
    }
}