Unique Paths I [Leetcode]

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: dynamic programming; we also can solve this problem mathematically: m+n-2 choose m-1.

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