62 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?

Solution:

class Solution {
public:
    int uniquePaths(int m, int n) {
        if ( n == 0 or m == 0 ) return 0;
        if ( n == 1 or m == 1 ) return 1;
        vector< vector<int> > paths(m, vector<int>(n, 0));
        for ( int i = 0; i <= n-1; i++ ) paths[0][i] = 1;
        for ( int i = 0; i <= m-1; i++ ) paths[i][0] = 1;
        for ( int i = 1; i <= m-1; i++ ) {
            for ( int j = 1; j <= n-1; j++ ) {
                paths[i][j] = paths[i-1][j] + paths[i][j-1];
            }
        }
        return paths[m-1][n-1];
    }
};