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?

unique_paths.cpp

class Solution {
public:
    int uniquePaths(int m, int n) {
        int pathCount[m][n];
        memset(pathCount, 0, sizeof(pathCount));
        pathCount[m - 1][n - 1] = 1;
        for (int i = n - 1; i >= 0; i--) { // col
            for (int j = m - 1; j >= 0; j--) { // row
                if (j + 1 < m) { // to the right
                    pathCount[j][i] += pathCount[j + 1][i];
                }
                if (i + 1 < n) { // to the bottom
                    pathCount[j][i] += pathCount[j][i + 1];
                }
            }
        }
        return pathCount[0][0];
    }
};