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?

第一反应是用排列组合方法，但是时间效率太低，不能通过。

最佳方案是用动态规划，f[i][j] = f[i-1][j] + f[i][j-1];

int uniquePaths(int m, int n){    int f[m][n];    for(int i = 0; i < n; i++)        f[0][i] = 1;    for(int i = 0; i < m; i++)        f[i][0] = 1;    for(int i = 1; i < m; i++)        for(int j = 1; j < n; j++)            f[i][j] = f[i-1][j] + f[i][j-1];    return f[m-1][n-1];}