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?

 

Example 1:

Input: m = 3, n = 2Output: 3Explanation:From the top-left corner, there are a total of 3 ways to reach the bottom-right corner:1. Right -> Right -> Down2. Right -> Down -> Right3. Down -> Right -> Right

Example 2:

Input: m = 7, n = 3 //7列 3行Output: 28 只能向右或者向下走，求从左上角到右下角一共有多少种走法 C++：

1 class Solution { 2 public: 3     int uniquePaths(int m, int n) { 4         vector
     
       dp(n+1,1) ; 5         for(int i = 1 ; i < m ; i++){ 6             for(int j = 1 ; j < n ; j++){ 7                 dp[j] = dp[j] + dp[j-1] ; 8             } 9         }10         return dp[n-1] ;11     }12 };