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.

开一个f[m][n]的数组，f[i][j] = f[i-1][j] + f[i][j-1]，空间时间复杂度O(m*n)。用滚动数组空间复杂度可降为O(n)

1 class Solution { 2 public: 3     int uniquePaths(int m, int n) { 4         // Start typing your C/C++ solution below 5         // DO NOT write int main() function 6         vector
     
      
        > f(m, vector
       
        (n)); 7          8         for(int i = 0; i < n; i++) 9             f[0][i] = 1;10             11         for(int i = 0; i < m; i++)12             f[i][0] = 1;13             14         for(int i = 1; i < m; i++)15             for(int j = 1; j < n; j++)16                 f[i][j] = f[i-1][j] + f[i][j-1];17                 18         return f[m-1][n-1];19     }20 };