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.

思路：使用动态规划求解。path[i][j]表示从(0,0)到达(i,j)的不同路径数。则(i,j)可以由(i-1,j)或者(i,j-1)达到，这两种是完全不同的走法。因此，path[i][j] = path[i-1][j] + path[i][j-1]。

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

Unique Paths