Question：

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.

Algorithm ：

动态规划 path[i][j]=path[i-1][j]+path[i][j-1]

Accepted Code：

class Solution {
public:
    int uniquePaths(int m, int n) {   //Dynamic Programming   path[i][j]=path[i-1][j]+path[i][j-1]
        vector<vector<int>> path(m,vector<int>(n,1));
        for(int i=1;i<m;i++)
        {
            for(int j=1;j<n;j++)
                path[i][j]=path[i-1][j]+path[i][j-1];
        }
        return path[m-1][n-1];
    }
};