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.

class Solution {public:    int uniquePaths(int m, int n) {        vector<vector<int> > grid(m,vector<int>(n));        for(int i=0;i<n;i++)            grid[0][i]=1;        for(int j=0;j<m;j++)            grid[j][0]=1;        for(int i=1;i<n;i++)            for(int j=1;j<m;j++)                grid[j][i]=grid[j-1][i]+grid[j][i-1];        return grid[m-1][n-1];    }};

Unique Paths