27_leetcode_ Unique Paths

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.

    int uniquePaths(int m, int n) {                if(m == 0 || n == 0)        {            return 0;        }        if(m == 1 || n == 1)        {            return 1;        }                vector<int> path(n, 0);                for(int i = 0; i < m; i++)        {            for(int j = 0; j < n; j++)            {                if( i == 0 )                {                    path[j] = 1;                }                else if(j == 0)                {                    path[j] = 1;                }                else                {                    path[j] = path[j-1] + path[j];                }            }        }        return path[n - 1];    }