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?

Note: m and n will be at most 100.

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