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?

class Solution {
public:
    int uniquePaths(int m, int n) {
       vector<int> vec;
       vec.clear();
       vec.push_back(1);
       
       if(m==1 || n==1)
           return 1;
           
       for(int i=1;i<m+n-2;i++)
       {
           vec.push_back(1);
           int j = vec.size()-1;
           while(j>=1)
           {
               vec[j] += vec[j-1];
               j--;
           }
       }
       return vec[m-1];
    }
};

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