Find out all divisor in efficient way!

1. Brute force approach:

  In this process, we use a for loop and iterate the whole 1 to n number. Then, we find out all the divisors by one by one. It is not a optimal solution for this problem. Because, it will take O(n) time to find out all divisors.

int main()
{
    optimize();
    ll n;
    cin>>n;
    for(ll i=1; i<=n; i++)
    {
        if(n%2==0) cout<<i<<" ";
    }
    cout<<endl;
    return 0;
}

Time complexity: O(n)

2. SQRT approach:

  In this process, we only iterate in the loop by half of the numbers. Because, if we see we don't need to go through whole n numbers.

int main()

{

    optimize();

    ll n;

    cin>>n;

    for(ll i=1; i * i<=n; i++)

    {

        if(n%2==0) cout<<i<<" "<<n/i<<endl;

    }

    return 0;

}

Time Complexity: O(sqrt(n))