Finding maximum Collatz sequence between 1-1000000

Question

I'm trying to find maximum the Collatz sequence between 1 and 1000000. I wrote the following code below. I guess it is correct but it is extremely slow. Can you give me a few hints to make it faster? Thanks.

#include <iostream>
#include <vector>
#include <algorithm>
using namespace std;
bool myfn(int i, int j) { return i<j; }

int collatz(int x);

int main()
{
    vector <int> myvector;
    for(int i = 1; i < 1000000; i++)
    {
        myvector.push_back(collatz(i));
    }

    cout<<*max_element(myvector.begin(),myvector.end(),myfn);


    return 0;

}

int collatz(int x)
{
    int counter = 1;


    while(1)
    {
        if(x == 1)
            break;

        if(x % 2 == 0)
        {
            x = x / 2;
            counter++;
        }
        else
        {
            x = 3 * x + 1;
            counter++;
        }
    }

    return counter;
}

Answer 1

Here are some tips:

Initialize vector to your capacity.
The vector may be expanding while you are pushing elements. Worst case, one reallocation per push_back.

Treat vector as array
After you have initialized your vector to its capacity, you can use the operator [] to access the vector slot instead of calling push_back.

Optimize collatz
This is probably your bottleneck. Try placing into a separate file and cranking up the compiler optimizations on it.

There may be a more optimal algorithm.