Skip List with each column having an integer instead of copying objects

I tried my best implementing a Skip List in C++ in which I had a particular idea that I wanted to try out. Instead having every element in the base level be a column vector, I only only have a singly-based list in the base level, and I store simple integers as to what level they are in.

For Example, instead of getting heads 5 times and copying an object of Cat 5 times, I simply did

while(coinFilp() == heads) {
   node.level++
}

and then I used node.level as a height indicator.

The following is how I implemented the Skip List:

  Iterator<T> after(int level, Iterator<T> it)
    {

        Node<T> *cNode = it.currentNode;
        Node<T> *nextNode = cNode->next;

        while (nextNode->level < level && nextNode != ll.getTrailer())
        {
            nextNode = nextNode->next;
        }
        return Iterator<T>(nextNode);
    }

    Iterator<T> skipSearch(T v)
    {
        Iterator<T> n = Iterator<T>(s);
        int currentLevel = s->level;

        while (currentLevel > -1)
        {

            n = Iterator<T>(s);

            // make sure one is not null
            while (after(currentLevel, n).currentNode != ll.getTrailer() && after(currentLevel, n).getValue() < v)
            {
                n = after(currentLevel, n);
            }
            currentLevel--;
        }
        return n;
    }

    Iterator<T> skipInsert(T v)
    {
        Iterator<T> it = skipSearch(v);
        Iterator<T> newElement = insertAfterSkip(v, it);
        Node<T> *n = newElement.currentNode;

        while (n->level >= currentLevel)
        {
            incrementLevel();
        }
        return newElement;
    }

    void incrementLevel()
    {
        s->level++;
        ll.getTrailer()->level++;
        currentLevel++;
    }

private:
    Iterator<T> insertAfterSkip(T val, Iterator<T> p)
    {

        Iterator<T> it = after(0, p);
        Node<T> *no = ll.insert(val, *(it.currentNode));
        n++;
        return Iterator(*no);
    }

These are just a few methods in my Skip List implementation. I mean I feel like instead of copying an object a certain number of times, we can just give it a random number and that would be its level. Firstly, is this implementation of a Skip List correct? And is assigning a number instead of copying objects a better way to approach it?

Thanks