Question

I am looking at skip list implementation in Java , and I am wondering the purpose of the following method:

public static int randomLevel() {
    int lvl = (int)(Math.log(1.-Math.random())/Math.log(1.-P));
    return Math.min(lvl, MAX_LEVEL);
}

And what the difference between the above method and

Random.nextInt(6);

Can anyone explain that? Thanks.

Answer 1

Random.nextInt should provide a random variable whose probability distribution is (approximately) a discrete uniform distribution over the interval [0, 6).
You can learn more about this here.
http://puu.sh/XMwn

Note that internally Random uses a linear congruential generator where m = 2^48, a = 25214903917, and c = 11.

---

randomLevel instead (approximately) uses a geometric distribution where p = 0.5. You can learn more about the distribution here.

http://puu.sh/XMwT

Essentially, randomLevel returns 0 with probability 0.5, 1 with 0.25, 2 with 0.125, etc. until 6 with 0.5^7 i.e. *0.0078125** — far different than the ~0.14 from Random.nextInt.

---

Now the importance of this is that a skip list is an inherently probabilistic data structure. By utilizing multiple sparse levels of linked lists, they can achieve average runtime performance of O(log n) search — similar to a balanced binary search tree, but less complex and using less space. Using a uniform distribution here would not be appropriate, seeing how to as higher levels are less densely populated in comparison to lower ones (note: below, the levels grow downward) — which is necessary for the fast searches.