What is a typical trade-off of using a skip list compared to a balanced binary search tree?

• A. They provide deterministic balancing guarantees.
• B. They replace logarithmic time with linear time in the worst case.
• C. They prohibit insertions and deletions.
• D. They offer probabilistic balancing with expected O(log n) search/insert/delete due to random promoted levels.

Answer: (D)

The key idea here is that skip lists balance themselves using randomness rather than strict structural rules. In a skip list, each element can appear at multiple levels, with higher levels created by promoting the element with a fixed probability (often 1/2). This creates many short pointers at lower levels and a few long pointers that “skip” ahead at higher levels. When you search, you climb up through the higher levels as long as you can, then drop down, which makes the search step through a number of elements proportional to the height of the tallest tower you encounter. Because the tower heights follow a geometric distribution, the tallest towers grow only about logarithmically with the number of elements, giving you an expected time of O(log n) for search, insert, and delete.

This is the trade-off compared to a balanced binary search tree, which guarantees logarithmic time in all cases because it maintains a strictly balanced height through rotations. Skip lists don’t provide those worst-case guarantees; they rely on randomness, so performance is probabilistically fast on average, with simpler structure and code as a practical benefit.

The other statements aren’t accurate because skip lists do permit insertions and deletions, and while they don’t offer deterministic balancing guarantees, they do provide the probabilistic with expected logarithmic performance, not a guaranteed worst-case linear time.