Introducing the probabilistic skip list data structure for fast search operations.
A Skip List is a probabilistic data structure that provides an alternative to balanced binary search trees (like AVL or Red-Black trees). It allows for efficient search, insertion, and deletion of elements from an ordered sequence, with an average time complexity of O(log n) for all these operations. A skip list is built in layers. The bottom layer (Level 0) is a standard sorted linked list. Each subsequent layer acts as an 'express lane' for the layers below it. A node in layer `i` also appears in all layers below `i`. A node is promoted to a higher layer based on a probabilistic coin toss. For instance, we might decide to promote a node to the next level with a probability of 1/2. To search for an element, we start at the head of the highest level. We traverse along this 'express lane' until we find a node whose next node is greater than the target element. Then, we drop down to the next lower level and continue the search from there. This process continues until we reach the bottom level, where the element is either found or determined to be absent. While their worst-case performance is O(n), the probability of this happening is extremely low. Skip lists are often easier to implement than balanced trees and can offer comparable performance in practice.