Skiplijst

Skiplijst is a probabilistic data structure that allows for efficient searching, insertion, and deletion operations, typically with an average time complexity of O(log n), where n is the number of elements in the list. It achieves this by maintaining multiple layers of linked lists, where each layer skips over some elements of the layer below.

The structure works by assigning a random level to each new element inserted. An element at level k will be present in k linked lists. The lowest level, level 0, contains all elements, forming a standard sorted linked list. Higher levels act as express lanes, allowing searches to bypass large portions of the list. When searching for an element, the algorithm starts at the highest level and moves forward until it either finds the element or determines it's not present. If it can't move forward on the current level, it drops down to the next lower level and continues the search.

Insertion involves creating a new node with a randomly assigned level and then inserting it into the appropriate positions in the linked lists up to its assigned level. Deletion is similar, requiring the removal of the node from all linked lists it participates in. The probabilistic nature of level assignment ensures that, on average, the structure remains balanced and efficient. Skiplijsten are often compared to balanced trees, offering similar performance characteristics but with a simpler implementation. They are useful in scenarios where dynamic ordering and fast access are required.