**What Is Skiplist in Data Structure?**

A skiplist is a data structure that provides efficient search, insertion, and deletion operations. It is a probabilistic alternative to balanced binary search trees.

Skiplists were invented by William Pugh in 1989 and have since found applications in various fields, such as databases and network routing algorithms.

__How Does a Skiplist Work?__

At its core, a skiplist is composed of multiple linked lists with different levels of granularity. Each list represents a specific level, starting from the bottom level containing all elements and gradually decreasing the number of elements as we move up.

The topmost level contains only two elements: the first element (the head) and the last element (the tail).

## The Search Operation

Searching for an element in a skiplist is similar to searching in a linked list. We start at the head of the skiplist and compare the Target element with each successive element until we find a match or reach an element greater than our Target value.

However, what makes skiplists efficient is the use of “express lanes.” These express lanes are shortcuts that allow us to skip several elements at once.

Each node in a skiplist has forward pointers that point to nodes on the same level or higher levels. By using these pointers strategically, we can quickly navigate through the skiplist while maintaining logarithmic search complexity.

## The Insertion Operation

Inserting an element into a skiplist involves two main steps: finding the proper position for insertion and adjusting the forward pointers accordingly. Similar to searching, we start from the head of the skiplist and compare our Target value with each successive element.

When we find the appropriate position, we insert the new element and update the forward pointers of the affected nodes.

To ensure a balanced skiplist, we typically use a random number generator to determine the level of each newly inserted element. The probability of an element being at level i is typically 1/2^i, which means higher-level elements are less likely to occur.

## The Deletion Operation

Deleting an element from a skiplist involves finding the element and updating the forward pointers to bypass it. Similar to searching and insertion, we start from the head of the skiplist and navigate through each level until we find the Target element.

Once found, we update the forward pointers of the preceding nodes to bypass the node being deleted.

It’s important to note that skiplists have average-case time complexity guarantees for search, insertion, and deletion operations. On average, they provide O(log n) time complexity for these operations, making them suitable for many applications where efficiency is crucial.

## Conclusion

In conclusion, a skiplist is a powerful data structure that offers efficient search, insertion, and deletion operations with guaranteed average-case time complexity. By incorporating linked lists with multiple levels and using express lanes to skip elements during navigation, skiplists strike a balance between simplicity and efficiency.

They have found significant applications in various domains due to their versatility and performance characteristics.