Skip Lists are a probabilistic data structure that can be used to efficiently search, insert, and delete elements in a sorted list. They are similar to linked lists, but with additional levels called lists that contain a subset of the elements.

The main advantage of skip lists is that they provide logarithmic time complexity for search, insertion, and deletion operations with a relatively simple implementation.

Skip lists consist of multiple levels. The bottom level contains all the elements in sorted order. Each higher level contains a subset of the elements from the level below it. Each element in a higher level has a pointer to the next element at the lower level.

To perform a search operation, we start from the top level and compare the target value with the next value in the current list. If the target value is greater, we move to the next element. If the target value is smaller, we move down to the lower level and continue the process until we find the target value or reach the bottom level.

Here's an example of a skip list:

1  10 -> 20 -> 30 -> 40
2        |                  
3        v                  
4  10 ->    -> 30 -> 40
5        |                  
6        v                  
7  10 ->             -> 40
8                      |   
9                      v   
10  10 ->                      

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}

#include <iostream>

#include <cstdlib>

#include <ctime>

using namespace std;

​

class SkipListNode {

public:

    int value;

    SkipListNode* next;

    SkipListNode* down;

​

    SkipListNode(int val) {

        value = val;

        next = nullptr;

        down = nullptr;

    }

};

​

class SkipList {

private:

    SkipListNode* head;

    int maxLevel;

    float probability;

​

public:

    SkipList(){

        head = nullptr;

        maxLevel = 1;

        probability = 0.5;