Splay Trees

Splay trees are a type of self-balancing binary search tree that prioritize recently accessed elements. Whenever an element is accessed or inserted, it is moved to the root of the tree, making it easier to access it again in the future.

Splay trees have a unique property called splay operation, which is used to move elements to the root. During a splay operation, the targeted element is rotated to the root, bringing it closer to the root for faster access.

The splay operation consists of three basic types of rotations:

• Zig: When the target node is the left child or right child of the root, a single rotation is performed to bring it to the root.
• Zig-Zig: When the target node and its parent are both left children or both right children, two rotations are performed to bring both of them to the root.
• Zig-Zag: When the target node and its parent are different children, two rotations are performed to bring the target node to the root.

The splay operation helps maintain a balance in the splay tree and ensures quick access to frequently accessed elements. It is a form of data reshuffling that adapts the tree's structure to the access pattern.

Splay trees are commonly used in scenarios where elements that have been recently accessed are more likely to be accessed again. Examples include caches, garbage collectors, and network protocols.

Here's an example of a splay tree:

1    50              40
2   /  \           / \
3  30   100   =>  30  50
4      /  \           /  \
5    40   200       100  200

In the above example, the element with key 40 is accessed, and it is moved to the root of the tree using the zig rotation.

Benefits of Splay Trees

Splay trees offer several benefits:

• Adaptive: Splay trees adapt their structure based on the access pattern, improving the performance of frequently accessed elements.
• Simple operations: The basic operations of accessing and inserting elements are simple and efficient, as elements are always moved to the root during these operations.
• No additional space: Splay trees do not require any additional space beyond the memory required to store the elements.

Splay trees are a powerful data structure that combines the benefits of a binary search tree with efficient access to frequently accessed elements. They are a great tool to have in your arsenal when dealing with applications that involve caching or frequent element access.

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}

#include <iostream>

using namespace std;

​

// Splay Tree node

struct Node {

  int key;

  Node* left;

  Node* right;

};

​

// Helper function to create a new node

Node* newNode(int key) {

  Node* node = new Node();

  node->key = key;

  node->left = node->right = NULL;

  return node;

}

​

int main() {

  // Create a new splay tree

  Node* root = newNode(100);

  root->left = newNode(50);

  root->right = newNode(200);

  root->left->left = newNode(40);

  root->left->left->left = newNode(30);

​

  // Perform operations on the splay tree

  // ...

​