What is a self-adjusting binary search tree?

A self-adjusting binary search tree is a type of binary search tree that automatically reorganises itself after every operation to maintain balance.

In more detail, a binary search tree (BST) is a tree data structure where each node has a value, and all the values in the left subtree are less than the node, and all the values in the right subtree are greater than the node. This property allows operations like insertion, deletion, and search to be performed efficiently. However, in a standard BST, if data is inserted in a particular order, the tree can become unbalanced, leading to inefficient operations.

This is where self-adjusting binary search trees come in. These trees automatically adjust their structure after every operation (like insertion or deletion) to ensure that the tree remains approximately balanced. This means that the height of the tree (the maximum distance from the root to any leaf) remains logarithmic in the number of nodes, ensuring that operations can be performed in logarithmic time. This is a significant improvement over standard BSTs, where in the worst case, operations can take linear time.

There are several types of self-adjusting binary search trees, including splay trees, AVL trees, and red-black trees. These trees use different strategies to maintain balance. For example, splay trees move the accessed key to the root of the tree using a process called splaying. AVL trees, on the other hand, keep track of a balance factor for each node and rebalance the tree as necessary after each operation. Red-black trees maintain balance by colouring each node red or black and enforcing certain properties about the colours of nodes.

In conclusion, a self-adjusting binary search tree is a powerful data structure that combines the benefits of a binary search tree with automatic balancing. This makes it an excellent choice for many applications where efficient search, insertion, and deletion operations are required.