A tree is a data structure composed of nodes, where each node has a value and pointers to its child nodes. The topmost node is called the root, and nodes without children are called leaves. Trees are used to model hierarchical data, such as organizational structures or file systems.
A binary search tree is a special type of tree where each node has at most two children, referred to as the left and right child. The BST property ensures that for any given node, all nodes in its left subtree have lesser values, and all nodes in its right subtree have greater values. This property allows for efficient searching, insertion, and deletion operations, with average time complexities of O(log n).
Binary search trees are widely used in applications that require dynamic data sets, such as databases and memory management systems. They form the basis for more advanced data structures like AVL trees and Red-Black trees, which maintain balance to ensure optimal performance.
While hash tables provide average O(1) time complexity for data retrieval, binary search trees offer O(log n) time complexity with the added benefit of maintaining order, making them suitable for range queries and sorted data storage.
An AVL tree is a type of binary search tree that maintains balance by ensuring the heights of two child subtrees of any node differ by no more than one. This property allows AVL trees to keep operations efficient, even in the worst case, with O(log n) time complexity.