Binary trees are tree data structures where each node has at most two children, widely used in various applications like expression parsing, searching, and sorting.

Binary trees are a fundamental type of tree data structure in which each node can have at most two children, referred to as the left child and the right child. This simple structure forms the basis for more complex tree types, including binary search trees (BST), balanced trees (like AVL trees or Red-Black trees), and binary heaps.

The hierarchical organization of binary trees allows for efficient data storage and retrieval. One common use case for binary trees is in searching algorithms. In a binary search tree, for example, the left child of a node contains values less than the node’s value, while the right child contains values greater than the node’s value. This property allows for efficient searching, insertion, and deletion operations, all of which can be performed in average O(log n) time complexity.

Additionally, binary trees are widely used in expression parsing and evaluation, such as in compilers and interpreters, where binary expression trees represent mathematical expressions. Each internal node corresponds to an operator, while the leaves represent operands.

Another application of binary trees is in data compression algorithms, such as Huffman coding, where binary trees are used to create variable-length codes based on the frequency of characters.

Understanding binary trees and their various forms is essential for solving a wide range of algorithmic problems and optimizing data structures in computer science.