What is a binary tree?

A binary tree is a type of data structure in which each node has at most two children, typically referred to as the left child and the right child.

In more detail, a binary tree is a tree-like structure made up of nodes, where each node contains a value and has two 'branches' leading to other nodes. The top node is known as the root. Each node in the tree has a maximum of two children, hence the term 'binary'. These two children are distinguished as the left child and the right child.

The binary tree is a fundamental concept in computer science, used in many areas such as search algorithms, sorting algorithms, and even in the design of certain data storage systems. It is particularly useful in situations where data needs to be stored and retrieved in a hierarchical manner.

Each node in a binary tree contains a key (or value), and two pointers which are the address to their child nodes. If a node does not have a child, the pointer for that child will be null. The node without a parent is called the root node, and nodes without children are called leaf nodes.

Binary trees can be further classified into different types based on their properties. For example, a binary search tree (BST) is a binary tree where each node's key is greater than all keys in its left child and less than all keys in its right child. Another type is the balanced binary tree, where the left and right subtrees of every node differ in height by at most one.

Binary trees are used extensively in programming and computer science. They are the underlying data structure for heaps, binary search trees, and binary indexed trees. They are also used in algorithms for searching, sorting, and more. Understanding binary trees and their properties is crucial for any computer science student.