Binary Trees

Overview

A binary tree is a tree data structure where each node has at most two children, referred to as the left child and right child. This hierarchical structure makes binary trees useful for organizing data in a way that enables efficient searching and sorting.

Tree Terminology

The topmost node is called the root. Nodes with children are internal nodes, and nodes without children are leaves. The depth of a node is the number of edges from the root to that node. The height is the maximum depth in the tree.

Node Structure

Each node typically stores data and pointers to its left and right children. A node with no children has both pointers set to null. This simple structure allows recursive algorithms to process entire subtrees elegantly.

Properties of Binary Trees

In a full binary tree, every node has either zero or two children. A complete binary tree has all levels fully filled except possibly the last, which is filled from left to right. A balanced tree has roughly equal depths on both sides.

Why Binary Trees Matter

Binary trees form the foundation for more advanced structures like binary search trees and heaps. They enable efficient hierarchical data organization and support operations like searching, insertion, and deletion in logarithmic time under ideal conditions.