Understanding Tree Data Structures: A Detailed Overview

Introduction to Trees

A tree is a non-linear hierarchical data structure consisting of nodes connected by edges. Unlike linear data structures like arrays or linked lists, trees have a hierarchical shape, making them perfect for representing relationships with multiple levels of data.

The nodes in a tree can be connected by edges. For example, in the following tree structure, we have a root node with various child nodes connected to it:

Tree Terminology

Let's explore some important terminology related to trees:

• Root Node: The topmost node of the tree, from which all other nodes are descended.
• Height of a Node: The number of edges from a node to the deepest leaf. This is also known as the longest path from the node to a leaf node.
• Depth of a Node: The number of edges from the root to the node.
• Parent Node: A node that has one or more child nodes connected to it.
• Child Node: A node that is a descendant of another node.
• Degree of a Node: The total number of branches (children) connected to that node.

Types of Trees

There are several types of trees used in different applications. Some of the most commonly used trees include:

• General Tree: A tree in which a node can have any number of children, ranging from 0 to n.
• Binary Tree: A tree in which each node can have at most two children. This is the foundation for many other types of trees.
• Binary Search Tree (BST): A type of binary tree where the left child of a node is less than the node, and the right child is greater.
• AVL Tree: A self-balancing binary search tree where the difference in heights between the left and right subtrees is at most 1 for all nodes.
• Trie Tree: A tree used for dynamic spell checking and efficiently storing multiple words, commonly used in dictionaries and search engines.
• Heap Tree: A complete binary tree used to implement priority queues. It is typically implemented as a min-heap or max-heap.

Binary Tree Example