Types Of Trees In Data Structures

Trees are the most important form of data structure, which makes organizing vast amounts of data in an effective way by following different patterns. This article will cover all the details about types of trees in data structures. You just need to stay till the end of the article to know all in detail.

Table of Contents

What is a tree in Data Structures?

A tree is a special way of organizing information, like a family tree or a company hierarchy. It’s a data structure where each piece of data is connected to others in a specific pattern.

A tree can have branches that connect data in a non-linear way, unlike a list where data is arranged in a straight line. As a result, finding information related to one another is more manageable.

The tree structure is useful for representing relationships between different pieces of data, like a parent-child relationship. It’s also known as a hierarchic data structure.

This article will walk you through each of the main types of trees in data structures, along with their uses and characteristics. All you have to do is stick with us through the end of the article.

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Types of Tree Important Terminologies

Some important terminologies related to the tree data structure are given below.

Types of Tree Important Terminologies
Terminology	Description
Node	Each vertex of a tree is a node.
Root	Topmost node of a tree.
Parent Node	The node has an edge-sharing to a child node.
Child Node	The sub-node of a parent node is the child node.
Leaf	The last node that does not have any sub-node is the leaf node.
Edge	Connecting link between two nodes.
Siblings	Nodes with the same parent are siblings.
Height	The length of the longest path from the root to a leaf node.
Depth	The number of edges from the root node to that node.
Level	Each step from top to bottom is called a Level.
Sub-Tree	Descendants of a node represent a subtree.
Degree of Node	The total number of children of a node.

Also read: Analysis of Algorithm in Data Structure

Types of Trees in Data Structures

The four major types of trees in the data structure are given here.

1. Binary Tree

A Binary tree is a specific kind of tree in data structures where each parent node can have a maximum of only two child nodes.

The two child nodes are often called the Right Child and the Left Child. This means that each node can have either no children, one child, or two children.
Each node in a binary tree has pointers connecting it to its left and right Child Nodes.
The nodes with no children are called leaf nodes, as they have null pointers for both the left and right child positions.

Binary trees are widely used because of their simplicity and efficiency. They have specific characteristics that allow for various applications. For example, Binary Search Tree (BST) is a type of binary tree that is used for efficient searching and sorting operations.

Binary trees are a fundamental and popular data structure used as building blocks for more complex tree structures in computer science and data processing.

Properties of Binary Tree

Some of the important properties of the binary tree are given here.

At any level in a binary tree, there can only be a maximum of two nodes.
The smallest binary tree with a height of H will have H + 1 nodes.
The largest binary tree with a height of H will have 2H + 1 – 1 nodes.
The number of leaf nodes in a binary tree is equal to the number of nodes with two children, plus one.
The maximum number of nodes at level i in a binary tree is 2i.
Searching in a binary tree takes a time complexity of O(log2N) time (where N is the number of nodes).

Types of binary trees are:

There are some important classifications of binary trees, and some of their types are mentioned here in this article.

Perfect binary tree: In the Perfect Binary Tree structure, all internal nodes have two children and leaf nodes are at the same level.
Full binary tree: In this type of tree, parent nodes have either two children or no children.
Complete binary tree: All levels, except the last one, are filled with nodes from left to right.
Degenerate binary tree: All internal nodes have only one child.
Balanced binary tree: In the Balanced Binary Tree, the difference in the number of nodes between the left and right subtrees is at most 1.

2. Binary Search Tree

A Binary Search Tree (BST) is a type of tree structure where each node has at most two child nodes. This type of tree is called a binary search tree. The two most important key properties of a BST are as follows:

Left Child Property: The value in the left subtree of any node must be less than or equal to the value of the root node.
Right Child Property: The value in the right subtree of any node must be higher than or equal to the value in the root node.

These properties ensure that the elements in the BST are organized in a way that makes searching efficient. In the BST, you can quickly choose whether to move to the left or right subtree based on a comparison with the current node’s value.

This binary tree structure is ideal for fast search operations due to the specific ordering of its elements.

Properties of Binary Search Tree

Some of the major properties of the binary search trees are given here.

Each node can have up to two children, not more.
All the values in the left sub-tree of any node are smaller than the value in that node.
All the values in the right sub-tree of any node are greater than or equal to the value in that node.

All left and right branches that branch off from the main root of the tree must follow by these rules. This arrangement ensures that the elements are arranged in a way that makes searching and sorting operations efficient.

Applications of Binary Search Trees

Some of the major contributions of the binary search trees are mentioned here.

A Binary Search Tree (BST) efficiently stores data in sorted order which makes it easy to access and search elements quickly.
If we have a sorted array called “A,” we can effectively use BST to count the instances of a particular element called “x” in “A.”
They are used in the implementation of the search algorithms.
BSTs are also used in the working of the Huffman coding algorithm.
BSTs are used in spelling checkers also.

Also read: Binary Search Trees And Its Uses

3. AVL Trees

AVL trees are named after its inventors whose name was Adelson-Belsky and Landis. These trees are the type of binary tree that automatically maintains a balanced structure of itself.

The unique feature of AVL trees is that they keep the height of the left and right subtrees balanced. Each node is assigned a balancing factor condition due to which balancing occurs in the tree and the height of the tree remains balanced.

AVL trees rotate to restore balance if a tree loses it as a result of the addition of a new node. The balancing factor of each node is crucial in deciding when and how these rotations are performed.

The AVL tree makes sure that each node’s balance factor stays between -1 and 1 or between 0 and 1. This balance keeps the tree’s height in check and guarantees efficient operations like insertion, viewing, and removal. They generally have a time complexity of O(log2N).

Properties of AVL Trees

Some of the most important features of the AVL trees are mentioned here in this article.

An AVL tree is a type of binary search tree where the heights of the left and right subtrees of any node are balanced. They differ only by at most one level, which can be between -1, 0, 1.
The height difference between a node’s left and right subtrees is quantified by the balance factor.
The left subtree is one level higher when the balance factor is 1, the right subtree is one level higher when it is -1, and both subtrees are the same height when it is 0 and 1.
For a given height “H,” the maximum number of nodes an AVL tree can have are

2H + 1 – 1.

For a given height “H”, the minimum number of nodes an AVL tree is repeatedly calculated as

N(H) = N(H-1) + N(H-2) + 1.

The minimum possible height of an AVL tree with N number of nodes is the floor value of log base 2 of N.
The maximum height of an AVL tree with ‘N’ nodes is calculated using the recursive relation:

N(H) = N(H-1) + N(H-2) + 1

Applications of the AVL Trees

Some of the major applications of AVL trees are given here in this article.

AVL trees are used to efficiently organize and search large amounts of data in databases.
They are also used for in-memory collections like sets and dictionaries.
They are used to efficiently handle and retrieve data in a variety of corporate settings and storyline games.

4. B Tree

B Tree is a generalized version of a binary search tree which is also known as a Height-balanced m-way tree. Here, ‘m’ is the order of the tree. B Trees permit nodes to have more than two child nodes and multiple keys, unlike binary trees.

All of the leaf nodes on a B Tree are at the same level, which guarantees a balanced structure. This balance helps with efficient searching and organizing large amounts of data in a structured way, making it one of the most efficient types of tree in data structure.

Properties of AVL Trees

Some major properties of the AVL Trees are given here.

Firstly, all the major nodes must contain at most M children.
Every node must have at least M/2 children, only the root node and the leaf node in the tree can have less than M/2 nodes.
All the keys are in increasing order for each node, say N.
Internal nodes can have at most “N-1” keys, where ‘N’ is the order of the tree. They also have pointers for each child.
B tree root nodes must have a minimum of two nodes.
Also, all leaf nodes should be on the same level.
If the minimum degree is “t” and the order of the tree is “N,” then the height “H” of any B Tree with “N” keys must be at least log base “t” of (N+1)/2. This characteristic makes sure that, for effective operations, the height of the B Tree stays within a certain range.

Applications of B Tree

Some of the major applications of the B Tree are given here in this article.

Used in multilevel indexing.
Major use in business sectors to store the records of employees working in the organization.
It is used for quick retrieval of the data stored on the disks.
Used to store huge data.

Also read: What Is Sorting In Data Structure, And Its Types?

FAQs

What is a tree in data structures?

A tree is a way of organizing information where each data point is connected to others following a specific pattern. There are four major types of trees mentioned in this article.

What is the major difference between Binary Search tree and Binary Tree?

In a binary search tree, all the nodes to left of the root are less than or equal to the root element, whereas the right nodes are greater than or equal to root element. However, the binary tree does not have such arrangement.

What are some important properties of AVL Trees?

Some of the important properties of AVL Trees are balancing factor, height restrictions, and fast search operations. However, the complete details are given in this article, which you must check once.

What are the self balancing types of trees?

Self-balancing trees are a part of binary search trees that maintain structural balance on their own whenever a new node is added. This balancing ensures that the tree remains efficient and well-organized.

Examples of self-balancing trees include AVL trees, Splay Trees, and Red-Black Trees.

What is the need for self balancing trees?

The self-balancing trees ensure that data is arranged in a balanced and optimizer manner. They help make different operations fast and efficient.