Table of contents
1.
Introduction
2.
What are trees in data structures?
3.
Why Use Tree Data Structure?
3.1.
Easily Manageable Hierarchical Data
3.2.
Efficient Search and Sort Operations
3.3.
Dynamic Data
3.4.
Easy Manipulation of Sorted Lists
3.5.
Abstract Data Types and Algorithms
3.6.
Parse Trees
4.
Types of tree data structure
4.1.
General tree
4.2.
Binary tree
4.3.
Binary search tree
4.4.
AVL tree
4.5.
Red-Black Tree
4.6.
B-tree
5.
Basic Terminologies Used in Tree Data Structure
5.1.
Node
5.2.
Root
5.3.
Edge
5.4.
Child
5.5.
Parent
5.6.
Siblings
5.7.
Leaf
5.8.
Subtree
5.9.
Depth of a Node
5.10.
Height of a Node
5.11.
Degree of a Node
5.12.
Level
6.
Properties of tree data structure
7.
Other Applications of Tree Data Structure:
7.1.
Storing data hierarchically
7.2.
Webpage layout
7.3.
Decision-making
7.4.
Decision trees
7.5.
Expression trees
7.6.
Network routing tables
7.7.
Database Indexing
8.
Advantages of Tree Data Structure
9.
Frequently Asked Questions
9.1.
What are non-linear data structures?
9.2.
What is a tree data structure?
9.3.
What are siblings in a binary tree?
9.4.
What is the degree of a node in a tree?
9.5.
What is a leaf node in a tree?
10.
Conclusion
Last Updated: Mar 27, 2024

Application of Tree in Data Structure

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Introduction

Trees are an essential Data structure for organising and manipulating data. We use trees in various fields like data storage and software development. This article will discuss the types of trees, their properties and their applications.

Application of a tree in data structures

So, without further ado, let’s begin!

What are trees in data structures?

A tree is a data structure representing a hierarchical relationship between elements. Unlike sequential data structures like arrays and linked lists, trees are non-linear data structures. A tree comprises nodes and edges, where nodes represent individual data points, and edges define the relationships between those points. 

The root is the topmost node of a tree. Each node in a tree contains data and references to the nodes that are its children.

Why Use Tree Data Structure?

Tree data structure plays a crucial role in organizing data in a hierarchy so that operations like searching, inserting, and deleting data can be performed efficiently. Here's why tree data structures are so important:

Easily Manageable Hierarchical Data

  • A tree data structure is incredibly effective when it comes to managing hierarchical data. This includes anything from family trees and organizational charts, to web pages and the file system of an operating system.

Efficient Search and Sort Operations

  • Trees, particularly binary search trees, allow for efficient search and sort operations. These operations can often be performed much quicker than they would be able to in other structures, such as linked lists or arrays.

Dynamic Data

  • Tree structures can grow and shrink as required, making them an excellent choice for situations where data might be dynamically added or removed. This is especially true for trees that automatically balance themselves, such as AVL trees or Red-Black trees.

Easy Manipulation of Sorted Lists

  • Balanced trees like AVL trees and Red-Black trees make it easy to insert, delete, and locate elements in a sorted list of items. With these types of trees, these operations can all be performed in logarithmic time.

Abstract Data Types and Algorithms

  • Many abstract data types and algorithms make use of tree structures. This includes many forms of search trees, heaps, and even some graph algorithms. Understanding how to use tree structures can be key to implementing these types of data types and algorithms efficiently.

Parse Trees

  • In compilers, trees are used for syntax analysis and to generate a syntax tree (a type of parse tree).

In essence, the importance of tree data structures stems from their hierarchical nature, efficiency, and their utility in various computer science applications. They allow for more complex and organized data handling, leading to more efficient algorithms and improved system organization.

Types of tree data structure

General tree

The most basic type of tree data structure is a general tree. Each node in a general tree can have any number of children (including zero). Other trees, such as binary, AVL, B-trees, and Red-Black trees, are built on top of general trees.

General tree

Binary tree

A binary tree is one in which each node can have no more than two children, the left and right child. 

Binary tree

There are various varieties of binary trees, including:

  1. Full Binary Tree: A full binary tree is a binary tree that, except for the leaf nodes, has exactly two children at each node. All leaf nodes are at the same level in a full binary tree, and the number of nodes at each level is a power of two.
     
  2. Complete Binary Tree: A complete binary tree is one in which every level, possibly except the last, is fully filled, and every node is as far to the left as possible. Remember that the last level might be partially filled in a full binary tree.
     
  3. Perfect Binary Tree: A binary tree is considered perfect if all of its levels are fully occupied and every node, excluding the leaf nodes, has two child nodes. There are 2^h-1 nodes in a perfect binary tree, where h is the tree's height.
     
  4. Balanced Binary Tree: A balanced binary tree is one whose left and right subtree heights of each node differ by no more than one.
     
  5. Degenerate (or pathological) Binary Tree: A binary tree with only one child node for each parent node is considered degenerate. A degenerate binary tree of height n is essentially a linked list of length n.
All types of binary trees

Binary search tree

A binary search tree is a rooted binary tree where the value of every node in the left subtree is less than the value of its parent node, and the value of every node in the right subtree is greater than the value of its parent node.

Binary search tree

AVL tree

AVL trees are a type of self-balancing binary search tree that maintains a balance factor for each node, ensuring that the difference in height between the left and right subtrees is at most one.

Red-Black Tree

Red-Black trees are self-balancing binary search trees where each node has an extra associated bit denoting its colour (red or black). Red-Black trees balance black nodes on each path from the root to the leaves, ensuring that no path is more than twice as long as any other.

B-tree

B-tree is a self-balancing search tree with a large key and value storage capacity. A node in B-tree can store many keys in one node and have many child nodes. They are less tall than other trees because they have a higher branching factor.


Basic Terminologies Used in Tree Data Structure

Understanding tree data structures requires knowledge of some basic terminologies. Here are the essential terms associated with tree data structures:

Node

  • A node is the basic unit of a tree. It can have a name, also called a "key." A node may also have additional information, which we call "payload."

Root

  • The root of the tree is the only node in the tree that has no parent. Every tree has exactly one root.

Edge

  • An edge is the link between two nodes. It connects a parent node to its child node.

Child

  • A node 'c' is said to be a child of node 'p' if 'p' is directly connected to 'c' via an edge.

Parent

  • In the context of trees, a node 'p' is the parent of node 'c' if there is an edge directly from 'p' to 'c'.

Siblings

  • Nodes that have the same parent are known as siblings.

Leaf

  • A node is known as a leaf if it has no children.

Subtree

  • A subtree is a portion of a tree data structure that can be viewed as a complete tree in itself. It consists of a node and its descendants.

Depth of a Node

  • The depth of a node is the number of edges from the root to the node.

Height of a Node

  • The height of a node is the number of edges from the node to the deepest leaf.

Degree of a Node

  • The degree of a node is the total number of branches (or children) of that node.

Level

  • Level of a node represents the generation of a node. If the root node is at level 0, then its subsequent child node is at level 1, its grandchild is at level 2, and so forth.

Properties of tree data structure

  1. Trees have a single root node at the top. All other nodes descend from the root node. This property allows for efficient access to the entire tree from a single starting point using recursion. This property makes trees a recursive data structure because the root node contains links to the roots of its subtrees.
     
  2. In a tree, there is always one fewer node than edges. A Tree with n nodes, therefore, has n-1 edges.
     
  3. The height of a tree is the length of the longest path from the root to a leaf node.
     
  4. The depth of a node is the distance of a node from the root of the tree. The root is at a depth of 0.
     
  5. Trees are acyclic, which means they do not contain any cycle.
     
  6. Each node in a tree has a unique parent node, whereas the root node has no parent.

Other Applications of Tree Data Structure:

Storing data hierarchically

Data is organised hierarchically using trees. For instance, a computer's file system stores files in a hierarchical structure, with each node representing a file or directory and child nodes representing sub-files or subdirectories.

File system

Similarly, in an organisational structure, nodes represent employees, and child nodes represent their subordinates.

Organisational chart

Webpage layout

The hierarchical structure of trees is used to organise and navigate web pages efficiently. A tree structure can manage web pages, with the home page at the root and child pages below.

Webpage layout

Decision-making

To model decision-making processes, we use trees, where each node denotes a decision point, and each branch represents a potential outcome.

Decision-making tree

Decision trees

In machine learning and data mining, decision trees are represented by tree data structures. Each node in a decision tree represents a choice or a feature, and the child nodes represent the feature's possible outcomes or values.

Expression trees

In programming languages, arithmetic expressions are represented by tree data structures. In an expression tree, each node represents an operator or an operand, and the child nodes represent the sub-expressions or the operator's operands.

Expression tree

Network routing tables

Tree data structures describe network routing tables, with each node representing a network or subnet and the child nodes representing the subnets or the hosts within the network.

Database Indexing

We use trees (B-trees and AVL trees) in database indexing to quickly and effectively organise and access large amounts of data. 

Advantages of Tree Data Structure

Tree data structures offer several significant benefits when it comes to data management and operations. Here are some of the advantages:

  1. Hierarchical Structure: Trees provide a hierarchical structure to data, which is valuable for applications that require a hierarchical relationship amongst data elements.
  2. Efficient Search: Balanced search trees, such as AVL trees, provide logarithmic time complexity for search operations. This is more efficient than linear time complexity in other data structures like linked lists or arrays.
  3. Sorted Data Access: Trees, especially binary search trees, allow you to access data in a sorted manner without additional sort operations.
  4. Efficient Insertion and Deletion: In tree data structures, data can be inserted or deleted relatively quickly, making them very dynamic.
  5. Flexible Size: Unlike arrays, trees don't have an upper limit on the number of nodes as they don't require a contiguous block of memory. The size of a tree can grow and shrink during the execution of the program.
  6. Suitability for Disk Access: Trees, particularly B-trees, are widely used in databases and file systems as they are designed for efficient disk access in scenarios where all data cannot fit into main memory.
  7. Use in Networking: Trees are used in networking for routing tables to route network packets.
  8. Used in Decision-making Algorithms: Decision trees are used in machine learning for decision-making algorithms.
  9. Formulating Complex Problems: Trees are useful in formulating and solving complex real-life problems, as they help break down these problems into manageable parts.
    Also read - Data Structure MCQ

Frequently Asked Questions

What are non-linear data structures?

The data structures whose elements are not arranged sequentially are called non-linear data structures.

What is a tree data structure?

A tree is a non-linear data structure that consists of nodes connected by edges and is used to represent hierarchical relationships between data elements.

What are siblings in a binary tree?

Nodes with the same parent are called siblings.

What is the degree of a node in a tree?

The degree of a node in a tree is the number of children of a node.

What is a leaf node in a tree?

A leaf (terminal) node in a tree is a node that does not have any child nodes.

Conclusion

In this article, we discussed various applications of trees in data structures and the various types of trees and their propertiesYou can also read the article Introduction to tree data structure to improve your knowledge about tree data structure.

To learn more, check out our articles:

If you want to learn more about trees and want to practice some questions which require you to take your basic knowledge on these topics a notch higher, then you can visit our Guided Path for Trees on  Coding Ninjas Studio. To be more confident in data structures and algorithms, try out our DS and Algo Courses. Until then, All the best for your future endeavours, and Keep Coding.

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