Tree Data Structure - Types, Operations, Applications

A tree data structure is important when creating a computer language. It supports operations like insertion, deletion and searching of elements.

A data structure is a way of efficiently organising, managing, and storing data for future use. They are essential in various computer algorithms and help programmers design efficient software. Data structures are used in multiple computer science domains, like operating systems and artificial intelligence. 

The tree data structure starts with a root node and has descendant branches. It has nodes connected by edges, where each node has a value, and some nodes have child nodes while others don't. This type of data structure resembles a tree, hence its name.

A tree data structure helps organise a data hierarchy and is a non-linear data structure. Moreover, it helps in accessing data faster because it is non-linear.

Types of Tree Data Structure

A tree data structure stores and organises data in a hierarchical structure. The various types of the tree data structure are:

Binary Tree

The binary tree in data structure is one where every element or parent node has up to two children. Hence, each node could have 1, 2, or 0 children. The two children are called the left child and the right child. The properties of a binary tree are:

• It is either an empty tree or consists of nodes - root node, right subtree, and left subtree. 
• The topmost node in the binary tree data structure is called the root.
• The nodes that don't have children are called terminal or leaf nodes.
• The tree's height is measured as the longest distance between the root node and a leaf node.
• The depth of the node is equal to the length of the path to its root.

Binary Search Tree

Every node in the binary search tree has a key and associated value. This provides quick addition, lookup, and removal. It also has a maximum of two nodes, like binary trees. However, every binary search tree is a binary tree, but not vice versa.

The difference between the two is that in a binary search tree, the left child node's value is less than the parent's, while the right side node's value is higher. The properties of a binary search tree are:

• The value of the root node must be higher than the value in all the nodes of the left subtree.
• The value of the root node must be higher than all the values in nodes of a right subtree.

AVL Tree

In a tree data structure, the AVL tree is a binary tree that is self-balanced after checking the balance factor of every mode. Hence, the right and left subtree heights must be balanced. The balance factor could be either 0.1 or -1. The biggest difference between the left subtree and the right subtree should be 1. If the difference between the subtrees is more than 1, the trees must be re-balanced using the rotation techniques. The properties of an AVL tree are:

• The difference between the height of any two child subtrees should be at most one.
• The balance factor is the difference between the left subtree's height and the right subtree's height.
• The -1 balance factor states that the right subtree is one level higher than the left subtree.
• The 0 balance factor states that the left and right subtree heights are equal.
• 1 balance factor means the left subtree is one level higher than the right subtree.

B-Tree

B-tree in data structure is a self-balancing tree where each node has more than one key and more than two children. It can store multiple keys in a single node and have many child nodes. This leads to a reduction in the height of the tree and enables fast desk access. The properties of a B-tree include:

• There are at most m children in every node.
• Every node, except the root node and leaf node, has at least m/2 children.
• All leaf nodes are at the same level.
• All root nodes have a minimum of 2 nodes.

Operations of Tree Data Structure

The basic operations that can be performed in a tree data structure include:

• Insertion: There are multiple ways to insert an element depending on the location, like inserting the element in the rightmost or the leftmost vacant position or inserting the element in the first empty position available. 
• Searching: It is a simple process to search in a binary tree to check if the current node value matches the required value. The process can be repeated to the right and left subtrees with a recursive algorithm until a match is found. 
• Deletion: Deleting is a tricky process in a tree data structure. When we delete a node, complications may occur to the right and left children. A deleted node is a leaf node that occurs. Thus, the deletion process of a node includes:
• Checking if the root is NULL.
• Searching for an item in the left and right subtree and recursing it.
• Deleting the root node of a tree.

Applications of a Tree Data Structure

The tree data structure stores the data in a hierarchical manner. The nodes are arranged at multiple levels. Thus, the application of a tree data structure is:

• Information in the computer is stored hierarchically. There are multiple folders in a drive, and each folder has many sub-folders. The files include images, documents etc. 
• It is easy to search for a node in a tree data structure. Operations like insertion and deletion are easy to perform.
• The tree data structure is used to store data in the routing tables.
• Programmers also use syntax trees to verify the syntax of the programs they write.

Data structures are the building blocks of a programming language. They are used for simple and complex computations in various areas of computer science. Having strong knowledge of tree data structures is important as they are the foundation of writing code. Hence, this knowledge can help one secure well-paying jobs.