APPLICATIONS OF TREE DATA STRUCTURES

 We read the linear data structures like an array, linked list, stack and queue in which all the elements are arranged in a sequential manner. The different data structures are used for different kinds of data.

Some factors are considered for choosing the data structure:

· What type of data needs to be stored?: It might be a possibility that a certain data structure can be the best fit for some kind of data.

· Cost of operations: If we want to minimize the cost for the operations for the most frequently performed operations. For example, we have a simple list on which we have to perform the search operation; then, we can create an array in which elements are stored in sorted order to perform the binary search. The binary search works very fast for the simple list as it divides the search space into half.

· Memory usage: Sometimes, we want a data structure that utilizes less memory.

A tree is also one of the data structures that represent hierarchical data. Suppose we want to show the employees and their positions in the hierarchical form then it can be represented as shown below:

Let's understand some key points of the Tree data structure.

· A tree data structure is defined as a collection of objects or entities known as nodes that are linked together to represent or simulate hierarchy.

· A tree data structure is a non-linear data structure because it does not store in a sequential manner. It is a hierarchical structure as elements in a Tree are arranged in multiple levels.

· In the Tree data structure, the topmost node is known as a root node. Each node contains some data, and data can be of any type. In the above tree structure, the node contains the name of the employee, so the type of data would be a string.

· Each node contains some data and the link or reference of other nodes that can be called children.

Some basic terms used in Tree data structure.

Let's consider the tree structure, which is shown below:

 

In the above structure, each node is labeled with some number. Each arrow shown in the above figure is known as a link between the two nodes.

· Root: The root node is the topmost node in the tree hierarchy. In other words, the root node is the one that doesn't have any parent. In the above structure, node numbered 1 is the root node of the tree. If a node is directly linked to some other node, it would be called a parent-child relationship.

· Child node: If the node is a descendant of any node, then the node is known as a child node.

· Parent: If the node contains any sub-node, then that node is said to be the parent of that sub-node.

· Sibling: The nodes that have the same parent are known as siblings.

· Leaf Node:- The node of the tree, which doesn't have any child node, is called a leaf node. A leaf node is the bottom-most node of the tree. There can be any number of leaf nodes present in a general tree. Leaf nodes can also be called external nodes.

· Internal nodes: A node has atleast one child node known as an internal

Ancestor node:- An ancestor of a node is any predecessor  

·  node on a path from the root to that node. The root node doesn't have any ancestors. In the tree shown in the above image, nodes 1, 2, and 5 are the ancestors of node 10.

· Descendant: The immediate successor of the given node is known as a descendant of a node. In the above figure, 10 is the descendant of node 5.

Properties of Tree data structure

· Recursive data structure: The tree is also known as a recursive data structure. A tree can be defined as recursively because the distinguished node in a tree data structure is known as a root node. The root node of the tree contains a link to all the roots of its subtrees. The left subtree is shown in the yellow color in the below figure, and the right subtree is shown in the red color. The left subtree can be further split into subtrees shown in three different colors. Recursion means reducing something in a self-similar manner. So, this recursive property of the tree data structure is implemented in various applications.

· Number of edges: If there are n nodes, then there would n-1 edges. Each arrow in the structure represents the link or path. Each node, except the root node, will have atleast one incoming link known as an edge. There would be one link for the parent-child relationship.

· Depth of node x: The depth of node x can be defined as the length of the path from the root to the node x. One edge contributes one-unit length in the path. So, the depth of node x can also be defined as the number of edges between the root node and the node x. The root node has 0 depth.

· Height of node x: The height of node x can be defined as the longest path from the node x to the leaf node.

Implementation of Tree

The tree data structure can be created by creating the nodes dynamically with the help of the pointers. The tree in the memory can be represented as shown below:

 

 

In programming, the structure of a node can be defined as:

1. struct node  

2. {  

3.   int data;  

4. struct node *left;  

5. struct node *right;   

6. }  

Applications of trees

The following are the applications of trees:

· Storing naturally hierarchical data: Trees are used to store the data in the hierarchical structure. For example, the file system. The file system stored on the disc drive, the file and folder are in the form of the naturally hierarchical data and stored in the form of trees.

· Organize data: It is used to organize data for efficient insertion, deletion and searching. For example, a binary tree has a logN time for searching an element.

· Trie: It is a special kind of tree that is used to store the dictionary. It is a fast and efficient way for dynamic spell checking.

· Heap: It is also a tree data structure implemented using arrays. It is used to implement priority queues.

· B-Tree and B+Tree: B-Tree and B+Tree are the tree data structures used to implement indexing in databases.

· Routing table: The tree data structure is also used to store the data in routing tables in the routers.

Types of Tree data structure

The following are the types of a tree data structure:

· General tree: The general tree is one of the types of tree data structure. In the general tree, a node can have either 0 or maximum n number of nodes. There is no restriction imposed on the degree of the node (the number of nodes that a node can contain). The topmost node in a general tree is known as a root node. The children of the parent node are known as subtrees.

 

There can be n number of subtrees in a general tree. In the general tree, the subtrees are unordered as the nodes in the subtree cannot be ordered.
Every non-empty tree has a downward edge, and these edges are connected to the nodes known as child nodes. The root node is labeled with level 0. The nodes that have the same parent are known as siblings.

Binary tree

: Here, binary name itself suggests two numbers, i.e., 0 and 1. In a binary tree, each node in a tree can have utmost two child nodes. Here, utmost means whether the node has 0 nodes, 1 node or 2 nodes.

 

· Binary Search tree

· : Binary search tree is a non-linear data structure in which one node is connected to n number of nodes. It is a node-based data structure. A node can be represented in a binary search tree with three fields, i.e., data part, left-child, and right-child. A node can be connected to the utmost two child nodes in a binary search tree, so the node contains two pointers (left child and right child pointer).
Every node in the left subtree must contain a value less than the value of the root node, and the value of each node in the right subtree must be bigger than the value of the root node.

A node can be created with the help of a user-defined data type known as struct, as shown below:

 struct node  

. {  

.     int data;  

.     struct node *left;  

. struct node *right;   

. }