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# Types of Trees in Data Structure: Terminologies and Applications

A tree data structure consists of nodes connected by edges, and it’s defined by a set of rules that govern how nodes are organized and connected. Unlike arrays, linked lists, stacks, heaps, and queues, which are linear data structures, trees are hierarchical data structures.
Let’s begin our exploration of how the various types of trees have established themselves at the core of innovation in computer science.

## What is a Tree in Data Structure?

A tree is a hierarchical structure that starts at a singular point, known as the root and expands outwards with elements called nodes. These nodes are connected by links, often referred to as edges.
It represents a hierarchical relationship between elements, similar to the branches of a tree. It consists of nodes connected by edges, with a single node called the root. Each node can have child nodes, forming a parent-child relationship.

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## Types of Trees in Data Structure

In the data structure, there are several types of trees that are used to organize and represent data in a hierarchical manner.

Let’s explore some of the most common types of trees:

• Binary Tree: In this type, each node can have no more than two children, referred to as the left child and the right child. This structure allows for efficient searching, insertion, and deletion operations. Binary trees are widely used in various algorithms and data storage applications.
• Binary Search Tree (BST): A binary search tree has a certain ordering attribute. Every value in a node’s left subtree is less than its value, while every value in its right subtree is greater. This property enables fast searching and sorting operations.
• AVL Tree (Adelson-Velsky and Landis): It is a self-balancing binary search. It maintains a balance for each node, guaranteeing that the heights of the left and right subtrees differ by no more than one. This balancing property helps to maintain efficient operations even after multiple insertions or deletions.
• B-Tree: A B-tree is a self-balancing tree commonly used in databases and file systems. It is designed to handle large amounts of data efficiently. B-trees have multiple child nodes and can store a large number of elements at each node, reducing the height of the tree and improving search performance.
• Trie: A trie, also known as a prefix tree, is a specialized tree structure used for efficient string storage and retrieval operations. It is commonly used in applications such as spell-checking, autocomplete, and IP routing. Each node in a trie represents a character, and paths from the root to the leaves form complete words.

## Terminologies Used in Tree Data Structure

When working with tree data structures, it is important to understand their key terminologies.

Here are some commonly used terminologies:

• Node: A node is a fundamental building block of a tree. It represents an element or a data item within the tree. Each node can have a value associated with it and may have references to its child nodes.
• Root: The root is the topmost node of a tree. It serves as the starting point for accessing and navigating the entire tree structure. There is only one root in a tree.
• Parent: A parent node is a node that has one or more child nodes connected to it. It is located higher in the hierarchy than its child nodes.
• Child: A child node is a node directly connected to another node when moving away from the root. Each parent node can have zero or more child nodes.
• Leaf: A leaf node, also known as a terminal node, is a node that does not have any children. It is located at the bottom of the tree hierarchy.
• Sibling: Sibling nodes are nodes that share the same parent. They are at the same level in the tree and have different values.
• Depth: The depth of a node refers to the distance between that node and the root. It is determined by counting the number of edges from the root to the node.
• Height: The length of the longest path from a node to a leaf node is the height of that node. It is measured by counting the number of edges along the longest downward path.
• Subtree: A subtree is a smaller tree within a larger tree. It consists of a node and all of its descendants, including their children, grandchildren, and so on.
• Forest: A forest is a collection of disjoint trees. In other words, it is a group of trees that are not connected to each other.

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Here is a basic C++ code that demonstrates the terminologies of a tree in data structure:

#include <iostream>
#include <vector>
class Node {
public:
std::string value;
std::vector<Node*> children;
Node* parent;
Node(std::string val) : value(val), parent(nullptr) {}
children.push_back(child);
child->parent = this;
}
int getDepth() {
int depth = 0;
Node* currentNode = this;
while (currentNode->parent) {
depth++;
currentNode = currentNode->parent;
}
return depth;
}
int getHeight() {
if (children.empty()) return 0;
int maxHeight = 0;
for (Node* child : children) {
int childHeight = child->getHeight()
if (childHeight > maxHeight) {
maxHeight = childHeight;
}
}
return 1 + maxHeight;
}
void display(int level = 0) {
for (int i = 0; i < level; i++) {
std::court << "  ";
}
std::cout << value << std::endl;
for (Node* child : children) {
child->display(level + 1);
}
}
};
int main() {
Node root("Root");
Node child1("Child1");
Node child2("Child2");
Node child3("Child3");
Node child1_1("Child1_1");
Node child1_2("Child1_2");
root.display();
std::cout << "\nDepth of " << child1_1.value << ": " << child1_1.getDepth() << std::endl;
std::cout << "Height of " << root.value << ": " << root.getHeight() << std::endl;
return 0;
}

Output:

Root
Child1
Child1_1
Child1_2
Child2
Child3
Depth of Child1_1: 1
Height of Root: 2

The output of the program represents that:

The tree is displayed first. The root node is “Root“, which has three children: “Child1”, “Child2”, and “Child3”.
“Child1” further has two children: “Child1_1” and “Child1_2”.
“Child2” and “Child3” don’t have any children.
The depth of “Child1_1” is calculated. The depth is the distance from the root, so for “Child1_1“, it’s 1 (it’s one level below the root).
The height of the root (“Root“) is calculated. The height is the length of the longest path from that node to a leaf. In this case, the longest path is from “Root” to “Child1_1” or “Child1_2“, which is 2 levels deep.

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## Applications of Tree in Data Structure

Trees are fundamental data structures in computer science and have a wide range of applications.

Here are some of the most common applications of trees in data structures:

• Hierarchical Data Representation: Trees are used to represent hierarchical data structures, such as file systems where files and directories have a parent-child relationship.
• Database Systems: Trees, especially B-trees and B+ trees, are used in databases to enable quick searching, insertion, and deletion operations.
• Balanced Trees: AVL trees and Red-Black trees are self-balancing binary search trees used in various applications where the tree needs to be balanced to ensure operations, like add, delete, and find, are efficient.
• Priority Queue Implementation: Binary heaps, which can be visualized as trees, are used to implement priority queues. Priority queues are essential in algorithms like Dijkstra’s shortest path.
• Syntax Tree: In compilers, syntax trees are used to represent the structure of a program. They help in syntax checking and generating machine code.
• Network Routing Algorithms: Trees are used in algorithms that find the shortest path in networking, like the OSPF (Open Shortest Path First) protocol.
• Spatial Data Structures: Trees like Quad-trees (for 2D data) and Oct-trees (for 3D data) are used in computer graphics for things like collision detection.
• Decision Trees: In machine learning, decision trees are used for classification and regression tasks. They split the data based on certain conditions to make decisions.
• Game Trees: In artificial intelligence, trees are used to represent possible moves in a game. The minimax algorithm, for example, explores possible moves in games like chess or tic-tac-toe to decide the best move.
• Compression Algorithms: Trees are used in algorithms like Huffman coding, which is used for data compression. The frequency of data elements is used to build a tree that helps in efficient compression.
• DOM (Document Object Model): In web development, the structure of an HTML document is represented using a tree called the DOM, which allows developers to manipulate elements on a webpage.

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## Benefits of Tree

Following are some of the key advantages of trees in data structures:

• Hierarchical Structure: Trees provide a natural way to represent hierarchical structures, such as file systems, organizational charts, family trees, and more. It makes it adjustable to manage and organize data with parent-child relationships.
• Efficient Data Retrieval: Binary Search Trees (BSTs) and other balanced trees, like AVL trees and Red-Black trees, offer efficient data retrieval and search operations. These trees ensure that data can be located quickly, often in O(log n) time complexity, making them suitable for use in databases and search engines.
• Ordered Data: Some types of trees, like BSTs, maintain the data in a specific order. This ordering can be used to efficiently perform operations like finding the minimum or maximum element, finding elements within a specific range, and more.
• Balancing: Balanced trees, such as AVL trees and Red-Black trees, automatically maintain a balanced structure, which ensures that the height of the tree remains relatively small. This property helps to prevent performance degradation in search and insertion operations.
• Sorting: Trees can be used for efficient sorting algorithms like Heap Sort and Tree Sort. Heap Sort utilizes a binary heap (a type of binary tree) to sort elements in O(n log n) time complexity.

## Conclusion

Trees are foundational structures in computer science, elegantly representing hierarchical data. Trees stand as versatile and powerful tools that come in various types, like binary search trees, AVL trees, and more.
The terminology used in tree structures clarifies relationships and behaviors, enhancing our ability to design and implement efficient algorithms. Like the roots of a tree, which provide stability, the roots of tree data structures anchor the foundations of countless applications.

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