Section 1.1: Arrays

Arrays are fixed-size collections that can store multiple items of the same data type, such as integers, floats, strings, or even other arrays. They provide indexed access to their elements, enabling random access.

Array Operations:

• Traversal: Iterate through all elements to perform operations.
• Search: Locate a specific element by value or index.
• Update: Change the value of an element at a specified index.

Adding or removing elements from an array necessitates creating a new array of the desired size and copying the existing elements. Arrays serve as the foundation for more complex data structures like array lists, heaps, hash tables, vectors, and matrices.

Section 1.2: Linked Lists

A linked list comprises nodes linked via pointers. Each node contains data and a reference to the next node. They can be singly linked (pointing to the next node) or doubly linked (pointing to both the next and previous nodes).

Linked List Operations:

• Insertion: Add a new node at the beginning, end, or within the list.
• Deletion: Remove a node from the list.
• Traversal: Access or modify elements in the list.

Linked lists offer dynamic memory allocation, allowing for easy insertion and removal of nodes. They are particularly useful when the size of the dataset is variable.

Subsection 1.2.1: Visual Overview of Linked Lists

Section 1.3: Stacks

Stacks are last-in, first-out (LIFO) structures that support two primary operations: push and pop. Elements are added and removed from the top of the stack, which can be implemented using arrays or linked lists.

Stack Operations:

• Push: Add an element to the top.
• Pop: Remove the top element.
• Peek: View the top element without removing it.

Stacks are widely employed in programming languages to manage function calls and in algorithms like depth-first search.

Section 1.4: Queues

Queues operate on a first-in, first-out (FIFO) basis, supporting enqueue and dequeue operations. Elements are added at the rear and removed from the front.

Queue Operations:

• Enqueue: Add an element to the rear.
• Dequeue: Remove an element from the front.
• Peek: View the front element without removal.

Queues are ideal for scenarios where processing order is crucial, such as managing tasks in an operating system.

Section 2.1: Trees

Trees are hierarchical structures where nodes are connected by edges. Each node can have multiple child nodes, while the root node has no parent. Trees are widely used to represent hierarchical relationships.

Section 2.2: Hash Tables

Hash tables (or hash maps) utilize a hash function to associate keys with values, enabling average-case constant time complexity for search, insert, and delete operations.

Hash Table Operations:

• Insert: Add a key-value pair.
• Search: Retrieve a value by key.
• Delete: Remove a key-value pair.

Hash tables are commonly used for dictionaries, caches, and databases.

Section 2.3: Graphs

Graphs represent relationships between entities, where nodes (vertices) are connected by edges. They can be directed or undirected, weighted or unweighted.

Graph Operations:

• Traversal: Visit all vertices.
• Shortest Path: Find the shortest route between two vertices.
• Minimum Spanning Tree: Identify the edges that connect all vertices with the least total weight.

Graphs have applications in network routing, social media, and recommendation systems.

Section 2.4: Tries

Tries, or prefix trees, are tree-like structures designed for efficient key retrieval. They excel in managing large sets of strings, making them ideal for dictionaries and autocomplete functions.

Trie Operations:

• Insert: Add a new key.
• Search: Check for key existence.
• Prefix Search: Find all keys starting with a specific prefix.

Tries are prevalent in applications involving extensive text storage and search, such as search engines and spell checkers.