Data Structures

1. Introduction

1. Data Types - Explanation of different types of data in programming.
2. Reference Type - Understanding objects stored by reference.
3. Value Type - How value types store data directly in memory.
4. Storing Data in Computer Memory - Overview of how data is managed in memory.

2. Array

1. Introduction and Basic Concepts - Fundamentals of arrays and their importance.
2. Static Array - Arrays with fixed size and their characteristics.
3. Dynamic Array - Resizable arrays and how they manage memory.
4. Array Operations - Common operations like insertion, deletion, searching, and sorting.
5. Application Areas of Arrays - Practical applications of arrays in real-world scenarios.

3. Singly Linked List

1. Introduction and Basic Concepts - Understanding singly linked lists and their significance in data structures.
2. Node Structure - Explanation of the SinglyLinkedListNode class, which stores data and a pointer to the next node.
3. Singly Linked List Operations
   • Insertion - Adding elements at the beginning, end, or a specific position.
   • Deletion - Removing the first, last, or a specific node.
   • Traversal - Iterating through the linked list using an enumerator.
   • Searching - Finding a specific node in the list.
4. Memory Management in Singly Linked Lists - How nodes are dynamically allocated and deallocated.
5. Application Areas of Singly Linked Lists - Practical uses in software development, such as queue implementations, undo features, and memory-efficient data storage.

4. Stack

1. Introduction and Basic Concepts

   • Understanding the LIFO (Last-In, First-Out) principle that defines a stack.
   • Real-world analogies like a stack of plates or books.
   • Importance in algorithm design and memory management.

2. Stack Structure

   • Explanation of the internal structure of a stack.
   • Common implementations using arrays and linked lists.
   • Core components: push, pop, peek, and isEmpty operations.

3. Stack Operations

   • Push - Adding an element to the top of the stack.
   • Pop - Removing the top element from the stack.
   • Peek (or Top) - Viewing the top element without removing it.
   • IsEmpty - Checking if the stack is empty.
   • Size - Getting the number of elements in the stack.

4. Memory Management in Stack

   • Stack memory allocation and deallocation.
   • Call stack usage during function execution.
   • Stack overflow issues and limitations in memory-constrained environments.

5. Application Areas of Stacks

   • Function call management in programming languages (call stack).
   • Expression evaluation and syntax parsing.
   • Backtracking algorithms (e.g., maze solving, undo operations).
   • Depth-First Search (DFS) in graph traversal.

5. Queue

1. Introduction and Basic Concepts

• Understanding the FIFO (First-In, First-Out) principle that defines a queue.
• Real-world analogies such as queues in supermarkets or print job scheduling.
• Importance in algorithm design, scheduling, and resource management.

2. Queue Structure

• Explanation of the internal structure of a queue.
• Common implementations using arrays, linked lists, and circular buffers.
• Core components: enqueue, dequeue, peek, and isEmpty operations.

3. Queue Operations

• Enqueue - Adding an element to the rear (end) of the queue.
• Dequeue - Removing an element from the front of the queue.
• Peek (or Front) - Viewing the front element without removing it.
• IsEmpty - Checking if the queue is empty.
• Size - Getting the number of elements currently stored in the queue.

4. Memory Management in Queue

• Dynamic vs. static memory allocation for queues.
• Circular queue implementations to optimize space utilization.
• Buffer overflow/underflow issues and preventive mechanisms.

5. Application Areas of Queues

• Scheduling processes in operating systems (CPU scheduling, IO queues).
• Managing print jobs in printers (print spooling).
• Breadth-First Search (BFS) in graph traversal.
• Simulation systems (e.g., customer service systems, traffic flow models).
• Message queues in distributed systems and asynchronous programming.

6. Sorting Algorithms

1. Introduction to Sorting Algorithms

• Importance of sorting in computer science.
• Comparison of different sorting techniques based on time complexity, space complexity, and stability.

2. Bubble Sort

• Simple comparison-based algorithm.
• Repeatedly swaps adjacent elements if they are in the wrong order.
• Best case: O(n), Worst case: O(n²), Space: O(1).

3. Insertion Sort

• Builds the final sorted array one element at a time.
• Good for small or nearly sorted datasets.
• Best case: O(n), Worst case: O(n²), Space: O(1).

4. Selection Sort

• Repeatedly finds the minimum element and moves it to the sorted portion.
• Always O(n²) time complexity.
• Not stable but simple to implement.

5. Merge Sort

• Divide-and-conquer algorithm that divides the list into halves, sorts them, and merges.
• Time complexity: O(n log n) in all cases.
• Space complexity: O(n).

6. Quick Sort

• Divide-and-conquer algorithm that picks a pivot and partitions the array.
• Best/Average case: O(n log n), Worst case: O(n²) (can be improved with randomized pivot).
• Space: O(log n) due to recursion stack.

7. Sorting.cs - Main Controller

• Central entry point to call and compare different sorting methods.
• Useful for benchmarking or switching between algorithms dynamically.