Unit 280: Algorithms and Data Structures

1. Introduction to Algorithms

• Definition and role of algorithms in computer science
• Importance of algorithms in problem-solving
• Characteristics of good algorithms
• Examples of simple algorithms

2. Complexity Analysis

• Concept of algorithmic complexity
• Time complexity: Big O notation
  • Best, average, and worst-case scenarios
• Space complexity overview
• Analyzing and comparing efficiency of algorithms

3. Sorting Algorithms

• Overview and importance of sorting
• Bubble Sort
  • Working principle
  • Algorithm steps
  • Complexity analysis
• Selection Sort
  • Working principle
  • Complexity analysis
• Insertion Sort
  • Working principle
  • Complexity analysis
• Merge Sort
  • Divide and conquer strategy
  • Algorithm steps
  • Complexity analysis
• Quicksort
  • Partitioning method
  • Recursive approach
  • Complexity analysis

4. Searching Algorithms

• Introduction to searching and its applications
• Linear Search
  • Algorithm steps
  • Complexity analysis
• Binary Search
  • Preconditions: sorted data requirement
  • Algorithm steps
  • Complexity analysis
• Hash Tables
  • Concept of hashing
  • Handling collisions
  • Use cases

5. Data Structures Overview

• Definition and importance of data structures
• Overview of fundamental data structures:
  • Arrays
  • Linked Lists
  • Stacks
  • Queues
  • Trees
  • Graphs
• Applications and performance considerations

6. Arrays and Linked Lists

• Arrays
  • Structure and storage
  • Access operations
  • Advantages and limitations
• Linked Lists
  • Types: singly, doubly, circular
  • Node structure
  • Insertion, deletion, traversal operations
  • Comparison with arrays

7. Stacks and Queues

• Stacks
  • LIFO principle
  • Implementation using arrays and linked lists
  • Applications (e.g., undo mechanisms, expression evaluation)
• Queues
  • FIFO principle
  • Implementation using arrays and linked lists
  • Variants: circular queue, priority queue
  • Applications (e.g., scheduling, buffering)

8. Trees and Binary Trees

• Tree data structure basics
• Binary Trees
  • Properties and terminology
  • Tree traversal methods (inorder, preorder, postorder)
• Binary Search Trees (BST)
  • Structure and properties
  • Insertion and deletion operations
  • Searching in BST
• AVL Trees
  • Self-balancing property
  • Rotations to maintain balance
• B-Trees
  • Multi-way search tree
  • Applications in databases and filesystems

9. Graphs and Graph Algorithms

• Introduction to graphs
  • Definitions: vertices, edges, directed/undirected
  • Representations: adjacency matrix, adjacency list
• Graph traversal algorithms
  • Breadth-First Search (BFS)
  • Depth-First Search (DFS)
• Shortest path algorithms
  • Dijkstra's algorithm
• Minimum spanning tree algorithms
  • Prim's algorithm
  • Kruskal's algorithm

10. Hash Tables and Hashing

• Concept of hashing
• Hash functions and properties
• Collision resolution techniques
  • Chaining
  • Open addressing (linear probing, quadratic probing)
• Performance considerations
• Applications of hash tables