Unit 3: Data Structures and Algorithms

1. Introduction to Data Structures

• Definition and importance of data structures
• Overview of common data structures:
  • Arrays
  • Linked Lists
  • Stacks
  • Queues
  • Trees
• Criteria for selecting appropriate data structures based on problem requirements

2. Array and Linked List Implementation

2.1 Arrays

• Structure and characteristics
• Insertion, deletion, and searching operations
• Time complexity analysis

2.2 Linked Lists

• Types: singly, doubly, and circular linked lists
• Node structure and pointers
• Insertion, deletion, and searching operations
• Advantages and disadvantages compared to arrays

3. Stack and Queue Operations

3.1 Stacks

• Concept and LIFO principle
• Operations: push, pop, peek
• Implementation using arrays and linked lists
• Applications (e.g., expression evaluation, backtracking)

3.2 Queues

• Concept and FIFO principle
• Operations: enqueue, dequeue, front, rear
• Types: simple queue, circular queue, priority queue, deque
• Implementation methods
• Applications (e.g., scheduling, buffering)

4. Tree Data Structure

4.1 Basics of Trees

• Terminology: root, node, edge, leaf, height, depth
• Types of trees

4.2 Binary Trees

• Properties and structure
• Binary tree traversal techniques:
  • Inorder
  • Preorder
  • Postorder

4.3 Binary Search Trees (BST)

• Structure and properties
• Insertion, deletion, searching
• Advantages over general binary trees

4.4 Balanced Trees

• Concept of tree balancing
• Examples: AVL trees, Red-Black trees (overview)

5. Graph Representation and Traversal

5.1 Graph Basics

• Definitions: vertices, edges, directed vs undirected, weighted vs unweighted

5.2 Graph Representations

• Adjacency matrix
• Adjacency list
• Comparison of representations

5.3 Graph Traversal Algorithms

• Depth-First Search (DFS)
• Breadth-First Search (BFS)
• Applications of traversal algorithms

6. Sorting Algorithms

• Introduction and importance

6.1 Simple Sorting Algorithms

• Bubble Sort
• Selection Sort
• Insertion Sort
• Time and space complexity analysis

6.2 Efficient Sorting Algorithms

• Merge Sort
• Quick Sort
• Heap Sort
• Divide and conquer strategy
• Complexity analysis and comparison

7. Searching Algorithms

• Introduction to searching

7.1 Linear Search

• Algorithm and use cases

7.2 Binary Search

• Requirements: sorted array
• Algorithm steps
• Complexity analysis

7.3 Interpolation Search

• Concept and working
• Conditions for effectiveness
• Comparison with binary search

8. Hashing and Hash Tables

• Concept of hashing
• Hash functions and properties
• Hash table structure
• Collision resolution techniques:
  • Chaining
  • Open addressing (linear probing, quadratic probing, double hashing)
• Importance of good hash functions

9. Dynamic Programming

• Principles of dynamic programming
• Overlapping subproblems and optimal substructure
• Memoization vs tabulation
• Examples of problems:
  • Fibonacci sequence
  • Knapsack problem
  • Longest common subsequence

10. Greedy Algorithms

• Characteristics of greedy algorithms
• Differences from dynamic programming
• Steps to design greedy algorithms
• Examples:
  • Activity selection problem
  • Huffman coding
• Limitations and when greedy algorithms fail