Unit 892: Algorithms and Data Structures

1. Introduction to Algorithms

• Definition and importance of algorithms in computer science
• Characteristics of good algorithms: correctness, efficiency, clarity, and scalability
• Common algorithm design techniques:
  • Divide and conquer
  • Greedy algorithms
  • Dynamic programming
  • Backtracking

2. Analysis of Algorithms

• Measuring algorithm performance
• Time complexity:
  • Big O, Big Omega, Big Theta notation
  • Worst-case, average-case, and best-case analysis
• Space complexity considerations
• Examples of complexity calculation

3. Sorting Algorithms

• Overview and importance of sorting
• Basic sorting algorithms:
  • Bubble Sort
  • Selection Sort
  • Insertion Sort
• Efficient sorting algorithms:
  • Merge Sort
  • Quick Sort
• Implementation details and step-by-step walkthroughs
• Efficiency comparisons and use cases

4. Searching Algorithms

• Importance and applications of searching
• Linear Search: concept, implementation, and analysis
• Binary Search: prerequisites, implementation, and complexity
• Graph search algorithms:
  • Depth-First Search (DFS)
  • Breadth-First Search (BFS)
• Applications in real-world problems

5. Data Structures Overview

• Definition and role of data structures
• Introduction to:
  • Arrays
  • Linked Lists
  • Stacks
  • Queues
  • Trees
  • Graphs
• Basic operations and use cases

6. Arrays and Linked Lists

• Arrays:
  • Structure and storage
  • Operations: traversal, insertion, deletion
  • Advantages and disadvantages
• Linked Lists:
  • Structure: singly, doubly, and circular linked lists
  • Operations: traversal, insertion, deletion
  • Advantages and disadvantages
• Performance comparison: arrays vs linked lists
• Use case scenarios

7. Stacks and Queues

• Stack data structure:
  • LIFO principle
  • Operations: push, pop, peek
  • Implementation using arrays and linked lists
  • Applications: expression evaluation, backtracking
• Queue data structure:
  • FIFO principle
  • Operations: enqueue, dequeue, front
  • Implementation using arrays and linked lists
  • Variants: circular queue, priority queue
  • Applications: scheduling, buffering

8. Trees and Binary Trees

• Tree concepts and terminology
• Binary Trees:
  • Properties and types
  • Traversal methods: inorder, preorder, postorder
• Binary Search Trees (BST):
  • Structure and properties
  • Operations: search, insertion, deletion
• AVL Trees:
  • Balanced trees
  • Rotations for balancing
• Practical applications

9. Graphs and Graph Algorithms

• Graph introduction:
  • Definitions and terminology
  • Types: directed, undirected, weighted, unweighted
• Graph representations:
  • Adjacency matrix
  • Adjacency list
• Graph traversal algorithms:
  • Depth-First Search (DFS)
  • Breadth-First Search (BFS)
• Shortest path algorithms:
  • Dijkstra's algorithm
  • Bellman-Ford algorithm
• Minimum spanning tree algorithms:
  • Prim's algorithm
  • Kruskal's algorithm
• Applications in networking, pathfinding, and social networks

10. Advanced Data Structures

• Hash Tables:
  • Concept and hashing functions
  • Collision resolution techniques
  • Applications
• Heaps:
  • Min-heap and max-heap
  • Heap operations
  • Use in priority queues and heapsort
• Trie:
  • Structure and storage
  • Applications in string searching and autocomplete
• Segment Trees:
  • Structure and purpose
  • Range queries and updates
  • Use cases in competitive programming and databases