Unit 385: Algorithms and Data Structures

1. Introduction to Algorithms

• Definition and role of algorithms in computer science
• Importance of algorithm design and analysis
• Characteristics of good algorithms: correctness, efficiency, clarity

2. Complexity Analysis

• Time complexity and space complexity
• Big O notation: formal definition and examples
• Best-case, worst-case, and average-case analysis
• Common complexity classes (constant, logarithmic, linear, polynomial, exponential)

3. Data Structures Overview

• Definition and importance of data structures
• Classification: linear vs nonlinear structures
• Overview of key data structures: arrays, linked lists, stacks, queues, trees, graphs

4. Arrays and Linked Lists

4.1 Arrays

• Structure and memory layout
• Implementation details
• Operations: insertion, deletion, traversal, searching
• Advantages and disadvantages

4.2 Linked Lists

• Types: singly linked list, doubly linked list, circular linked list
• Node structure and pointers
• Operations: insertion, deletion, traversal, searching
• Advantages and disadvantages compared to arrays

5. Stacks and Queues

5.1 Stacks

• Definition and LIFO principle
• Implementation using arrays and linked lists
• Operations: push, pop, peek
• Applications: expression evaluation, backtracking

5.2 Queues

• Definition and FIFO principle
• Variants: simple queue, circular queue, priority queue, deque
• Implementation using arrays and linked lists
• Operations: enqueue, dequeue, front, rear
• Applications: scheduling, buffering

6. Trees and Binary Trees

6.1 Trees

• Tree terminology: root, parent, child, leaf, height, depth
• Types of trees: general trees, binary trees

6.2 Binary Trees

• Structure and properties
• Binary Search Trees (BST): insertion, deletion, searching
• Balanced trees: AVL trees overview

6.3 Tree Traversal Methods

• Depth-first traversals: pre-order, in-order, post-order
• Breadth-first traversal (level order)

7. Graphs and Graph Algorithms

7.1 Graph Fundamentals

• Definition and terminology: vertices, edges, directed vs undirected, weighted vs unweighted
• Graph representations: adjacency matrix, adjacency list

7.2 Graph Algorithms

• Depth-First Search (DFS): algorithm and applications
• Breadth-First Search (BFS): algorithm and applications
• Dijkstra’s algorithm for shortest path
• Minimum Spanning Tree algorithms: Prim’s and Kruskal’s

8. Sorting and Searching Algorithms

8.1 Sorting Algorithms

• Bubble sort, selection sort, insertion sort: concepts and complexity
• Merge sort and quick sort: divide and conquer approach
• Heap sort: heap data structure and sorting

8.2 Searching Algorithms

• Linear search: method and use cases
• Binary search: preconditions, algorithm, and complexity

9. Dynamic Programming

• Principles of dynamic programming: overlapping subproblems, optimal substructure
• Comparison with divide and conquer
• Examples:
  • Fibonacci sequence
  • Knapsack problem
• Steps to design a dynamic programming solution

10. Hashing and Hash Tables

• Concept of hashing and hash functions
• Collision resolution techniques: chaining, open addressing
• Implementation of hash tables
• Applications: efficient data storage and retrieval