Learning Objectives
5 objectives- Understand fundamental concepts of algorithms and their significance in computer science.
- Analyze algorithm complexity using Big O notation and different case scenarios.
- Explore and implement key data structures such as arrays, linked lists, stacks, queues, trees, and graphs.
- Apply sorting, searching, and graph algorithms to solve computational problems.
- Develop problem-solving skills using dynamic programming and hashing techniques.
Content Outline
PreviewUnit 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
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