Introduction to Algorithms
This course introduces the fundamental principles of algorithms and algorithmic thinking. It focuses on how to design efficient algorithms, analyze their correctness and performance, and apply them to solve real-world computational problems. Students will learn how to compare algorithmic solutions, reason about time and space complexity, and select appropriate data structures to support algorithm design.
Course Outline
- Introduction to Algorithms
- What is an algorithm?
- Why algorithms matter
- Algorithmic problem-solving mindset
- Algorithm Analysis
- Time complexity and space complexity
- Big-O, Big-Ω, and Big-Θ notation
- Best, average, and worst-case analysis
- Basic Data Structures
- Arrays and strings
- Stacks and queues
- Linked lists
- Introduction to hash tables
- Algorithm Design Techniques
- Brute force
- Divide and conquer
- Greedy algorithms
- Introduction to dynamic programming
- Searching Algorithms
- Linear search
- Binary search
- Performance comparison
- Sorting Algorithms
- Bubble, Selection, and Insertion sort
- Merge sort and Quick sort
- Stability and efficiency trade-offs
- Recursion
- Recursive thinking
- Base cases and recursion trees
- Recursive vs iterative solutions
- Introduction to Graph Algorithms
- Graph representation
- Depth-First Search (DFS)
- Breadth-First Search (BFS)
- Algorithm Correctness
- Proving correctness
- Loop invariants
- Common algorithmic pitfalls
- Practical Applications
- Real-world algorithm examples
- Choosing the right algorithm
- Performance considerations in software systems
