Learning Objectives
5 objectives- Understand fundamental data structures and their applications.
- Implement and manipulate arrays, linked lists, stacks, queues, trees, and graphs.
- Analyze and apply sorting and searching algorithms with respect to their efficiency.
- Explore advanced algorithmic techniques such as dynamic programming and greedy algorithms.
- Develop problem-solving skills by selecting appropriate data structures and algorithms.
Content Outline
PreviewUnit 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
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