Stack, DSA Complete Syllabus

Course Curriculum: Mastering Stack Data Structure and Algorithms

This course is designed to cover every aspect of stacks, starting from the fundamentals to advanced applications. By the end of this course, learners will have a comprehensive understanding of the stack data structure and its applications, enabling them to solve complex problems with confidence.

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Module 1: Introduction to Stacks

1. Understanding Data Structures
   • Overview of Linear and Non-linear Data Structures.
   • Real-life examples and use cases.
2. What is a Stack?
   • Definition and concept of Last-In-First-Out (LIFO).
   • Characteristics of stacks.
3. Real-world Applications of Stacks
   • Undo/Redo functionality in applications.
   • Backtracking (e.g., Maze solving).
   • Parsing and parenthesis balancing.
4. How Stacks Differ from Other Data Structures
   • Stack vs Queue.
   • Stack vs Linked List.
5. Environment Setup
   • Tools and programming environments for practicing stacks.

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Module 2: Implementing Stacks

1. Stack Implementation Basics
   • Representation of stacks in memory.
   • Operations: Push, Pop, Peek/Top, IsEmpty, Size.
2. Stack Implementation Using Arrays
   • Fixed-size stack.
   • Dynamic resizing techniques.
3. Stack Implementation Using Linked List
   • Node structure.
   • Efficient memory utilization.
4. Comparison of Implementations
   • Time and space complexity analysis.
   • Trade-offs between array-based and linked-list-based stacks.

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Module 3: Intermediate Stack Operations

1. Stack Traversal
   • Iterative and recursive traversal methods.
2. Reverse a Stack
   • Using recursion.
   • Using auxiliary stacks.
3. Stack Sorting
   • Sorting using temporary stacks.
   • Sorting with recursion.
4. Merging Two Stacks
   • Maintaining sorted order.
   • Handling duplicate elements.

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Module 4: Applications of Stacks

1. Expression Evaluation
   • Infix to Postfix Conversion.
   • Postfix Evaluation.
   • Infix to Prefix Conversion.
   • Prefix Evaluation.
2. Parenthesis Checking
   • Balancing parentheses, brackets, and braces.
   • Handling nested structures.
3. Function Call Stack
   • Understanding recursion with the call stack.
   • Stack overflow scenarios.
4. Backtracking Problems
   • Solving mazes.
   • Generating permutations.
   • N-Queens problem.

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Module 5: Advanced Stack Concepts

1. Monotonic Stacks
   • Definition and properties.
   • Applications in interval problems.
2. Next Greater/Smaller Element Problems
   • Optimized solutions using stacks.
   • Circular arrays.
3. Histogram Problems
   • Largest rectangle in a histogram.
   • Maximum area in binary matrices.
4. Stack in Graph Algorithms
   • DFS using stacks.
   • Topological sorting.

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Module 6: Optimized Techniques and Variants

1. Two Stacks in One Array
   • Efficient management of memory.
   • Solving overflow conflicts.
2. Min/Max Stack
   • Extending stack to support minimum or maximum retrieval in O(1).
   • Implementation using auxiliary stacks.
3. Stack with Middle Element Access
   • Designing a stack with efficient middle element retrieval.
   • Doubly linked list-based implementation.
4. Circular Stack
   • Implementation and use cases.
   • Handling stack overflow in circular arrays.

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Module 7: Practical Projects and Case Studies

1. Expression Validator
   • Building a program to validate complex expressions.
2. Browser History Navigation
   • Implementing a forward-backward navigation system using stacks.
3. Undo-Redo Operations
   • Simulating text editor functionality.
4. Stock Span Problem
   • Solving real-world problems involving financial data.

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Module 8: Competitive Programming with Stacks

1. Common Stack Problems in Competitions
   • Practice problems from platforms like Codeforces, LeetCode, and HackerRank.
2. Problem-Solving Techniques
   • Identifying stack-based solutions.
   • Debugging stack-related errors.
3. Time Optimization
   • Reducing overhead in stack operations.
   • Optimizing space usage.

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Module 9: Advanced Stack Applications in Real-world Systems

1. Parsing Algorithms
   • Compilers and interpreters.
   • Abstract syntax trees.
2. Operating Systems
   • Stack usage in memory management.
   • Role in interrupt handling.
3. Database Management
   • Query evaluation and optimization using stacks.
4. AI Pathfinding Algorithms
   • DFS in AI for game trees and puzzle solving.

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Module 10: Final Assessment and Mastery

1. Comprehensive Coding Projects
   • Implementing a full-stack-based calculator.
   • Solving large-scale problems using stack-based methods.
2. Capstone Project
   • Students design and implement a real-world application heavily reliant on stacks.
3. Final Examination
   • Theory and practical coding exam to assess mastery.
4. Feedback and Next Steps
   • Personalized feedback for improvement.
   • Recommendations for further study and advanced topics.

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This curriculum provides a structured, step-by-step approach to mastering stacks, making it suitable for beginners and advanced learners alike.