Open Data Structures: An Introduction (Open Paths to Enriched Learning) by Morin, Pat (FREE PDF)

 

Introduction

Understanding data structures is a foundational skill for software engineers, computer scientists, algorithm developers and anyone working with programming at scale. The book Open Data Structures: An Introduction (Open Paths to Enriched Learning) offers a modern, accessible and practical guide to data structures — from lists, stacks and queues to trees, hash tables, skip lists and advanced topics — with an emphasis on clear explanations, hands-on code and practical implementations.

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Why This Book Matters

• The book is designed to be open and freely available, aligning with modern educational values and making the content accessible to a wide audience.

• It takes a building-blocks approach: presenting each data structure, its operations, how to implement it, and how to analyze its performance. This bridges the gap between algorithmic theory and real code.

• For learners who already know programming (say in Java or C++), this book helps deepen their understanding of how data structures are designed, how operations work, and what trade-offs exist (time vs space, worst-case vs average case).

• Because the topics cover both core and advanced data structures, it’s valuable both as a primary learning resource and as a reference.

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What the Book Covers

Here are key topics you’ll encounter:

Fundamental Data Structures

You’ll begin with the basics: arrays, singly and doubly linked lists, stacks, queues, deques. You’ll learn how to implement them, how to use them, and how their performance characteristics differ.

Abstract Data Types & Interfaces

The book emphasizes the concept of abstract data types (ADTs): specifying what operations a structure must support (insert, delete, find) without worrying first about how they’re implemented. Understanding ADTs helps you focus on design and modularity.

Trees and Hierarchical Structures

Moving beyond linear structures, the book introduces binary search trees (BSTs), balanced trees (AVL trees, red-black trees), heaps, and priority queues. You’ll explore how trees store data in a hierarchical way and how operations like insert/search/erase work.

Hash Tables and Skip Lists

These are powerful data structures for fast look-ups. You’ll learn how hashing works, how collisions are dealt with, how skip lists provide probabilistic alternatives to balanced trees, and when each structure is appropriate.

Advanced Structures and Analysis

Finally, the book explores advanced topics and rigorous analysis: amortized analysis, amortized time bounds for operations, dynamic arrays, memory allocation costs, structural invariants, and how real-world implementations differ from textbook versions.

Code Implementations and Pseudocode

Throughout, the author provides pseudocode, often actual code in Java/C++ (or other languages depending on edition) so you can see how concepts translate into working code. This is helpful for converting theory into practice.

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Who Should Read This Book

This book is an excellent choice if you:

• Have programming experience (with one of C, C++, Java, Python) and want to deepen your knowledge of data structures.

• Are studying computer science or software engineering and want a rigorous, yet practical, data-structures textbook.

• Are preparing for technical interviews or coding contests and want to strengthen your understanding of structures, algorithms and performance trade-offs.

• Want a resource you can refer back to when implementing your own systems or libraries.

If you are brand new to programming and have never used a data structure beyond lists/arrays, you may find parts of the book challenging. It’s best when you already have basic programming proficiency.

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What You’ll Walk Away With

After working through this book, you should be able to:

• Understand how common data structures (lists, queues, stacks, trees, hash tables) are designed and implemented.

• Choose the right data structure for a given problem, based on operations you need and performance constraints.

• Write code (or pseudocode) that correctly implements those structures and their operations.

• Analyze and compare data structure performance: worst-case, average case, amortized, memory usage.

• Recognize how data structure design affects real systems (e.g., how hash table choices affect performance in large systems).

• Use this knowledge to build more efficient, robust software, or prepare for advanced algorithmic challenges.

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Tips to Get the Most Out of It

• Work through examples: Type out or implement each data structure discussed. Seeing it in code helps internalise the logic.

• Test your implementations: Write small programs that insert, delete, search in your structures, measure performance, see how they differ.

• Compare different structures: For example, compare a hash table implementation vs balanced tree implementation for the same operations. See how performance differs.

• Use the book as a reference: After reading, keep the book handy. When you implement a system or library, you’ll often revisit chapters.

• Solve problems: Use online problem sets (e.g., data-structure practice sites) to apply what you’ve learned. This reinforces the concepts.

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Hard Copy: Open Data Structures: An Introduction (OPEL: Open Paths to Enriched Learning)

PDF Kindle: Open Data Structures An Introduction

Final Thoughts

Open Data Structures: An Introduction (Open Paths to Enriched Learning) is a standout resource for anyone serious about data-structures mastery. Its combination of clear exposition, practical code, and thorough analysis makes it a go-to textbook and reference. Whether you’re a student, developer or competitive programmer, this book will equip you with the tools and understanding to implement efficient data structures and make informed design decisions.

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Simplifying Data Structures: Dataclasses, Pydantic, TypedDict, and NamedTuple Explained

When working with Python, one of the most common tasks is organizing and managing structured data. Whether you’re designing APIs, modeling business objects, or just passing around structured values in your code, Python gives you multiple tools to make data handling easier, safer, and more readable.

In this post, we’ll break down four popular approaches:

• Dataclasses

• Pydantic

• TypedDict

• NamedTuple

Each has its own strengths and use cases—let’s dive in.

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1. Dataclasses – The Pythonic Default

Introduced in Python 3.7, dataclasses reduce boilerplate when creating classes that mainly store data.

Example:

from dataclasses import dataclass

@dataclass 
class User: 
    id: int
    name: str 
    active: bool = True
u = User(1, "Alice")
print(u) # User(id=1, name='Alice', active=True)

✅ Why use Dataclasses?

• Automatic __init__, __repr__, and __eq__.

• Default values supported.

• Type hints guide usage (but not enforced at runtime).

• Great for simple data modeling.

⚠️ Limitation: No runtime type validation. You can assign name=123 and Python won’t complain.

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2. Pydantic – Validation and Parsing Powerhouse

If you need runtime type checking, data validation, or JSON parsing, Pydantic is the tool of choice. Widely used in frameworks like FastAPI.

Example:

from pydantic import BaseModel

class User(BaseModel):
 id: int
 name: str
 active: bool = True

u = User(id=1, name="Alice")
print(u.dict()) # {'id': 1, 'name': 'Alice', 'active': True}

✅ Why use Pydantic?

• Enforces type validation at runtime.

• Parses input data (e.g., from JSON, APIs).

• Rich ecosystem (validators, schema generation).

• Essential for production APIs.

⚠️ Limitation: Slightly slower than dataclasses (due to validation).

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3. TypedDict – Dictionaries with Types

Sometimes, you want the flexibility of a dictionary, but with type safety for keys and values. Enter TypedDict, part of Python’s typing module.

Example:

from typing import TypedDict

class User(TypedDict):
    id: int
    name: str
    active: bool
u: User = {"id": 1, "name": "Alice", "active": True}

✅ Why use TypedDict?

• Lightweight way to type-check dictionaries.

• Perfect for legacy code or when JSON/dict structures dominate.

• Works well with static type checkers like mypy.

⚠️ Limitation: No runtime validation—errors only caught by static checkers.

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4. NamedTuple – Immutable and Lightweight

A NamedTuple is like a tuple, but with named fields. They’re immutable and memory-efficient, making them great for simple data containers.

Example:

from typing import NamedTuple

class User(NamedTuple):
    id: int
    name: str
    active: bool = True 
u = User(1, "Alice")
print(u.name) # Alice

✅ Why use NamedTuple?

• Immutable (safer for certain use cases).

• Lightweight and memory-efficient.

• Tuple-like unpacking still works.

⚠️ Limitation: Cannot modify fields after creation.

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Quick Comparison

Feature	Dataclass	Pydantic	TypedDict	NamedTuple
Boilerplate-free	✅	✅	✅	✅
Runtime validation	❌	✅	❌	❌
Immutable support	Optional	Optional	❌	✅
JSON parsing	❌	✅	❌	❌
Static typing	✅	✅	✅	✅

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When to Use Which?

• Use Dataclasses if you just need clean, boilerplate-free classes.

• Use Pydantic if you need data validation and parsing (APIs, user input).

• Use TypedDict when working with dictionaries but want type safety.

• Use NamedTuple when you need lightweight, immutable records.

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Final Thoughts

Python gives us multiple ways to structure data—each optimized for a different balance of simplicity, safety, and performance. By choosing the right tool for the job, you make your code cleaner, safer, and easier to maintain.

Mathematics with Python Solving Problems and Visualizing Concepts

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Master Data Structures & Algorithms with Python — Bootcamp Starting 14th September, 2025

 

Are you preparing for coding interviews, competitive programming, or aiming to sharpen your problem-solving skills? The DSA with Python Bootcamp is designed to take you from Python fundamentals to mastering advanced Data Structures and Algorithms — in just 2 months.

This instructor-led, hands-on bootcamp combines live coding, real-world projects, and 100+ curated problems to give you the confidence and skillset needed to excel in technical interviews and real-world programming challenges.

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What You’ll Learn

✅ Python Essentials — Build a strong foundation in Python syntax, data types, and functions.
✅ Core DSA Concepts — Arrays, recursion, searching & sorting, stacks, queues, linked lists, trees, graphs, heaps, and more.
✅ Dynamic Programming — Solve complex problems using DP strategies.
✅ Interview Prep — Focused practice with 100+ problems, mock tests, and weekly assignments.
✅ Capstone Projects — Apply everything you learn in real-world coding projects.

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Course Details

• 🌐 Language: English

• ⏱️ Duration: 2 Months

• 🗓️ Start Date: 14th September, 2025

• 🕓 Class Time: 4 PM – 7 PM IST (Sat & Sun)

  • 2 hours live class

  • 1 hour live doubt-clearing session

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Why Join This Bootcamp?

• Instructor-Led Live Sessions — Learn step by step with expert guidance.

• Hands-On Learning — Practice-driven teaching methodology.

• Curated Assignments & Guidance — Stay on track with personalized feedback.

• Portfolio-Ready Projects — Showcase your skills with real-world examples.

• Job-Focused Prep — Build confidence for coding interviews & competitive programming.

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Enroll Now

Spots are limited! Secure your place in the upcoming batch and start your journey toward mastering DSA with Python.

👉 Check out the course here

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MITx: Understanding the World Through Data

 MITx: Understanding the World Through Data

Learn How to Analyze, Interpret, and Make Sense of Data in Everyday Life

In an era where data fuels everything from personal decisions to global policy, being data-literate is no longer a luxury — it’s a necessity. Whether you're evaluating news headlines, monitoring your health, or running a business, the ability to understand and interpret data is a skill that empowers better decisions.

That's why MIT created the course "Understanding the World Through Data", offered via edX as part of the MITx suite of introductory courses.

Course Overview

"Understanding the World Through Data" is a non-technical, highly engaging course designed to equip learners with a foundational understanding of how data works — what it means, how it's collected, how it can be misleading, and how to use it responsibly.

This course is ideal for beginners, non-STEM learners, or anyone who wants to make sense of the numbers that shape our world — from surveys and polls to charts, graphs, and media headlines.

Taught by Experts

This course is developed by faculty from MIT's Institute for Data, Systems, and Society (IDSS) — a leader in interdisciplinary research at the intersection of data, social science, and technology.

The instructors bring a unique perspective that blends statistical literacy, social awareness, and critical thinking, making complex topics highly accessible.

What You’ll Learn – Course Modules

The course content is built around real-world issues and questions, not just equations and theory. Here's what you'll explore:

1. The Role of Data in Society

Why data matters in daily life

How organizations and governments collect and use data

Bias, ethics, and misinformation

2. Understanding Uncertainty

What is uncertainty and why it matters in decision-making

Probability basics (in plain English)

Real-life applications (COVID-19 data, risk analysis, etc.)

3. Descriptive Statistics

Mean, median, mode, standard deviation

How summaries can distort or clarify information

Visualization tools: charts, histograms, pie graphs

4. Making Comparisons and Understanding Variation

Correlation vs. causation

Data comparisons across groups and categories

Sampling bias and confounding factors

5. Statistical Inference

How to draw conclusions from data

Polling and margin of error

Confidence intervals and statistical significance

6. Data in Action

Using data to tell stories and drive change

How data is used in journalism, health, education, policy

Responsible use of data and avoiding manipulation

Tools & Format

• No programming or math background required
• Uses interactive visualizations, case studies, and real-world examples
• Exercises involve interpretation, critical thinking, and simple calculations — all doable in a browser

The course also includes:

• Short quizzes
• Mini projects (e.g., analyzing survey data or interpreting a dataset)
• Optional reading materials and data stories

What You'll Be Able to Do

By the end of the course, you'll be able to:

Interpret graphs, charts, and statistical summaries in news and research

Identify misleading or biased use of data

Ask the right questions when confronted with a statistic

Make informed, evidence-based decisions in your personal and professional life

Explain data findings clearly and responsibly

Who Should Take This Course?

This course is perfect for:

• Students of any background who want to develop data literacy
• Journalists, policy makers, and educators
• Business leaders making data-driven decisions
• Nonprofits and community advocates using data for impact
• Everyday individuals who want to better understand the world around them
• No programming, calculus, or technical knowledge required — just curiosity and an open mind.

Why It Matters

In a world of information overload, those who can understand and analyze data hold a major advantage. Whether you're evaluating election polls, reviewing health guidelines, or making investment decisions — knowing how to spot good data from bad data is an essential life skill.

MITx: Understanding the World Through Data gives you the tools to do just that.

Join Now : MITx: Understanding the World Through Data

Final Thoughts

This course isn’t about turning you into a data scientist. It’s about empowering you with data confidence — helping you navigate headlines, dashboards, and datasets without feeling overwhelmed or misled.

If you've ever asked, "Can I trust this chart?" or "What does this statistic really mean?" — this course is your answer.

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Data Processing Using Python

Data Processing Using Python: A Key Skill for Business Success

In today's business world, data is generated continuously from various sources such as financial transactions, marketing platforms, customer feedback, and internal operations. However, raw data alone does not offer much value until it is processed into an organized, interpretable form. Data processing is the critical step that transforms scattered data into meaningful insights that support decision-making and strategic planning. Python, thanks to its simplicity and power, has become the preferred language for handling business data processing tasks efficiently.

What is Data Processing?

Data processing refers to the collection, cleaning, transformation, and organization of raw data into a structured format that can be analyzed and used for business purposes. In practical terms, this might include combining monthly sales reports, cleaning inconsistencies in customer information, summarizing financial transactions, or preparing performance reports. Effective data processing ensures that the information businesses rely on is accurate, complete, and ready for analysis or presentation.

Why Choose Python for Data Processing?

Python is particularly well-suited for business data processing for several reasons. Its simple and readable syntax allows even those without a formal programming background to quickly learn and apply it. Furthermore, Python's extensive ecosystem of libraries provides specialized tools for reading data from different sources, cleaning and transforming data, and conducting analyses. Unlike traditional spreadsheet tools, Python scripts can automate repetitive tasks, work with large datasets efficiently, and easily integrate data from multiple formats such as CSV, Excel, SQL databases, and APIs. This makes Python an essential skill for professionals aiming to manage data-driven tasks effectively.

Essential Libraries for Data Processing

Several Python libraries stand out as fundamental tools for data processing. The pandas library offers powerful functions for handling tabular data, making it easy to filter, sort, group, and summarize information. Numpy provides efficient numerical operations and is especially useful for working with arrays and large datasets. Openpyxl focuses on reading and writing Excel files, a format heavily used in many businesses. Other important libraries include csv for handling comma-separated values files and json for working with web data formats. By mastering these libraries, business professionals can greatly simplify complex data workflows.

Key Data Processing Tasks in Python

Reading and Writing Data

An essential first step in any data processing task is reading data from different sources. Businesses often store their data in formats such as CSV files, Excel spreadsheets, or JSON files. Python allows users to quickly import these files into a working environment, manipulate the data, and then export the processed results into a new file for reporting or further use.

Cleaning Data

Real-world data is often imperfect. It can contain missing values, inconsistent formats, duplicates, or outliers that distort analysis. Data cleaning is necessary to ensure reliability and accuracy. Using Python, users can systematically detect and correct errors, standardize formats such as dates and currencies, and remove irrelevant or incorrect entries, laying a solid foundation for deeper analysis.

Transforming Data

Once the data is clean, it often needs to be transformed into a more useful format. This could involve creating new fields such as a "total revenue" column from "units sold" and "price per unit," grouping data by categories such as regions or months, or merging datasets from different sources. These transformations help businesses summarize and reorganize information in a way that supports more effective reporting and analysis.

Analyzing and Summarizing Data

With clean and structured data, businesses can move toward analysis. Python provides tools to calculate descriptive statistics such as averages, medians, and standard deviations, offering a quick snapshot of key trends and patterns. Summarizing data into regional sales performance, customer demographics, or monthly revenue trends helps businesses make informed strategic decisions backed by clear evidence.

What You Will Learn from the Course

By taking this course on Data Processing Using Python, you will develop a strong foundation in handling and preparing business data efficiently. Specifically, you will learn:

The Fundamentals of Data Processing: Understand what data processing means, why it is essential for businesses, and the typical steps involved, from data collection to final analysis.

Using Python for Business Data: Gain hands-on experience with Python programming, focusing on real-world business datasets and practical data problems rather than abstract theory.

Working with Key Python Libraries: Become proficient in popular libraries such as pandas, numpy, openpyxl, and csv, which are widely used in business environments for manipulating, cleaning, and organizing data.

Reading and Writing Different Data Formats: Learn how to import data from CSV, Excel, and JSON files, process it, and export the results for use in reports, dashboards, or presentations.

Real-World Applications in Business

Python's capabilities in data processing extend across different business domains. In finance, Python can automate budget tracking, consolidate expense reports, and even assist in financial forecasting. In marketing, Python scripts can scrape campaign data from social media platforms, clean and organize customer response data, and generate campaign performance summaries. Operations teams can use Python to monitor inventory levels, manage supply chain records, and streamline order processing. Human resources departments might process employee data for payroll and performance evaluations. Across industries, Python transforms raw, chaotic data into clean, actionable intelligence.

Join Free : Data Processing Using Python

Conclusion

Data processing using Python is a game-changer for businesses aiming to leverage their data effectively. With Python’s simplicity, powerful libraries, and automation capabilities, even non-technical professionals can perform complex data tasks with ease. Mastering these skills not only saves time and improves data accuracy but also empowers businesses to make better, faster, and smarter decisions. As companies continue to move toward a more data-driven future, learning how to process data with Python is not just an advantage — it’s a necessity.

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EQUILIBRIUM INDEX IN ARRAY in Python

 

The Equilibrium Index of an array is an index where the sum of the elements on the left side of the index is equal to the sum of the elements on the right side.

def find_equilibrium_index(arr):

    total_sum = sum(arr)

    left_sum = 0

    for i, num in enumerate(arr):

        total_sum -= num  

        

        if left_sum == total_sum:

            return i 

        

        left_sum += num  

    

    return -1  

# Example usage

arr = [1, 3, 5, 2, 2]

equilibrium_index = find_equilibrium_index(arr)

print(f"Equilibrium Index: {equilibrium_index}")

#source code --> clcoding.com

Equilibrium Index: 2

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Foundations of Data Structures and Algorithms Specialization

 

In the realm of computer science, data structures and algorithms are the backbone of efficient programming and software development. They form the fundamental concepts that every aspiring software engineer, data scientist, and computer scientist must master to solve complex problems effectively. Coursera's "Data Structures and Algorithms" Specialization, offered by the University of Colorado Boulder, provides an in-depth journey into these essential topics, equipping learners with the skills needed to excel in the tech industry.

Why Data Structures and Algorithms Matter

Data structures and algorithms are the building blocks of all software applications. They enable programmers to handle data efficiently, optimize performance, and ensure that applications run smoothly. Understanding these concepts is crucial for:

• Problem Solving: Algorithms provide a set of instructions to solve specific problems, while data structures organize and store data for efficient access and modification.
• Efficiency: Efficient algorithms and data structures improve the speed and performance of applications, making them scalable and robust.
• Competitive Programming: Mastery of these topics is essential for acing technical interviews and excelling in competitive programming contests.
• Software Development: From simple applications to complex systems, every software development project relies on the principles of data structures and algorithms.

Course Overview

The Coursera Specialization on Data Structures and Algorithms consists of several courses designed to take learners from basic to advanced levels. Here's a glimpse of what each course offers:

1. Algorithmic Toolbox:

   • Introduction to the basic concepts of algorithms.
   • Study of algorithmic techniques like greedy algorithms, dynamic programming, and divide-and-conquer.
   • Practical problem-solving sessions to reinforce learning.

2. Data Structures:

   • Comprehensive coverage of fundamental data structures such as arrays, linked lists, stacks, queues, trees, and graphs.
   • Exploration of advanced data structures like heaps, hash tables, and balanced trees.
   • Hands-on exercises to implement and manipulate various data structures.

3. Algorithms on Graphs:

   • Detailed study of graph algorithms including breadth-first search (BFS), depth-first search (DFS), shortest paths, and minimum spanning trees.
   • Real-world applications of graph algorithms in networking, web search, and social networks.

4. Algorithms on Strings:

   • Techniques for string manipulation and pattern matching.
   • Algorithms for substring search, text compression, and sequence alignment.
   • Applications in bioinformatics, data compression, and text processing.

5. Advanced Algorithms and Complexity:

   • Exploration of advanced topics such as NP-completeness, approximation algorithms, and randomized algorithms.
   • Analysis of algorithmic complexity and performance optimization.

Key Features

• Expert Instruction: The courses are taught by experienced professors from the University of Colorado Boulder, ensuring high-quality instruction and guidance.
• Interactive Learning: Each course includes a mix of video lectures, quizzes, programming assignments, and peer-reviewed projects to enhance learning.
• Flexibility: Learners can progress at their own pace, making it convenient to balance studies with other commitments.
• Certification: Upon completion, participants receive a certificate that can be shared on LinkedIn and added to their resumes, showcasing their proficiency in data structures and algorithms.

Who Should Enroll? Foundations of Data Structures and Algorithms Specialization

This specialization is ideal for:

• Aspiring Programmers: Beginners looking to build a strong foundation in data structures and algorithms.
• Software Engineers: Professionals seeking to improve their problem-solving skills and prepare for technical interviews.
• Computer Science Students: Individuals aiming to deepen their understanding of core computer science concepts.
• Tech Enthusiasts: Anyone with a passion for technology and a desire to learn how to solve complex problems efficiently.

Conclusion

Mastering data structures and algorithms is a crucial step towards becoming a proficient software engineer and problem solver. Coursera's "Data Structures and Algorithms" Specialization offers a comprehensive and structured learning path to achieve this mastery. With expert instruction, interactive learning experiences, and the flexibility to learn at your own pace, this specialization is an invaluable resource for anyone looking to excel in the tech industry.

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Python Data Structures

 

What you'll learn

Explain the principles of data structures & how they are used

Create programs that are able to read and write data from files

Store data as key/value pairs using Python dictionaries

Accomplish multi-step tasks like sorting or looping using tuples

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There are 7 modules in this course

This course will introduce the core data structures of the Python programming language. We will move past the basics of procedural programming and explore how we can use the Python built-in data structures such as lists, dictionaries, and tuples to perform increasingly complex data analysis. This course will cover Chapters 6-10 of the textbook “Python for Everybody”.  This course covers Python 3.

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Object Oriented Programming [OOP]

 Basic Concepts:

a. Define what an object is in the context of OOP.

b. Explain the difference between a class and an object.

Encapsulation:

a. Describe the concept of encapsulation and its benefits.

b. Provide an example of encapsulation in a programming language of your choice.

Inheritance:

a. Explain the concept of inheritance and its purpose.

b. Differentiate between single inheritance and multiple inheritance.

Polymorphism:

a. Define polymorphism and explain its types.

b. Provide an example of compile-time and runtime polymorphism.

Abstraction:

a. Discuss the importance of abstraction in OOP.

b. Provide an example of abstraction in a real-world scenario.

Class and Object Relationships:

a. Explain the difference between a class method and an instance method.

b. Describe the concept of composition in OOP.

Interfaces and Abstract Classes:

a. Define an interface and explain its role in OOP.

b. Differentiate between an interface and an abstract class.

Design Patterns:

a. Discuss the singleton design pattern and its use cases.

b. Explain the observer design pattern.

Exception Handling:

a. Describe how exception handling is implemented in an object-oriented language.

b. Discuss the importance of try-catch blocks in OOP.

Object-Oriented Analysis and Design (OOAD):

a. Explain the phases of Object-Oriented Analysis and Design.

b. Discuss the importance of UML (Unified Modeling Language) in OOAD.

Generic Programming:

a. Define generic programming and its advantages.

b. Provide an example of using generics in a programming language.

Reflection:

a. Explain the concept of reflection in OOP.

b. Discuss situations where reflection can be useful.

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Data Structures- Leture 4

                                                  Data Structures
                                     Lecture 4
Stack Representation

Let us start with how stacks are represented. So stacks are represented with a node in the linked list with the node containing data. That is what is to be represented and link pointing to the next node. And the also you have and access to a stack throw a node. Which is designated to a stack and also maintain the count the no. of elements of the stack. Now first think we going doing is create a stack. To creating a stack, you have to first dynamically the allocate a stack. Who size is equal to the size of the stack and if the stack top is equal to null. When that is what you are doing. To the initialize the top and we are also since creating the stack. And any top initialize equal to be null and count to be equal to zero. You are not a actually create a node. This is first step in creating a stack. So once you created a stack we went to do the operation from stack. Important operation has push already seen push operation. This is if you look at linked list representation of stack. In the push operation similar to inserting a node in the front of a list. Because already operations are done with a stack at the top of the you can access the stack accessed to throw only the top. Insertion and deletion when you represent a stack as the linked list is in the front. So here. Same as inserting a new element to the list before the first. So let us assume that this is the element. You want to insert and this is the previous stack. So previous stack has this is the count and is the top. So top is pointing to the first element in the stack. Are you wanted to insert the new element? First to create an element for the node. And this is the address of the node. And this is containing the data red and pointer next. So that’s what is available. When you are going to insert this into the stack. It’s come like this. Now this is Pnew and which know this is address of this. You create next. Change the next pointer to point to the address of blue. And change to things top to point to address of red and increment the count be equal to 3. So this is insertion of push operation. We don’t call it insert in stacks. We call it push operation. Push into the stack. Which is represented as a linked list. So this is the push operation. The code for the push operation so first thing will you do introduce create a node. In that node you creating a node. You have get it from the allocated area. If there is no allocated area. That is can’t get a new node. You can’t insert. Once you got that. In the new position you put data. Pointed to that data whatever to insert. And you make the pointer of the new location of the new node. That is to be created.
Pointed to original stack top. And now change the stack top pointed to the new pointer implement top to the point to the new node. And increment the count of the stack by one. And return one. And Return one this is indicated. So this is what we do for insertion into a stack. As we consider to this is very similar to the insertion into the front of the linked list. Now let us look at the next operation of stack. Which is pop. Pop is to delete the element and as you know you can only the delete element from top of the stack. That is the constraint that you have on stack. So this is the same as the removing first element from a linked list. So what you have to do is. This is an original stack. Now the only element you can delete or remove from the stack from and do the pop operation. In this element. No other element can remove. So what you do is. You make the pop. Now point to blue. Ok. That is it. So now you can access the stack. Only. Throw this. Now you have a node which is short of bankling. So this can be recycled. So you make a pointer to Point to this node. So that it can be recycled. So this is the pop operation. So the code for the pop operation. As follows. So you have a pointer to point to the node. Which you want to the return. And if the stack already discussed you want to a deletion and what do you want we consume must. First ensure that the data structure from which you want do the deletion. Is not empty. So that is what is doing here. Just checking the count what whether equal to zero. You saying that will return zero. Which means that is an underflow. That is no element. To be delete it. Otherwise you make this pointer to point to the original stack. This is for recycling purposes. And then what you do is. Make the stack top. Point to the new stack. Top and if free, dlt pointer. What do you going to doing here is, string is the node. That has been deleted. And decrement the stack count and return the value of stack. This is code for the pop stack. Both these cases the stack is represented using a linked list and these particular data structure is very useful. When we are doing for organizing the nodes in an allocated list. It is called allocation list. And these represented linked list. Who store all the nodes are has been deleted are when you want to delete. You store for recycling take allocated list. Which is represented as stack. When you want to insert to take a node from same allocated list. So the next stack top is already discussed before stack top doesn’t change stack at all. Just access the top element of the stack. So again if the count is only greater than zero. That mean stack doesn’t contain anything. Then just take out the pointer to the top element. Make that data to be returned in data pointer and return 1. If it is less than 0. That means no stack. So you return. So that is top. Know hearing to change of the list, this is can normal thing. And empty stack a stack count. So what you do here in. if the count is equal to zero then the return value. Otherwise the stack is not empty. This is a code for Boolean function. This is an empty stack. Which
is return value from the stack is empty. Which is value is false. The stack is not empty. This is return a count. So already maintain the count. There are implementation do not maintain count of the stack. Certain implementation you maintain count .so return stack. That is it. So the count can be equal to zero. The stack is empty. You can also check for full stack. This is assuming that u have decided that only so many nodes going to give for the stack. This is a stack. If you have stack full condition then malloc is failed. If malloc is failed, it means, you cannot there is no temporary node to be given to for the operation. In which case you have a return 1. So this is a full stack. Where you cannot, remember that in full stack condition checking whether there are nodes available for putting into the stack. If there are not saying full otherwise putting full. This is not like an array implementation already allocated the size of the stack. This is the destroying stack Destroying complete stack. So you want to delete all the nodes in the stack. So if the stack top is null it means already stack is empty. You don’t have after do any destroying. So if it is not null. Then you make delete pointer to point to the top of the stack top of the point to the next node and free delete pointer. You keep doing this. Till the stacks it will come. Come to the last node in the stack. The Stack is now empty then the destroy the head node. So free that and you return null. So this here having a by loop. Here this is the logic. Where you keep on deleting nodes of push. Popping of the nodes. Till start becomes. Now what you seen upto now is the some of the implementation of stacks. Where we look at linked list implementation of the stack. In this particular implementation of the stack. What you done is we are assume that you have a count. Also it is not necessary. So in case you don’t have a count the code has to be appropriately modified. Stack Applications Now let us go to next some of the application. Using stack. Very interesting applications. I said used in no.of places in computer science itself. For example, the stack is a particular specific data structure that is used for quick sort algorithm is a difficult data structure. It also used in other applications. Like very important application where you have to maintain the program counter and return address in the case of recursive calls in function calls. So this is very important data structure as well as computer science.is concerned. We are looking at 2 very different application. One is the depth first search. And one is the N_Queens problem. So let us first look at the depth first search. The depth first search actually backtracking type of concept. That it uses. And this backtracking type of concept we do use stack. Stack is a difficult data structure that is used for doing back tracking. So this problem as follows discover a part from start to goal and
the solution you have to go deep. If there is an unvisited neighbour go there then you retreat along the path to find an unvisited neighbour. The outcome is if there is a path from the stack to goal. DFs very finds such a path. So that is going to go deep and cannot enough to do. Go to DFS wise. That is an idea. So this is a difficult application of a stack. So let us soon given a tree and if you want to find the goal. So initialize to start at 1. That is pushed on to the stack. Then you go to two depth number. To get to the child. So push 2. When you push 5. 5 has no children so you go to the sibling with 6. Then Go to child 9. After then you don’t have anything. So Pop it up. Pop is 6 out. Then pop 5 out. Pop 2 out. When you go to the next child which is 3. Then you go to 7. Then you go to 10. That is depth first we go to 10. Now you have identifying the value. So that the path followed 1,2,5,6,9. Then back tracking up and then go to 1. Find the next child go down. Ok. That is the path followed by the depth first search. So let us algorithm for the DFS. So the stack is first initialized. And you stack the operation look at push start. Now while the stack is a not empty. This is keep track. You data in the top element. If it is the goal you just put access. If T has a unvisited neighbour. Choose an unvisited neighbour n. Mark N as visited and push n into the stack. Otherwise that is if doesn’t have a unvisited neighbour. When you backtrack take in the next node from the stack. Keep doing this. Till stack is empty. Are you reach the goal? So this is the DFS algorithm. Of course you searching the node in a algorithm you can also happen that here may be a failure. So this is a difficult application of stack. Where the stack is used to maintain the node. When we want to do the DFS algorithm. As specially backtracking algorithm. This is a difficult data structure that used many concept used back tracking. Also used stack is a basic data structure. For implementation purpose. N-Queens Problem
Now you going to look at what is the N_Queens problem? This is a difficult problem in artificial intelligence and the N_Queens problem is actually problem associated with the chess board. So in this lecture I will explain the problem and then how it is solved using the stack. OK. So first let us see what the problem is the NQueens problem can be defined as follows. It is a backtracking problem to solve the NQueens. Suppose you have 8 chess queens & and a chess board. Can the queens be placed on the board? So that no two queens are attacking each other? Now what do you mean by attacking. We will see that as we go long. So the problem is this. Two queens are not allowed in the same row, or in the same column. Or along the same diagonal. So that is the idea. So 2 queens are not allowed on the same row, and the same column, or along the same diagonal, the no.of queens and the size of the board can vary.
Normally use all this problem for the NQueens problem. We are going to take it can simple example and show you. But basically solve it for any queen. It after all chess board is the square. So you can 64 * 64. Where N = 64 and so on. So basically NQueens can be represented this way you consist of NQueens. And chess board that you have consist of N rows and N columns. So your aim is placed NQueens on the boards. Such that if you have a queen here. We don’t have queen anywhere here and also don’t have anywhere queen here. So you gone queen same diagonal on the same row, same columns, along this same row. That’s the problem so are idea is to try to find solution to this problem. The computer program to solve this problem. Program tries to find a way to place N queens on the N * N chess board. Following the instruction we already seen. Now comes the application of stack. We going to uses a stack to keep track of where each queen as already been placed. So first place a queen on the board. The position of the new queen is stored in a record which is placed in the stack. And also you have an integer variable to keep track of how many rows have been filled so for. So these are two things that a going to use keep track of how to place the NQueens. So the is how the program works you have take 4 */ 4 board in very simple example to show the how the program works and this is the no. of queens to be filed. Which is 4 and this is stack to be used. Stack contains record. Which gives the position of the queen. Which is 1,1 is the position 1,2 mean this 1, 4 means first row , 4th column and so on. And this is the variable. Which keeps track of how many queens have already been placed. OK. This is the way. This is the complete show. You have a N * N board. You have NQueens, you have a stack. Which give the position of queen and you have the no. of queens that mean placed directly as the program. Now let us start the program. So first you place 1 here. Then you come do this what happen so that is 1,1 has been placed here. Then you come here. Now can you placed queen here, you can’t the queen placed here. Because along it a same diagonal so the logic uses that you shift it once to the right and see whether breaks it in a rules now that is no queen along the column, that is no queen along the row, that is no queen along the diagonal. So this is allowed. Now you have a queen at 1,1 you have a queen at 2,3 and 2 have been filled. Now we are to place this. N row you can place it here. Can’t place it here. Because if it is in the diagonal. So what you do is? Go up here and place it here. can you place it here 3, 4 so 3 rd row, 4 Th column you can’t place it here. Because of the fact at that along diagonal. How the program works? When we run out of remove in or row, pop the stack,
reduce filled by 1 and continue working on the previous row. Let us look at that. What is mean these? When you can’t place, pop it off. Go to the previous row and you see whether place it along that. Along the right or left. You will see the logical as we see go long. Again I tell you. When we run out of room in a row, pop the stack, reduced filled by 1 and continue working on the previous row. Whatever you placed in the previous row, here are having so ok. That is what is happened here. This is r th position. We still have to queens 2. And reduced filled by 1. Now we continue working on row 2, shifting the queen to the right. Now instant have it here. We pop it up. And shifting the queen here. Now thus has to been incremented this position has no conflicts, so we can increase filled by 1, and move to row 3. So now we move to row 3. Ion row 3 what happens, we can’t place it here. Because diagonal. So placed it here. And then we go to 3 one. And this is the conflicts. We stack again first column conflicts. Second column that is no conflicts. So that is how we so along to the problem. You can work it on row. You see how 4 queens are filled. So the logical basically to be repeat. That is you take the row placed a queen there. Then you go to the next row place the queen there. When conflict arises. What you do is? You tried to push the queen to right. If it is possible and you know no conflicts arises. If you come across a conflict then you pop the top element from the stack. That’s you are a backtracking. You are not using that. Already placed it, removing from the stack. Which remove it. And try again to reworks on the previous row and that’s how you do the queen. Nqueens problem. So for are nqueens problem. Let us see this is slightly different from the problem. That mean normally used. We are going to first talk about the pseudo code.so here what we do is. We first initialize the stack. Which is date structure. We want to use. Keep track of artificians and we also place the first queen. Pushing its position onto the stack and setting filled it equal to be 0. This is pseudo code repeat these steps. If there are no conflicts in the queen then we do else if there is a conflict and there is room to shift the current queen right ward do it. Else if there is a conflict and there is no room to shift the current queen right ward then what we do. You have do keep on doing this. Repeat these steps. There are no conflicts increase filled by 1. If filled is now what then doing here and take this each of the steps and giving the details. If there are no conflicts with the queen what we do increase filled by 1. If filled row is now N. That means filled all the queens then the algorithm is over. Otherwise, move to the next row and place a queen in the first column. So that this steps is over. So what we and done is. We done this. If you take one queen ok. We are placed it the first in the row. We see there is a conflict. Then there is a conflict moving a right. If there is a conflict and
there is a room to shift the current queen rightward. Move the current queen rightward adjusting the record on top of the stack to indicate the new position. So, this is in the same row. Even that you can’t do. Position where you have can’t fill the there is conflict. Can’t move rightward and fill. Because there is a conflict again. If there is a conflict and there is a room to shift the current queen right ward. This is place to have do a back. So what you do. You keep popping the stack and reducing filled by 1. Until you reach a row where the queen can be shifted rightward. When you shift this queen right. Then what you doing is. What ever done before you backtracking. Can backtracking till you reach the position? Where you can have another alternative. Which is not placing that. But moving it to the right. If it is possible. So the movement to the right once step of the time. But you move one also. So that is the NQueen problem. By the NQueens problem is very challenging is that. We are actually redoing the work. We already done. So that we get the choice of what we doing actually in the algorithm is we first start with the easiest method. Placed the first row that we see. Then we keep on doing it till the and the second we can take is every ok. When I placed in that place there is a conflict. So I will let move right to see. If you move to right and see, fill a conflicts. So I will let more right to se. If you move to right and see, fill a conflicts. Only then I go back. And I check whether. What I will done can be changed so that’s can be accompanied. You can properly try thus for 6 * 6 or 4*4 on your own on. Similarly act how it works. That will be a good exercise for you. When you for you do understand. How the stack works and how backtracking algorithm work also. That is explain both the concept of backtracking as well as the application of stack to backtracking. Now let us look at some problems. Associated with stacks. There is know up to implementation of stack.

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Data Structures - Lecture 3

 Data Structures - Lecture 3
Data Structure
Lecture 3
STACKS Stacks are a very important data structure and are necessary for implementing the logic behind many programmers. So let us look at start at the end of this lesson. we objective of this lesson this to introduce the concept of this stacks and then look at the operations of the stack and then the applications of the stacks these are thinks we going to talk about in this lesson before we go to on to the complete aspect of stacks as you know there are stacks every day in our life like stack of shirt, stack of books and stack of boxes and so on. As you see the idea is that normally when you take out the first shirt you take give be the top shirt of this stack and so on. So these are otherwise (57 sec) fall down and this catch in very carefully the same concept in applied to stacks in data structure. So this is the typical application of stack there will have stacks of book and stacks of coins at the same think represented in computer stack. Computer stack has gone to number of object set of placed one on top of other in a sense so another common linear data structure that I already talk to you about is stacks one you already seen its list and in one way the stack is nothing but the list but getter lot of restriction of how the list is used, then it became a stacks with the stack we have restricted to the access to the list to one end we take out the element from the stack using the pop element and we push element in to the stack using push operations. So the result of this restriction is that the list pile one on top of the other so basically talk about stacks we talk about when we what is call the last in first out policy. To get to the bottom item, we must first remove all the items above it another words so the behaviour is sometimes described as this is the policy we that talk about which is called is last in first out. So whenever you think of stacks you must think of it has last in first out whatever you put in last will be taken out first are so it’s called a LIFO and this is because I already told you that last item put in the stack the item removed first. So elements can be added and removed only at one end this end will call as the top of the stack with this stack the top item is always the last item to enter the stack and it is always the first item to leave the stack because no other items can be removed or added on to the stack without affecting the top element so let’s look at some terminology above the stack so the depth of stack is the number of elements it continues so suppose you have ten elements this stack it’s deep ten and you say that there are the depth is stack is ten and normally as obviously an empty stack is get a depth is zero. So why to be used a stack. Stacks provide a very efficient storage structure for manipulating data that is last in first out policy and stacks are often used as temporary storage to speculate the solution of a problem. So stack are restricted linear list as already told you of where
additions and detections are made only to the top and what happened is because of this specialization are restrictions that we do on the stack we can implement the stack using link list and we can also implement the stack using arrays and we think of ways in which in efficiency of the implementation can be improved. So as before you just seen basically what I stack data structure is you must remember that stack data structure is that restricted types of list and its follows the last in first out policy all access to the stack is to through the pointer call pop and through the top you can instead element and delete elements and the last item which has to be which has been instead the first item that is to be removed. Now let us look at all the operations that you can do on stacks. So first operations the do on the stacks .what is called a max item. Max that is nothing but the maximum number of items that would be on a stack. Now before you going to details about this that what the meaning of max item depends on the implementation of the stack so if it is arrays implementation. You already discuss array implementation they will be maximum size of the array and that will be the maximum number of elements you can put in the stack but how many elements has actually we put is the max item and item type can vary it can single and simple integer are we can a structure and we can as we saw list san be any data item they others are make empty that is an operation that make a stack completely and you can also have a Boolean operation call is empty that is to test whether the stack is empty or not similarly you can have Boolean is full the test whether the stack is full this actually make sense only you can talking about array implementation and next you have push (X,S) this is to add push an element X to the top of a stack S and then this is the function as this is the adds X to the top of the stack and the pre-condition is that in order to push in a element to the stack. The stack should not be full and the post condition is at after the push operation the element X becomes the top elements of the stack next you have pop S this is nothing but up to delete element an a stack it’s call pop the top most elements of from the stack and the functions of obviously its remove the element stack and return the item and the pre-condition has for any deletion operation for that can be matters this stack should next be a empty it has to be initialize and it has cannot be empty if it’s empty the pop operation is become un defined the post condition is that the top element would have remove from the stack and copy of item will be available and the top has been modified then you have something call has top S the stack S has it is hear is axis to the top most element of the stack hear no change occurs to the stack and only the top most element you will get the value of the element that’s it . So let us go little more in details about the operation of the stack so you have first the push. Push is add and item and the problem here is that you can over flow suppose you say the stack in contain ten item and it’s already full within ten item then you try to added another element eleventh element then the stack is overflow condition occurred this is the only for the array implementation and for the pop element you remove an element you can have already total you can have a underflow and the stack top is what the top is stack so this is the pop operation you end element and this is the stack pop operation where you take out it so let’s take this more in details so you have the take this more in details so you have the data that you want to push on the stack this is the initial stack of the stack. So for example the stack has to element and assuming the stack starts with the top is equal to one here you have the top is equal to two so now when you sit what happened is this the element data is pushed on to like this the top increment is one and the element stack size increases. Now let us assume we want explain the pop operation as you already know it moves data element from top of the stack initially the stack has three element and top now points to three when you do a pop operation there is no questions of which element to delete you can only delete the top most element the way the stack is defined so what you do you give the pop operation the top most element is deleted that is return and top reduces by one so this is the pop operation. Then look at this operation this is the stack top operation you don’t have any change in the stack. Stack has three element and also a three element top value here is three here top value is three and only think is you are able to access the element and value is given out please not when I say top is equal to 1, 2, 3 am assuming the array on the stack is which is told in a array and top start from one it’s not necessary you can start stack from hundred you can array location hundred and you can also store stack in link list then the meaning of this is different it here is explain it’s so you understand what the operation is this so let’s look at simple figure here if you look here in this step one you have the empty stack and given a data that you want to push on the stack now what happens here you will note the tope is equal to zero and the stack is empty now incremented top by one and pushing into green into the stack now this is the new condition is the stack is end. Then with that you add another element which is blue here so now top becomes two and belay pushed on the stack this is the condition of the stack after the second push operation then what you do you go to the see the pop given the stack of the stack if I just give pop there is no questions of which element is pop because pop the top most element so what happened after the pop operation blue comes out and this is new condition of the stack where top is been decremented by the one and blue is no longer present in the stack then next let’s see if you want added another element that element is push this is similar to at do it here and top increments by one then doing a stack top operation here what happens the state a stack is before and after the operation is same but only think if you can access the element then this operation and this operation is the same you just removed a element and here also you doing pop operation . you see here that is green has been removed that is top most element
from the stack has been remove the stack is empty now if you give pop operation there is error in the condition because the stack has is empty .so let us look at stack as an abstract data type so that means we are not bother about the implementation we going to using this stack so basically for any stack. Whatever the implementation the following at the operation of function that associated with the stack so one is create this means you just create an a empty stack for the implementation then the push you seen in of about the push. Push means added an element top of the stack then you have pop which means pop an element from the top of the stack you don’t have to specify the element because only think at pop from the stack is top element then stack top which you already defined that is you are accessing the top element of the stack no changing in the stack that is the top remains in the same number of element in the stack remains the same then you can also have full condition the question mark that we put here is you cannot check a full condition when you do a link list implementation of a stack because you can keep an adding notes dynamically but fill make sense in the stack is implemented as an a array and then empty is when the stack is element that is does not contain any element so this is the stack in empty condition so you can just look at this small data structure of this so you have a external interface you have a data structure and can have the data here so this is the data you want to input in to the stack this is just giving feeling of what is available outside. The outside is when you doing push you have indicate which element it is X. which stack you want to put it and similarly when you defining the stack you have to also know the access point that is top of the stack so one typical application of a stack is the famous parenthesis matching or matching of brackets so what it do here this you don’t have a matching parenthesis here so what it do you input when you see the traverses list from this corner when you see the bracket you put it in the stack then you see the other bracket . Put it the stack then you see an a just pass it don’t be anything you see plus B don’t be anything then you see the closing bracket. So you look at this stack and C whether whatever you have top of the stack matches this if it matches you removed that so now you left with is one bracket one that we put here then you see a divide sign don’t be anything just pass it C. don’t be anything then you finished you come to the end of the expression when you come to the end of the expression if it was matching expression. You should have add the stack is empty unfortunately now the stack is contain the single bracket so you know that the equation has not brackets have not been matched if you look at this same think you can do it surffency you see that this you will put on the stack. Then here you will you put on the stack again are left with closing bracket that is not matching so here are matching we a put in this on the stack then you putting a open parenthesis and the stack then you have a matching closing parenthesis which will cancel each other that will left with in
open parenthesis here you will left with the closing parenthesis but however you do that always you should have the stack is empty then only it’s matched now in this example you take on simple example there is only one type of bracket you can have any type you can have square bracket and check the corresponding matching. 

 

So you can actually do parenthesis matching automatically using the stack data structure for any type of complex expression so as we already saw the stack ADT can have several implementations. Implementations may be different but implementation details are be hidden and the interface function have to be the same and most application programmes should not see any difference just because using array implementation arm using a stack implementation. So let us first look at the stack implementation using an array so stack is stored as an array when you stored stack is an array immediately it means that the number of element has to be allocated that is how many element this stack in cold so I can here constantly look at the stack as we done before so I have defined something called as defined stack array and then have a something called as stack max. Stack max is maximum number of elements that I can store is physical array and top tells be the top element you can actually not have the count also the doesn’t matter but stack array, stack max, and top has to be defined. If you want to define a stack using array so implementing stack using array. It’s a simple implementation. The size of the stack must be determined when a stack object is declared space is wasted if we use less elements suppose you have a stack you declared it have hundred elements and usually the stack within ten and fifteen then you wasting the space and we cannot push the more element and then the array can hold. So this is the typical definition of stack of integers in an array implementation. So what you doing here is we are declaring the array call stack array and then this is the number of element at count then stack max this is equivalent to what we saw before for this . We are defining the structure so this is the maximum element and this top is the index of the top element. So all of them are integers in this case so first step here is creating a stack so you will say the create a stack with maximum elements ok so if the stack is equal to null check as stack is empty you return a null otherwise you going to now you going to allocate the stack. So first what we do you initialize the top of the stack to be minas one and count is equal to zero remember this is stack which is empty. So doesn’t have anything. So you can defined the top of many way in this implementation have a initialize. The stack to be minas one and stack count be equal to zero that is same and then stack max has been initialize to the maximum. Number of elements that we want the stack hold and the stack array that is the complete array defined as allocate maximum element into size of the element size. So if stacks stack array is equal to null. Then that means free all free the stacks always return the null so it done here this you creates at a stack which called stack array which has top is equal to minas one
count is equal to zero and the stack max equal maximum number of element. So next let as look at the push operation so the push stack you have when you remember when I told you told that you have a push stack operation you have two think as to define one is the stack array which is the array in which you want to push into the next is data element that we want to push so first for any push operation infect this is two five any in session operation you have first check whether there is place to instant the element in other words. So for that we are doing a stack check full stack check. So here what you doing is if the count of the number of elements is equal to the maximum number of elements is stack can hold then we are returning zero let us it is over flow and the number of elements in this stack equal to the maximum number you can hold and you cannot add any more elements otherwise when you come out this it means that you have to place the hold elements but in case what you do is you increment the count so the number of elements in the stack increases by one you increment pop by one because now want to create to a place pointed at to this top, there you want to inset the element and then what you do you with array at the position calls top you inset the elements that you want to inset and you return one . just this indicate that the push operation has been success if it already full then you did have return zero which means that there is the problem there is an error and this condition the error is a overfull. So this is how you do please note here we are first incrementing talk to create place and then we are putting the element into the top position so next let look at pop operation again as you know in any deletion operation you should have something to delete so in deletion operation you will get an under flow the same is true for stack. So here what you do you given a stack given data output pointer this is the data you going to output and given a stack you can you did not have the as in input parameter you can gives the stack and you can delete from that but here want to get out what is top on the stack for that’s why having the extra parameter some pop operation implementation do not look at this is a separate parameter inside the pop operation. One of the example. We saw people we did not have to parameters for the pop – operation. So here what you do this please remember this is array implementations? So what you do is you first. Check whether stack is empty if it is empty then you cannot do a deletion operation, became you don’t know anything to delete. So you getting underflow condition otherwise what you do is you have to take out the them the list of the stack so what you do the access is top element of the stack and take it out is the variable call data output points and decrement the count by one because round in the count number of element is decreased and decrement top also by one because previously whatever top is pointing to is now a empty so end don’t want to access is you will decrement all and return one indicate one it is successful operation this is the top operation this function retrieve the data is the top of the stack without
changing the stack so again as we already saw pre-conditions stack is pointer to the stack and post return one its success zero is under flow so have what you do is we have the stack again and this is the output pointer as we did in the pop operation so it the count is greater than zero than only you can do the operation. If it is can then zero you don’t have to access at all because these stack in empty you don’t have a element so it is next zero that this then element greater than zero that is element so you just take out the elements not take out you just access the element but remember no top changing nothing change is the count does not decrease nothing happens only think is accessing the top element so hear after the top operation this stack remain same is as already told you and returning zero this return zero is if not able to do the operation because of count being not greater than zero which mean that’s the stack is this is the condition check whether the stack is empty as next so the pre-condition is stack is pointer to the stack and post condition is if returns one its empty and zero is there is data is this stack so here what you do is again the input the stack and you that’s the structure stack. If the count is equal to zero that means is an empty stack. You just Boolean you will return the value that is true value similarly full this function determine the stack is full so fully detained as heat full ok heap full for latter so pre stack is pointed to the stack head note suppose if return one heap for stack is full and zero is heap as room what you do here is this is full stack condition again we have the complete structure now here because its and array implementation then you know the stack is full then the count is equal to these stack max so if count is equal to these stack max so if the count is equal to the maximum element the stack in held then we know that the stack hen full then you return the value now Growable tray – based stack this is the slightly difference diversion of what will apposing to say In a push operation, when the array is full, instead of throwing an exception, we can replace the array with a larger one. How large should the new array be? Incremental strategy: increase the size by a constant C. doubling strategy, double the size, what you mean by here is we docent usually know cannot predict how much the size of stack will be now the problem here is that you have if you put stack is 1000 elements are using one 10 or 15 eliminating wasting are memory resources are then have you put is or 10 elements you against to 20 or 30 elements then you concisely you will getting a stack full condition. So one we doing this is have global array stating what will you do is if you get stack full condition that point you reallocated larger array and then put all the stack elements is to that array so this is not a very simple operation. This is changing of elements from one array to other bus assume that you can do that but two strategists of how the largers array allocated how much of how much should be one think you going to suppose the original stack size is 10 and you a have stack full condition you can increased by constancy size 5 and every time to get a stack full condition keep
increment, increasing it by 5 please not this depends of the explication purely on the application. How you have a doubling stratarge Initially I will put 10 I will act put 10 and then came now will have stack size of 20 again can put 20 and so on. So this is a predict. So depending of the application you do this now we go the next type of implementation plus please not but when I said we going of global array after you stack full condition is array happen when you allocate a larger array that is the lot of completion on work needed transfer this array implementation of next array implementation. So this not to travel operation so this not to say that global array is a solution to the problem of using of array stack operator so next implementation in the link list implementation. So here what you do is you have to understand the concept of an abstract data type again you already seeing this and you need to see understand nested implementation and you need to see some application of link list so every data of course touch a goes also top link list implementation of stack. So this is the typical link list implementation of a stack so here you see that this is conceptual view here the conceptual view of whether you implement of the stack using link list are whether implement the stack using array conceptual view is same but when you look at this now what you have the bottom most element will have the link pointer to be equal to zero and then you have the next element pointing to this element pointing to this, this element pointing to this and count is the number of element in the stack before and top now giving the address of the top most pointer, this link is given the address of the next top most the bottom most element. The address link will be equal to zero this is the link list implementation of the stack. Now let’s look at this is no count this is the top this is the before you create a stack now look here you are incremented. This is the a creating a empty stack so what happened this you have count equal to zero and top pointing to null still the stack is empty you just created a stack now let us look at push operation now what happens the count is zero the top most equal to zero now what am doing am creating a node to put green this is the same operation what we saw when we did link list implementation of a stack so what happens after this green I have to change the address of this stack from null to the address of this node and this next here has to be null so next is again a push operation now this has to be now node has to be created and please note that is new node will come here because now this is we comes the bottom most node and the top has point to the most reason node and top most node now what will have to increment the count by two this buy will point to the new node and the next of the new node will pointed to the previous top so this is what happens is the blue has to be removed so now top will point to green again and blue will be removed it’s blue will be entered here and blue will be removed from there so if you want to distributed stack what you do this you make a count zero. If you don’t have any point of from top address of

top immediately stack not accessible all so disturbed the stack. So here you have two data structure that we using two modes that using one this is stack head other this stack node so this stack will have a count and top which is count an integer and top is a doubt pointer this will have a data type and this will be a link which is again note point this is similar to structure that we used for this but here the operation are restricted I already told you that again this data type can be a single data type or have a large record whatever so the key data structure of this structure that used this CR again a node with key integer data and struck node which is an address and you can also have stack and the stack is represented by a count and the stack node pointing to the top so let us look at operation a stack so when you create a stack you have a pointer to the stack and you have allocate this equal to be size of the stack. So if stack equal to null then you initialize the top and have you going to this is creation of the stack remember and you already seeing here how do you create a stack what do you this to put the count equal to zero and top equal to null that is exactly what you a doing here putting the top equal to null and count is equal to zero and the address of the stack is return this is the allocating the size of the I mean allocating stack to be dynamic allocation of a node.

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