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DESIGN & ANALYSIS OF ALGORITHMS

Learning Outcome 1

LEARNING OUTCOME 1

Programming Paradigms

Programming paradigm refers to a fundamental style or approach to organizing code. Different paradigms dictate how data is structured and how operations are performed.

Imperative Programming

This paradigm focuses on describing the sequence of steps (commands) to be executed. It's like providing a recipe with explicit instructions. Variables are used to store data, and control flow statements (if-else, loops) guide the execution.

Object-Oriented Programming (OOP)

OOP models the real world as objects, each with properties (data) and behaviours (methods). It promotes code reusability through inheritance and encapsulation. Objects interact by sending messages to each other.

Functional Programming

Functional programming emphasizes functions as the building blocks. It avoids side effects and treats data as immutable. Functions are considered first-class citizens, meaning they can be passed as arguments and returned as values.

Event-Driven Programming

This paradigm is reactive, waiting for events to occur before responding. It's commonly used in graphical user interfaces (GUIs) and network programming. When an event happens (e.g., button click), a specific function is triggered.

Difference Between OOP and POP

Feature OOP POP
Focus:Objects and their interactionsSequence of instructions
Data:Encapsulated within objectsStored in variables
Code Organization:Classes and objectsProcedures and functions
Abstraction:Achieved through inheritance and polymorphismAchieved through procedures and functions
Reusability:Promoted through inheritance and encapsulationPromoted through modularization
Modularity:Encouraged by classes and objectsEncouraged by procedures and functions
Control Flow:Often event-driven or message-basedPrimarily sequential
Side Effects:Minimized through encapsulationMay be more prevalent

OOP CONCEPTS

Encapsulation

Encapsulation is the bundling of data and methods (functions) that operate on that data within a single unit, called a class. This hides the internal implementation details from the outside world, providing data security and preventing accidental modifications.

Polymorphism

Polymorphism allows objects of different types to be treated as if they were of the same type. This enables code to be written in a generic way, making it more flexible and reusable.

Inheritance

Inheritance is the mechanism where one class (derived class) acquires the properties and behaviors of another class (base class). This promotes code reusability and hierarchical relationships between classes.

Data Abstraction

Data abstraction is the process of hiding unnecessary details from the user and providing a simplified view of the data. This helps in managing complexity and focusing on essential features.

Class and Object

A class is a blueprint or template for creating objects. It defines the properties (data members) and behaviors (methods) that objects of that class will have. An object is an instance of a class. It represents a concrete realization of the class with its own values for the data members.

Examples that demonstrate the concepts above

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#include <iostream> #include <vector> // Encapsulation: Data and methods are bundled into a class class Circle { private: double radius; public: void setRadius(double r) { radius = r; } double getArea() { return 3.14159 * radius * radius; } }; // Inheritance: Cylinder inherits from Circle class Cylinder : public Circle { private: double height; public: void setHeight(double h) { height = h; } double getVolume() { return getArea() * height; } }; // Polymorphism: Different shapes with a common interface class Shape { public: virtual void draw() = 0; // Pure virtual function }; class Rectangle : public Shape { public: void draw() override { std::cout << "Drawing a rectangle\n"; } }; class Triangle : public Shape { public: void draw() override { std::cout << "Drawing a triangle\n"; } }; // Data Abstraction: Hiding implementation details class BankAccount { private: double balance; public: void deposit(double amount) { balance += amount; } void withdraw(double amount) { if (balance >= amount) { balance -= amount; } else { std::cout << "Insufficient funds!\n"; } } double getBalance() const { return balance; } }; int main() { // Encapsulation Demo Circle circle; circle.setRadius(5.0); std::cout << "Circle area: " << circle.getArea() << std::endl; // Inheritance Demo Cylinder cylinder; cylinder.setRadius(3.0); cylinder.setHeight(10.0); std::cout << "Cylinder volume: " << cylinder.getVolume() << std::endl; // Polymorphism Demo std::vector<Shape*> shapes = {new Rectangle(), new Triangle()}; for (Shape* shape : shapes) { shape->draw(); } for (Shape* shape : shapes) { delete shape; } shapes.clear(); // Data Abstraction Demo BankAccount account; account.deposit(1000.0); account.withdraw(500.0); std::cout << "Account balance: " << account.getBalance() << std::endl; return 0; }

Algorithms

What is an Algorithm?

An algorithm is a sequence of well-defined instructions designed to solve a specific problem or perform a task. Think of it as a recipe, where each step guides you towards a desired outcome. In computer science, algorithms are the backbone of problem-solving and software development.

Characteristics of an Algorithm

  • Finiteness: It must terminate after a finite number of steps.
  • Definiteness: Each step must be precisely defined and unambiguous.
  • Effectiveness: Each step must be executable.
  • Input: An algorithm takes zero or more inputs.
  • Output: An algorithm produces at least one output.
  • Correctness: It must produce the correct output for all valid inputs.

Benefits of Using Algorithms

  • Problem-solving: Algorithms provide a systematic approach to solving problems.
  • Efficiency: They can help in finding efficient solutions to problems.
  • Clarity: They improve the clarity and understanding of a solution.
  • Reusability: Well-designed algorithms can be reused in different contexts.
  • Automation: Algorithms can be automated to perform tasks repeatedly.

Types of Algorithms

Brute Force

This approach tries all possible solutions to a problem and selects the best one. It's often inefficient for large problems.

Greedy

A greedy algorithm makes locally optimal choices at each step, hoping to arrive at a globally optimal solution. It doesn't always guarantee the best solution.

Recursive

A recursive algorithm calls itself to solve smaller instances of the same problem. It's often used for problems that can be divided into smaller subproblems.

Backtracking

Backtracking explores different paths and backtracks if a path leads to a dead end. It's often used for problems with constraints.

Divide and Conquer

This approach divides a problem into smaller subproblems, solves the subproblems recursively, and combines the solutions to solve the original problem.

Dynamic Programming

Dynamic programming is used for problems that exhibit overlapping subproblems and optimal substructure. It avoids recomputing the same subproblems by storing their solutions in a table.

Data Structures

A data structure is a way of organizing and storing data in a computer's memory so that it can be accessed and manipulated efficiently. It provides a logical representation of data and defines the relationship between different data elements.

Advantages of Using Data Structures

  • Efficient memory utilization: They help to optimize memory usage by organizing data in a compact and efficient manner.
  • Improved performance: By choosing the right data structure, you can significantly improve the performance of your algorithms.
  • Better code organization: Data structures can help to make your code more organized and easier to understand.
  • Enhanced code reusability: Many data structures are commonly used and can be reused in different programming projects.

Linear vs. Non-Linear Data Structures

FeatureLinear Data StructuresNon-Linear Data Structures
ArrangementElements are arranged sequentially.Elements are not arranged sequentially.
AccessElements are accessed one after another.Elements can be accessed in multiple ways.
ExamplesArrays, linked lists, stacks, queuesTrees, graphs, sets, maps
TraversalElements are traversed in a linear fashion.Elements can be traversed in different ways (e.g., depth-first).

Static vs. Dynamic Data Structures

FeatureStatic Data StructuresDynamic Data Structures
Memory allocationMemory is allocated at compile time.Memory is allocated at runtime.
SizeThe size of the data structure is fixed.The size can change dynamically.
FlexibilityLess flexible as the size is fixed.More flexible as the size can change.
ExamplesArraysLinked lists, stacks, queues, trees, graphs

Major Operations on Data Structures

  • Insertion: Adding a new element.
  • Deletion: Removing an element.
  • Search: Finding a specific element.
  • Traversal: Visiting all elements.
  • Update: Modifying an existing element.
  • Sorting: Arranging elements in a specific order.

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