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Josephus Problem Solver with Graphical Visualization

This project provides a graphical simulation of the Josephus problem using C++ and SFML for visual rendering. In the Josephus problem, people stand in a circle and are eliminated at regular intervals until only one survivor remains. This program visualizes each elimination step and highlights the final survivor with a graphical user interface (GUI).

Problem Statement

The Josephus problem is a classic counting problem where:

  1. N people stand in a circle, waiting to be eliminated.
  2. Counting starts at a randomly selected person and proceeds clockwise.
  3. Every k-th person is eliminated until only one person remains, who is declared the survivor.

Features

  • Graphical Visualization: Using SFML, each person is represented as a sprite that visually shows the elimination process.
  • Sound Effects: Each elimination and victory display includes sound effects for an engaging experience.
  • User Input: The program accepts the number of people (N) and the step count (K) as input from the user.
  • Customizable Radius: The circle size adjusts based on the number of people to maintain readability.

Getting Started

Prerequisites

  • C++11 or newer.

  • SFML Library: You need to install SFML (Simple and Fast Multimedia Library) for graphics, window handling, and audio.

    To install SFML, use:

    sudo apt-get install libsfml-dev  # For Debian/Ubuntu
brew install sfml                 # For macOS

Installation

  1. Clone the repository:

    git clone <https://github.com/Rebelhere/Josephs-Problem>
cd JosephusProblemSolver

  2. Ensure you have the necessary assets in the same directory as the executable:

    • 1.mp3: Background music during the simulation.
    • 2.mp3: Sound effect for each elimination.
    • 3.mp3: Sound effect for the winner display.
    • alive.png: Image to represent alive participants.
    • dead.png: Image to represent eliminated participants.
    • winner.jpg: Image to represent the final survivor.
    • 1.ttf: Font file for displaying text.

Building the Project

Compile the code with SFML:

g++ josephus.cpp -o josephus -lsfml-graphics -lsfml-window -lsfml-audio -lsfml-system

Run the program:

./josephus

Usage

  1. Start the program and enter values for:
    • N: The number of people in the circle.
    • K: The interval for elimination (every k-th person will be removed).
  2. The graphical window will open, displaying the participants in a circle.
  3. The elimination process will start, with each elimination shown in the GUI and accompanied by a sound.
  4. Once only one participant remains, they will be highlighted as the survivor with a congratulatory message and sound effect.

Code Overview

Key Files and Functions

  • Queue Class: Custom queue implementation used to manage the circle of participants.

    • Enqueue(T val): Adds a participant to the queue.
    • Dequeue(): Removes a participant from the queue.
    • kill(): Executes the elimination process by removing every k-th person.
    • josephproblem(RenderWindow& window): Manages the Josephus process and updates the GUI.

  • printwindow: Displays the current state of the circle, marking each person as either alive or dead.

  • printwinner: Displays the winning participant after all others are eliminated.

Graphics and Audio

  • Sprites: The program uses alive.png and dead.png for participants. The survivor is shown with winner.jpg.
  • Sound Effects:
    • Elimination events play the sound from 2.mp3.
    • Background music plays from 1.mp3.
    • Winner announcement plays 3.mp3.

Example

For N = 7 and K = 3:

  • The program displays a circle of 7 participants.
  • Each 3rd person is eliminated in clockwise order until only one remains.
  • The GUI updates in real-time, showing the elimination sequence and final winner.

Future Enhancements

  • Adjustable Parameters: Add user controls for adjusting speed and volume.
  • Different Elimination Animations: Introduce more visual effects for eliminations.

Contributing

Feel free to open issues or submit pull requests for improvements or bug fixes.

Collaboration Guidelines

We welcome contributions from the open-source community. If you'd like to collaborate on this project, please adhere to the following guidelines:

  1. Fork the repository.
  2. Create a new branch for your feature or bug fix.
  3. Implement your changes and commit them with descriptive messages.
  4. Push your branch to your fork and submit a pull request.

Feel free to reach out if you have any questions or suggestions !