josephus_problem

#!/usr/bin/env python
# -*- coding: utf-8 -*-
# Filename: josephus_problem.py
# Version: 1.0.0
# Author: Jeoi Reqi

"""

Description:
    - This script simulates the Josephus problem, where a group of people
      stand in a circle and are sequentially eliminated based on a fixed counting
      rule until only one person remains.

Requirements:
    - Python 3.x

Functions:
    - find_last_person(n):
        Simulates the elimination process in the Josephus problem and returns
        the index of the last remaining person.

Usage:
    - Run the script and input the number of people when prompted. The script
      will then find and print the index of the last remaining person. To exit,
      type '0' when prompted for input.

Additional Notes:
    - The Josephus problem has a mathematical solution, but this script
      simulates the elimination process for demonstration purposes.

"""

def find_last_person(n):
    """
    Simulates the elimination process in the Josephus problem and returns
    the index of the last remaining person.

    Args:
        n (int): The number of people in the circle.

    Returns:
        int: The index of the last remaining person.
    """
    circle = list(range(1, n + 1))  # Represent the circle of people with indices starting from 1
    p = 0  # Pointer to the current person

    # Simulating the elimination process
    while len(circle) > 1:
        # Each person counts twice per round
        p = (p + 2) % len(circle)
        # Eliminate the person at the current index
        circle.pop(p - 1 if p > 0 else len(circle) - 1)
        # Adjust pointer if needed
        p = p - 1 if p > 0 else len(circle)

    # Return the index of the last remaining person
    return circle[0]

def main():
    """
    Main function to interact with the user and find the last remaining person.
    """
    while True:
        print("""
      _                           _
     | |                         | |
     | |  ___   ___   ___  _ __  | |__   _   _  ___
 _   | | / _ \ / __| / _ \| '_ \ | '_ \ | | | |/ __|
| |__| || (_) |\__ \|  __/| |_) || | | || |_| |\__ \\
 \____/  \___/ |___/ \___|| .__/ |_| |_| \__,_||___/
                          | |
                          |_|
""")
        # Input the number of people
        n = input("\nEnter the number of people (or type '0' to exit): ")

        if n == '0':
            print("\nExiting Program... GoodBye!\n")
            break

        n = int(n)

        # Find and print the index of the last remaining person
        print("\nThe index of the last remaining person is:", find_last_person(n))

        # Prompt the user to hit enter to continue
        input("\nPress Enter to continue...")

if __name__ == "__main__":
    main()