Step by Step solution about How to resolve the algorithm Sleeping Beauty problem step by step in the Java programming language

The provided Java code simulates the Sleeping Beauty problem, a thought experiment in Bayesian probability. In this problem, a princess is put to sleep for a hundred years and awakened by a prince at the end of that period. While she sleeps, the prince flips a fair coin and, depending on the outcome, either awakens her immediately or keeps her sleeping for another hundred years.

The code simulates this problem by flipping a coin a large number of times and counting the number of times the princess is awakened. It then uses this data to estimate the probability that the coin landed on heads, which is the probability that the princess should believe she was awakened in the first 100 years.

Here's a detailed breakdown of the code:

1. Importing necessary libraries:

   • The code imports the ThreadLocalRandom class from the java.util.concurrent package, which provides a thread-safe source of random numbers.

2. Defining the SleepingBeauty class:

   • The code defines a final class named SleepingBeauty that contains the main method for the program.

3. Main method:

   • The main method is the entry point of the program.

4. Constants:

   • The experiments constant specifies the number of experiments to run (1 million in this case).

5. Random number generator:

   • An instance of ThreadLocalRandom is created to generate random numbers.

6. Creating the Coin enum:

   • The code defines an enum called Coin with two values: HEADS and TAILS.

7. Variables:

   • heads: Counts the number of times the coin landed on heads.
   • awakenings: Counts the number of times the princess was awakened.

8. Simulation loop:

   • The code simulates the experiment experiments times.
   • For each experiment, it flips a coin and, depending on the outcome, either increments the heads count or the awakenings count.

9. Output:

   • After the simulation is complete, the code prints the number of awakenings and the estimated credence that the princess should have in the coin landing on heads.
   • The credence is calculated as the ratio of heads to awakenings, rounded to three decimal places.

Overall, the code simulates the Sleeping Beauty problem and estimates the credence that the princess should have in the coin landing on heads based on the number of awakenings she experiences.

import java.util.concurrent.ThreadLocalRandom;

public final class SleepingBeauty {

	public static void main(String[] aArgs) {
		final int experiments = 1_000_000;
	    ThreadLocalRandom random = ThreadLocalRandom.current();
	    
	    enum Coin { HEADS, TAILS }
	    
	    int heads = 0;
	    int awakenings = 0;	    
	    
	    for ( int i = 0; i < experiments; i++ ) {
	        Coin coin = Coin.values()[random.nextInt(0, 2)];
	        switch ( coin ) {
	        	case HEADS -> { awakenings += 1; heads += 1; }
	        	case TAILS -> awakenings += 2;
	        }
	    }
	    
	    System.out.println("Awakenings over " + experiments + " experiments: " + awakenings);
	    String credence = String.format("%.3f", (double) heads / awakenings); 
	    System.out.println("Sleeping Beauty should estimate a credence of: " + credence);
	}
	
}