Step by Step solution about How to resolve the algorithm 100 prisoners step by step in the Ruby programming language

The provided code is a Ruby program that simulates the Monty Hall Problem, which is a famous mathematical puzzle that involves a game show host, a contestant, and two doors.

The code first defines a list of prisoners numbered from 1 to 100. It then defines a function called generate_rooms that randomly shuffles the numbers from 1 to 100 and adds a nil value at the beginning of the list.

The code then runs two simulations, each with N iterations (10,000 in this case), to estimate the probability of a prisoner escaping under two different strategies:

1. Random strategy: For each iteration, it generates a random room arrangement and checks if each prisoner is found in at least one of the 50 rooms they visit.

2. Optimal strategy: For each iteration, it generates a random room arrangement and simulates the prisoners moving from room to room, checking if they ever find their own room.

The code calculates the number of iterations where all prisoners escaped and divides it by the total number of iterations to estimate the probability of success for each strategy. Finally, it prints the estimated probabilities for both strategies.

One important Python-specific aspect of this code is the use of the shuffle function on the list of numbers from 1 to 100. The shuffle function randomly reorders the elements of a list in-place, so each time generate_rooms[] is called, it returns a different random arrangement of the room numbers.

Overall, the code provides a good demonstration of how to simulate the Monty Hall Problem in Ruby and calculate the probabilities of success for different strategies.

The provided Ruby code simulates the prisoners and hat puzzle to estimate the probability of success using two different strategies: a random strategy and an optimal strategy.

In the puzzle, there are 100 prisoners and each prisoner wears a hat. Each hat has a number from 1 to 100 written on it, and each prisoner can see the numbers on the hats of the other prisoners but not their own. The prisoners can communicate with each other, and their goal is to guess their own hat number.

The random strategy randomly assigns prisoners to rooms, and then each prisoner randomly samples 50 hats from their room. If their hat number is among the sampled hats, they guess correctly.

The optimal strategy starts with each prisoner in a separate room. Then, each prisoner moves to the room with the number on their hat. If two or more prisoners have the same hat number, they all move to the same room. The process continues until each prisoner is in a room with only one other prisoner, or until 50 moves have been made. If a prisoner is in a room with only one other prisoner after 50 moves, they guess correctly.

The code simulates both strategies N times and counts the number of times the prisoners guess correctly. The probability of success for each strategy is then calculated by dividing the number of successes by N.

The results are printed to the console, showing the probability of success for the random strategy and the optimal strategy. The optimal strategy is expected to have a higher probability of success than the random strategy.

prisoners = [*1..100]
N = 10_000
generate_rooms = ->{ [nil]+[*1..100].shuffle }
 
res = N.times.count do
  rooms = generate_rooms[]
  prisoners.all? {|pr| rooms[1,100].sample(50).include?(pr)}
end
puts "Random strategy : %11.4f %%" % (res.fdiv(N) * 100)

res = N.times.count do
  rooms = generate_rooms[]
  prisoners.all? do |pr|
    cur_room = pr
    50.times.any? do
      found = (rooms[cur_room] == pr)
      cur_room = rooms[cur_room]
      found
    end
  end
end
puts "Optimal strategy: %11.4f %%" % (res.fdiv(N) * 100)