100 Prisoners Riddle Simulation

prisoner100.py

import random

# Increasing this will have a drastic effect of total running time
NUM_PRISONERS = 100
BOXES_ALLOWED = NUM_PRISONERS // 2

##### CONFIG #####

# Number of simulations to run
# It will run 100 times with 'NUM_PRISONERS' in each run
# Doesnot have much effect in total running time
NUM_SIMS = 1000

# Prints info such % completion of the simulation and
# number of prisoners who found thir numbered slip in each sim
OUTPUT = True

lives_random = 0
lives_loop = 0

for s in range(NUM_SIMS):
    # Create a list of numbers for the prisoners
    PRISONER_NUMBERS = [n for n in range(1,NUM_PRISONERS+1)]

    class box:
        def __init__(self,count):
            self.label = count
            self.slip = PRISONER_NUMBERS.pop(random.randint(0,len(PRISONER_NUMBERS)-1))

    # Create a list of boxes and add randomly numbered slips in them
    BOXES = []
    for count in range(1,NUM_PRISONERS+1):
        BOXES.append(box(count))

    random_count = 0
    loop_count = 0
    for my_prisoner_number in range(1,NUM_PRISONERS+1):

        # Pick randomly to find slip
        boxes_copy = BOXES.copy()
        for _ in range(BOXES_ALLOWED):
            picked_box = boxes_copy.pop(random.randint(0,len(boxes_copy)-1))
            if picked_box.slip == my_prisoner_number:
                random_count += 1
                break

        # Go in loop
        starting_box = BOXES[my_prisoner_number - 1]
        for _ in range(BOXES_ALLOWED):
            if starting_box.slip == my_prisoner_number:
                loop_count += 1
                break
            else:
                starting_box = BOXES[starting_box.slip - 1]
                 
        if random_count == NUM_PRISONERS: lives_random += 1
        if loop_count == NUM_PRISONERS: lives_loop += 1

    if OUTPUT:
        precentage_complete = f"{str(round(((s+1)/NUM_SIMS)*100,1)).zfill(5)}%"
        live_str = '   🥳'
        dead_str = '💀   '
        print(f"[{precentage_complete}]\t\tRandom : {live_str if random_count==NUM_PRISONERS else dead_str} ({str(random_count).zfill(3)})\t\tLoop : {live_str if loop_count==NUM_PRISONERS else dead_str} ({str(loop_count).zfill(3)})")


# Calculate probability
prob_random = (lives_random/NUM_SIMS)*100
prob_loop = (lives_loop/NUM_SIMS)*100

print("---------------------------------------------------------")
print(f"Probability Random : {prob_random}%\tProbability Loop : {prob_loop}%")
print("---------------------------------------------------------")