Approximates e using bogosort.

bogosort_approximator.py

# Calculates e using randomized bogosort. The average number
# of comparisons per round should be close to e-1 due to
# shortcircuiting, so we run bogosort and keep track of
# the number of rounds and number of comparisons, and use
# that to calculate e.

import random

n = 10
xs = list(range(n)) # start with a sorted list to rub it in.
num_rounds = 0
num_comparisons = 0
done = False
while not done:
    num_rounds += 1
    random.shuffle(xs)
    done = True
    for i in range(n-1):
        num_comparisons += 1
        if xs[i] > xs[i+1]:
            done = False
            break

print('n:', n)
print('num_rounds:', num_rounds)
print('num_comparisons:', num_comparisons)
print('e:', 1 + num_comparisons/num_rounds)

Sample output:

$ python3 bogosort_approximator.py 
n: 10
num_rounds: 5583731
num_comparisons: 9595517
e: 2.7184776630536103