Calculate the expected percentage of pairs of socks recovered after randomly washing a sample

socks.py

# Calculate the expected percentage of pairs of socks recovered
# after randomly washing a sample

from random import shuffle, sample
from collections import defaultdict
from time import clock

PAIRS = 20.0
EXPERIMENTS = 1000000



def pile(num_pairs):
  p = [sock for sock in range(int(num_pairs))]
	p.extend(p)
	shuffle(p)
	return p

	
socks = pile(PAIRS)

def num_washed_pairs(num_pairs,sample_size,debug=False):

	wash = sample(socks,sample_size)
	
	sock_counter = defaultdict(int)
	for sock in wash:
		sock_counter[sock] += 1

	

	
	result = float(sum([ v // 2 for v in sock_counter.values() ]))
	
	if debug:
		print socks
		print wash
		print sock_counter
		print result

	return result

def run(num_experiments,num_pairs,sample_size):
	results = []
	for i in range(int(num_experiments)):
		results.append(num_washed_pairs(num_pairs,int(sample_size))/num_pairs)

	print "expected %% of sock pairs: %.5f" % (sum(results) / len(results))

if __name__ == "__main__":
	#num_washed_pairs(PAIRS,PAIRS,debug=True)
	start = clock()
	run(EXPERIMENTS,PAIRS,0.75*2*PAIRS)
	print "time elapsed: %.4f" % (clock() - start)