from pprint import pprint
from collections import defaultdict

# Number of stats
STATS = 7

# Max SV value
MAX_SV = 50

# Minimum total SVs
MIN_TOTAL_SVS = 168

def calc_distribution():
	# distribution[(n, k)] = number of ways to get total svs n with exactly k perfect svs
	distribution = {(0, 0): 1}
	for stat in range(STATS):
		new_distribution = defaultdict(int)
		for sv_sum, num_perfect in distribution:
			for sv in range(1, MAX_SV+1):
				new_sum = sv_sum + sv
				new_perfect = num_perfect + (sv == MAX_SV)
				new_distribution[new_sum, new_perfect] += distribution[sv_sum, num_perfect]
		distribution = new_distribution
	return distribution

# Reduce on perfect_sv count given that sv_sum >= min_sv_sum
# Returns map of perfect_svs -> number of ways that this can be generated.
def reduce_distribution(d, min_sv_sum):
	distribution = defaultdict(int)
	for sv_sum, num_perfect in d:
		if sv_sum < min_sv_sum:
			continue
		distribution[num_perfect] += d[sv_sum, num_perfect]
	return distribution

def main():
	distribution = calc_distribution()
	x = reduce_distribution(distribution, MIN_TOTAL_SVS)
	pprint(dict(x))
	print "Total: %d" % sum(x.values())
	print "Probability of 1+ perfect SV: %f" % (float(sum(x.values()) - x[0]) / sum(x.values()))


if __name__ == '__main__':
	main()