Magic the Gathering faction list generator

faction_list.py

def check_faction_set_validity(factions):
	# count the number of on bits in each position for our list of faction IDs.  If they're all the same, then the faction list is valid.
	return factions and len({sum((faction >> k) & 1 for faction in factions) for k in range(5)}) == 1

def faction_string(faction):
	return ''.join('WUBRG'[i] for i in range(5) if (faction >> i) & 1)

def faction_list_string(factions):
	return ','.join(faction_string(faction) for faction in factions)

def faction_set(faction_group_id):
	return {i for i,k in enumerate(reversed(bin(faction_group_id)[2:])) if k == '1'}

def check_validity(faction_group_id):
	return check_faction_set_validity(faction_set(faction_group_id))

def number_from_bitset(bits):
	return sum(1 << k for k in bits)

alternates = []
for shift in range(5):
	alternate_list = []
	reversed_alternate_list = []
	for faction_group_id in range(32):
		bits = '{:05b}'.format(faction_group_id)
		shifted_bits = bits[shift:] + bits[:shift]
		new_number = int(shifted_bits,2)
		new_reversed = int(''.join(reversed(shifted_bits)),2)
		alternate_list.append(new_number)
		reversed_alternate_list.append(new_reversed)
	alternates.append(alternate_list)
	alternates.append(reversed_alternate_list)
print('\n'.join(' '.join(str(k) for k in alternate) for alternate in alternates))

primitive_groups = set()
faction_itinerary = [0]

for next_faction_id in range(32):
	print(next_faction_id, len(faction_itinerary))
	next_faction = 1 << next_faction_id
	factions_to_test = [group + next_faction for group in faction_itinerary]
	for faction_group_id in factions_to_test:
		if any(faction_group_id & primitive == primitive for primitive in primitive_groups):
			pass
		elif check_validity(faction_group_id):
			primitive_groups.add(faction_group_id)
		else:
			faction_itinerary.append(faction_group_id)

canonical_primitive_groups = set()

for primitive_group in primitive_groups:
	group_elements = faction_set(primitive_group)
	canonical_group = min(number_from_bitset(alternate[k] for k in group_elements) for alternate in alternates)
	print(primitive_group, canonical_group)
	canonical_primitive_groups.add(canonical_group)

print(canonical_primitive_groups)
for cpg in canonical_primitive_groups:
	print(hex(cpg), faction_list_string(faction_set(cpg)))