


'''simple docstring'''

_UpperCAmelCase					:			Optional[int]				     =					[
    ["""ab-e1""", """ac-e3""", """ad-e5""", """bc-e4""", """bd-e2""", """be-e6""", """bh-e12""", """cd-e2""", """ce-e4""",
     """de-e1""", """df-e8""", """dg-e5""", """dh-e10""", """ef-e3""", """eg-e2""", """fg-e6""", """gh-e6""", """hi-e3"""],
    ["""ab-e1""", """ac-e3""", """ad-e5""", """bc-e4""", """bd-e2""", """be-e6""", """cd-e2""", """de-e1""", """df-e8""",
     """ef-e3""", """eg-e2""", """fg-e6"""],
    ["""ab-e1""", """ac-e3""", """bc-e4""", """bd-e2""", """de-e1""", """df-e8""", """dg-e5""", """ef-e3""", """eg-e2""",
     """eh-e12""", """fg-e6""", """fh-e10""", """gh-e6"""],
    ["""ab-e1""", """ac-e3""", """bc-e4""", """bd-e2""", """bh-e12""", """cd-e2""", """df-e8""", """dh-e10"""],
    ["""ab-e1""", """ac-e3""", """ad-e5""", """bc-e4""", """bd-e2""", """cd-e2""", """ce-e4""", """de-e1""", """df-e8""",
     """dg-e5""", """ef-e3""", """eg-e2""", """fg-e6"""]
]

def 				__magic_name__(    lowerCamelCase):
						__lowerCAmelCase											=					set()
						for row in edge_array:
												for item in row:
																		distinct_edge.add(item[0])
						return list(lowerCamelCase)

def 				__magic_name__(    lowerCamelCase,					lowerCamelCase):
						__lowerCAmelCase											=					['''0'''] * len(lowerCamelCase)
						for i, row in enumerate(lowerCamelCase):
												for item in row:
																		if distinct_edge in item[0]:
																								__lowerCAmelCase											=					'''1'''
																								break
						return "".join(lowerCamelCase)

def 				__magic_name__(    lowerCamelCase):
						__lowerCAmelCase											=					get_distinct_edge(lowerCamelCase)
						__lowerCAmelCase											=					{}

						for item in distinct_edge:
												__lowerCAmelCase											=					get_bitcode(lowerCamelCase,					lowerCamelCase)
												# print('bit',bit)
												# bt=''.join(bit)
												__lowerCAmelCase											=					bit.count('''1''')
												__lowerCAmelCase											=					[s, bit]
						# Store [Distinct edge, WT(Bitcode), Bitcode] in descending order
						__lowerCAmelCase											=					[
						    [k, v[0], v[1]]
						    for k, v in sorted(frequency_table.items(),					key=lambda lowerCamelCase: v[1][0],					reverse=lowerCamelCase)
						]
						return sorted_frequency_table

def 				__magic_name__(    lowerCamelCase):
						__lowerCAmelCase											=					{}
						for _, item in enumerate(lowerCamelCase):
												nodes.setdefault(item[2],					[]).append(item[0])
						return nodes

def 				__magic_name__(    lowerCamelCase):
						__lowerCAmelCase											=					{}
						for key, value in nodes.items():
												__lowerCAmelCase											=					value
						return cluster

def 				__magic_name__(    lowerCamelCase):
						return [i * 1_0_0 / len(lowerCamelCase) for i in cluster]

def 				__magic_name__(    ):
						print('''\nNodes\n''')
						for key, value in nodes.items():
												print(lowerCamelCase,					lowerCamelCase)
						print('''\nSupport\n''')
						print(lowerCamelCase)
						print('''\n Cluster \n''')
						for key, value in sorted(cluster.items(),					reverse=lowerCamelCase):
												print(lowerCamelCase,					lowerCamelCase)
						print('''\n Graph\n''')
						for key, value in graph.items():
												print(lowerCamelCase,					lowerCamelCase)
						print('''\n Edge List of Frequent subgraphs \n''')
						for edge_list in freq_subgraph_edge_list:
												print(lowerCamelCase)

def 				__magic_name__(    lowerCamelCase,					lowerCamelCase,					lowerCamelCase,					lowerCamelCase):
						for i in cluster[ca]:
												__lowerCAmelCase											=					0
												__lowerCAmelCase											=					ca + 1
												while ca < max(cluster.keys()):
																		for j in cluster[ca]:
																								if int(lowerCamelCase,					2) & int(lowerCamelCase,					2) == int(lowerCamelCase,					2):
																														if tuple(nodes[i]) in graph:
																																				graph[tuple(nodes[i])].append(nodes[j])
																														else:
																																				__lowerCAmelCase											=					[nodes[j]]
																														count += 1
																		if count == 0:
																								__lowerCAmelCase											=					ca + 1
																		else:
																								break

def 				__magic_name__(    lowerCamelCase,					lowerCamelCase):
						__lowerCAmelCase											=					cluster[max(cluster.keys())]
						__lowerCAmelCase											=					'''Header'''
						__lowerCAmelCase											=					{}
						for i in x:
												if (["Header"],) in graph:
																		graph[(["Header"],)].append(x[i])
												else:
																		__lowerCAmelCase											=					[x[i]]
						for i in x:
												__lowerCAmelCase											=					[['''Header''']]
						__lowerCAmelCase											=					1
						while i < max(lowerCamelCase) - 1:
												create_edge(lowerCamelCase,					lowerCamelCase,					lowerCamelCase,					lowerCamelCase)
												__lowerCAmelCase											=					i + 1
						return graph

def 				__magic_name__(    lowerCamelCase,					lowerCamelCase,					lowerCamelCase,					lowerCamelCase=None):
						__lowerCAmelCase											=					(path or []) + [start]
						if start == end:
												paths.append(lowerCamelCase)
						for node in graph[start]:
												if tuple(lowerCamelCase) not in path:
																		my_dfs(lowerCamelCase,					tuple(lowerCamelCase),					lowerCamelCase,					lowerCamelCase)

def 				__magic_name__(    lowerCamelCase,					lowerCamelCase,					lowerCamelCase):
						__lowerCAmelCase											=					int(s / 1_0_0 * (len(lowerCamelCase) - 1))
						for i in cluster[k]:
												my_dfs(lowerCamelCase,					tuple(cluster[k][i]),					(['''Header'''],))

def 				__magic_name__(    lowerCamelCase):
						__lowerCAmelCase											=					[]
						for edges in paths:
												__lowerCAmelCase											=					[]
												for j in range(len(lowerCamelCase) - 1):
																		__lowerCAmelCase											=					list(edges[j])
																		for e in temp:
																								__lowerCAmelCase											=					(e[0], e[1])
																								el.append(lowerCamelCase)
												freq_sub_el.append(lowerCamelCase)
						return freq_sub_el

def 				__magic_name__(    lowerCamelCase):
						for i in range(len(lowerCamelCase)):
												for j in range(len(edge_array[i])):
																		__lowerCAmelCase											=					edge_array[i][j].split('''-''')
																		__lowerCAmelCase											=					t


if __name__ == "__main__":
	preprocess(edge_array)
	_UpperCAmelCase					:			str				     =					get_frequency_table(edge_array)
	_UpperCAmelCase					:			Optional[Any]				     =					get_nodes(frequency_table)
	_UpperCAmelCase					:			List[Any]				     =					get_cluster(nodes)
	_UpperCAmelCase					:			Dict				     =					get_support(cluster)
	_UpperCAmelCase					:			Optional[int]				     =					construct_graph(cluster, nodes)
	find_freq_subgraph_given_support(6_0, cluster, graph)
	_UpperCAmelCase					:			list				     =					[]
	_UpperCAmelCase					:			Union[str, Any]				     =					freq_subgraphs_edge_list(paths)
	print_all()





'''simple docstring'''

import math

def 				__magic_name__(    lowerCamelCase):
						__lowerCAmelCase											=					math.log(2,					1_0) * number
						__lowerCAmelCase											=					round((log_number - int(lowerCamelCase)),					1_5)

						return difference

def 				__magic_name__(    lowerCamelCase = 6_7_8_9_1_0):
						__lowerCAmelCase											=					9_0
						__lowerCAmelCase											=					0

						__lowerCAmelCase											=					math.log(1.23,					1_0)
						__lowerCAmelCase											=					math.log(1.24,					1_0)
						__lowerCAmelCase											=					0

						while position < number:
												__lowerCAmelCase											=					log_difference(lowerCamelCase)

												if difference >= upper_limit:
																		power_iterator += 9_3

												elif difference < lower_limit:
																		power_iterator += 1_9_6

												else:
																		__lowerCAmelCase											=					power_iterator
																		power_iterator += 1_9_6
																		position += 1

						return previous_power


if __name__ == "__main__":
	import doctest

	doctest.testmod()

	print(f"""{solution() = }""")

