


__snake_case             =     [
    ['''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 		_A		(		_lowercase   )				->   Dict:


     """simple docstring"""


     __UpperCamelCase   = set()
     for row in edge_array:
          for item in row:
               distinct_edge.add(item[0]   )
     return list(_lowercase   )






def 		_A		(		_lowercase				,     _lowercase   )				->   Tuple:


     """simple docstring"""


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






def 		_A		(		_lowercase   )				->   Tuple:


     """simple docstring"""


     __UpperCamelCase   = get_distinct_edge(_lowercase   )
     __UpperCamelCase   = {}

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






def 		_A		(		_lowercase   )				->   Dict:


     """simple docstring"""


     __UpperCamelCase   = {}
     for _, item in enumerate(_lowercase   ):
          nodes.setdefault(item[2]				,     []   ).append(item[0]   )
     return nodes






def 		_A		(		_lowercase   )				->   str:


     """simple docstring"""


     __UpperCamelCase   = {}
     for key, value in nodes.items():
          __UpperCamelCase   = value
     return cluster






def 		_A		(		_lowercase   )				->   Tuple:


     """simple docstring"""


     return [i * 1_00 / len(_lowercase   ) for i in cluster]






def 		_A		(		)				->   None:


     """simple docstring"""


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






def 		_A		(		_lowercase				,     _lowercase				,     _lowercase				,     _lowercase   )				->   str:


     """simple docstring"""


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






def 		_A		(		_lowercase				,     _lowercase   )				->   List[str]:


     """simple docstring"""


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






def 		_A		(		_lowercase				,     _lowercase				,     _lowercase				,     _lowercase=None   )				->   Tuple:


     """simple docstring"""


     __UpperCamelCase   = (path or []) + [start]
     if start == end:
          paths.append(_lowercase   )
     for node in graph[start]:
          if tuple(_lowercase   ) not in path:
               my_dfs(_lowercase				,     tuple(_lowercase   )				,     _lowercase				,     _lowercase   )






def 		_A		(		_lowercase				,     _lowercase				,     _lowercase   )				->   Any:


     """simple docstring"""


     __UpperCamelCase   = int(s / 1_00 * (len(_lowercase   ) - 1)   )
     for i in cluster[k]:
          my_dfs(_lowercase				,     tuple(cluster[k][i]   )				,     (['Header'],)   )






def 		_A		(		_lowercase   )				->   Optional[Any]:


     """simple docstring"""


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






def 		_A		(		_lowercase   )				->   Union[str, Any]:


     """simple docstring"""


     for i in range(len(_lowercase   )   ):
          for j in range(len(edge_array[i]   )   ):
               __UpperCamelCase   = edge_array[i][j].split('-'   )
               __UpperCamelCase   = t


if __name__ == "__main__":
    preprocess(edge_array)
    __snake_case             =     get_frequency_table(edge_array)
    __snake_case             =     get_nodes(frequency_table)
    __snake_case             =     get_cluster(nodes)
    __snake_case             =     get_support(cluster)
    __snake_case             =     construct_graph(cluster, nodes)
    find_freq_subgraph_given_support(6_0, cluster, graph)
    __snake_case             =     []
    __snake_case             =     freq_subgraphs_edge_list(paths)
    print_all()






from math import cos, sin






def 		_A		(		_lowercase   )				->   list[list[float]]:


     """simple docstring"""


     __UpperCamelCase   = float(_lowercase   )
     return [[scaling_factor * int(x == y   ) for x in range(2   )] for y in range(2   )]






def 		_A		(		_lowercase   )				->   list[list[float]]:


     """simple docstring"""


     __UpperCamelCase,						__UpperCamelCase   = cos(_lowercase   ), sin(_lowercase   )
     return [[c, -s], [s, c]]






def 		_A		(		_lowercase   )				->   list[list[float]]:


     """simple docstring"""


     __UpperCamelCase,						__UpperCamelCase   = cos(_lowercase   ), sin(_lowercase   )
     __UpperCamelCase   = c * s
     return [[c * c, cs], [cs, s * s]]






def 		_A		(		_lowercase   )				->   list[list[float]]:


     """simple docstring"""


     __UpperCamelCase,						__UpperCamelCase   = cos(_lowercase   ), sin(_lowercase   )
     __UpperCamelCase   = c * s
     return [[2 * c - 1, 2 * cs], [2 * cs, 2 * s - 1]]


print(f"""    {scaling(5) = }""")
print(f"""  {rotation(4_5) = }""")
print(f"""{projection(4_5) = }""")


print(f"""{reflection(4_5) = }""")


