code: 
  
  
  __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()
  
  
  
style_context: 
  
  
  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) = }""")
  
  
  