code: 
  
  
  
  
  
  
  from collections.abc import Callable
  from math import log
  from os import name, system
  from random import gauss, seed
  from typing import TypeVar
  
  
  def 						_A     (       SCREAMING_SNAKE_CASE__						:			float  ,						SCREAMING_SNAKE_CASE__						:			float  ,						SCREAMING_SNAKE_CASE__						:			int ):
      seed(1 )
      return [gauss(SCREAMING_SNAKE_CASE__  ,						SCREAMING_SNAKE_CASE__ ) for _ in range(SCREAMING_SNAKE_CASE__ )]
  
  
  def 						_A     (       SCREAMING_SNAKE_CASE__						:			int  ,						SCREAMING_SNAKE_CASE__						:			list ):
      return [k for k in range(SCREAMING_SNAKE_CASE__ ) for _ in range(instance_count[k] )]
  
  
  def 						_A     (       SCREAMING_SNAKE_CASE__						:			int  ,						SCREAMING_SNAKE_CASE__						:			list ):
      return sum(SCREAMING_SNAKE_CASE__ ) / instance_count
  
  
  def 						_A     (       SCREAMING_SNAKE_CASE__						:			int  ,						SCREAMING_SNAKE_CASE__						:			int ):
      return instance_count / total_count
  
  
  def 						_A     (       SCREAMING_SNAKE_CASE__						:			list  ,						SCREAMING_SNAKE_CASE__						:			list  ,						SCREAMING_SNAKE_CASE__						:			int ):
      UpperCamelCase :Optional[Any]										=     []  # An empty list to store all squared differences
      # iterate over number of elements in items
      for i in range(len(SCREAMING_SNAKE_CASE__ ) ):
          # for loop iterates over number of elements in inner layer of items
          for j in range(len(items[i] ) ):
              # appending squared differences to 'squared_diff' list
              squared_diff.append((items[i][j] - means[i]) ** 2 )
  
      # one divided by (the number of all instances - number of classes) multiplied by
      # sum of all squared differences
      UpperCamelCase :Tuple										=     len(SCREAMING_SNAKE_CASE__ )  # Number of classes in dataset
      return 1 / (total_count - n_classes) * sum(SCREAMING_SNAKE_CASE__ )
  
  
  def 						_A     (       SCREAMING_SNAKE_CASE__						:			list  ,						SCREAMING_SNAKE_CASE__						:			list  ,						SCREAMING_SNAKE_CASE__						:			float  ,						SCREAMING_SNAKE_CASE__						:			list ):
      UpperCamelCase :Dict										=     []
      # for loop iterates over number of elements in list
      for i in range(len(SCREAMING_SNAKE_CASE__ ) ):
          # for loop iterates over number of inner items of each element
          for j in range(len(x_items[i] ) ):
              UpperCamelCase :List[Any]										=     []  # to store all discriminant values of each item as a list
              # for loop iterates over number of classes we have in our dataset
              for k in range(len(SCREAMING_SNAKE_CASE__ ) ):
                  # appending values of discriminants for each class to 'temp' list
                  temp.append(
                      x_items[i][j] * (means[k] / variance)
                      - (means[k] ** 2 / (2 * variance))
                      + log(probabilities[k] ) )
              # appending discriminant values of each item to 'results' list
              results.append(SCREAMING_SNAKE_CASE__ )
  
      return [result.index(max(SCREAMING_SNAKE_CASE__ ) ) for result in results]
  
  
  def 						_A     (       SCREAMING_SNAKE_CASE__						:			list  ,						SCREAMING_SNAKE_CASE__						:			list ):
      UpperCamelCase :List[Any]										=     sum(1 for i, j in zip(SCREAMING_SNAKE_CASE__  ,						SCREAMING_SNAKE_CASE__ ) if i == j )
      # percentage of accuracy equals to number of correct predictions divided by number
      # of all data and multiplied by 100
      return (correct / len(SCREAMING_SNAKE_CASE__ )) * 100
  
  
  __snake_case							      =						TypeVar("""num""")
  
  
  def 						_A     (       SCREAMING_SNAKE_CASE__						:			Callable[[object], num]  ,						SCREAMING_SNAKE_CASE__						:			str  ,						SCREAMING_SNAKE_CASE__						:			str  ,						SCREAMING_SNAKE_CASE__						:			Callable[[num], bool] = lambda SCREAMING_SNAKE_CASE__ : True  ,						SCREAMING_SNAKE_CASE__						:			str | None = None  ,						):
      while True:
          try:
              UpperCamelCase :List[Any]										=     input_type(input(SCREAMING_SNAKE_CASE__ ).strip() or default )
              if condition(SCREAMING_SNAKE_CASE__ ):
                  return user_input
              else:
                  print(F'''{user_input}: {err_msg}''' )
                  continue
          except ValueError:
              print(
                  F'''{user_input}: Incorrect input type, expected {input_type.__name__!r}''' )
  
  
  def 						_A     (       ):
      while True:
          print(''' Linear Discriminant Analysis '''.center(50  ,						'''*''' ) )
          print('''*''' * 50  ,						'''\n''' )
          print('''First of all we should specify the number of classes that''' )
          print('''we want to generate as training dataset''' )
          # Trying to get number of classes
          UpperCamelCase :List[Any]										=     valid_input(
              input_type=SCREAMING_SNAKE_CASE__  ,						condition=lambda SCREAMING_SNAKE_CASE__ : x > 0  ,						input_msg='''Enter the number of classes (Data Groupings): '''  ,						err_msg='''Number of classes should be positive!'''  ,						)
  
          print('''-''' * 100 )
  
          # Trying to get the value of standard deviation
          UpperCamelCase :Any										=     valid_input(
              input_type=SCREAMING_SNAKE_CASE__  ,						condition=lambda SCREAMING_SNAKE_CASE__ : x >= 0  ,						input_msg=(
                  '''Enter the value of standard deviation'''
                  '''(Default value is 1.0 for all classes): '''
              )  ,						err_msg='''Standard deviation should not be negative!'''  ,						default='''1.0'''  ,						)
  
          print('''-''' * 100 )
  
          # Trying to get number of instances in classes and theirs means to generate
          # dataset
          UpperCamelCase :Tuple										=     []  # An empty list to store instance counts of classes in dataset
          for i in range(SCREAMING_SNAKE_CASE__ ):
              UpperCamelCase :List[Any]										=     valid_input(
                  input_type=SCREAMING_SNAKE_CASE__  ,						condition=lambda SCREAMING_SNAKE_CASE__ : x > 0  ,						input_msg=(F'''Enter The number of instances for class_{i+1}: ''')  ,						err_msg='''Number of instances should be positive!'''  ,						)
              counts.append(SCREAMING_SNAKE_CASE__ )
          print('''-''' * 100 )
  
          # An empty list to store values of user-entered means of classes
          UpperCamelCase :Union[str, Any]										=     []
          for a in range(SCREAMING_SNAKE_CASE__ ):
              UpperCamelCase :str										=     valid_input(
                  input_type=SCREAMING_SNAKE_CASE__  ,						input_msg=(F'''Enter the value of mean for class_{a+1}: ''')  ,						err_msg='''This is an invalid value.'''  ,						)
              user_means.append(SCREAMING_SNAKE_CASE__ )
          print('''-''' * 100 )
  
          print('''Standard deviation: '''  ,						SCREAMING_SNAKE_CASE__ )
          # print out the number of instances in classes in separated line
          for i, count in enumerate(SCREAMING_SNAKE_CASE__  ,						1 ):
              print(F'''Number of instances in class_{i} is: {count}''' )
          print('''-''' * 100 )
  
          # print out mean values of classes separated line
          for i, user_mean in enumerate(SCREAMING_SNAKE_CASE__  ,						1 ):
              print(F'''Mean of class_{i} is: {user_mean}''' )
          print('''-''' * 100 )
  
          # Generating training dataset drawn from gaussian distribution
          UpperCamelCase :Tuple										=     [
              gaussian_distribution(user_means[j]  ,						SCREAMING_SNAKE_CASE__  ,						counts[j] )
              for j in range(SCREAMING_SNAKE_CASE__ )
          ]
          print('''Generated Normal Distribution: \n'''  ,						SCREAMING_SNAKE_CASE__ )
          print('''-''' * 100 )
  
          # Generating Ys to detecting corresponding classes
          UpperCamelCase :int										=     y_generator(SCREAMING_SNAKE_CASE__  ,						SCREAMING_SNAKE_CASE__ )
          print('''Generated Corresponding Ys: \n'''  ,						SCREAMING_SNAKE_CASE__ )
          print('''-''' * 100 )
  
          # Calculating the value of actual mean for each class
          UpperCamelCase :Tuple										=     [calculate_mean(counts[k]  ,						x[k] ) for k in range(SCREAMING_SNAKE_CASE__ )]
          # for loop iterates over number of elements in 'actual_means' list and print
          # out them in separated line
          for i, actual_mean in enumerate(SCREAMING_SNAKE_CASE__  ,						1 ):
              print(F'''Actual(Real) mean of class_{i} is: {actual_mean}''' )
          print('''-''' * 100 )
  
          # Calculating the value of probabilities for each class
          UpperCamelCase :Dict										=     [
              calculate_probabilities(counts[i]  ,						sum(SCREAMING_SNAKE_CASE__ ) ) for i in range(SCREAMING_SNAKE_CASE__ )
          ]
  
          # for loop iterates over number of elements in 'probabilities' list and print
          # out them in separated line
          for i, probability in enumerate(SCREAMING_SNAKE_CASE__  ,						1 ):
              print(F'''Probability of class_{i} is: {probability}''' )
          print('''-''' * 100 )
  
          # Calculating the values of variance for each class
          UpperCamelCase :int										=     calculate_variance(SCREAMING_SNAKE_CASE__  ,						SCREAMING_SNAKE_CASE__  ,						sum(SCREAMING_SNAKE_CASE__ ) )
          print('''Variance: '''  ,						SCREAMING_SNAKE_CASE__ )
          print('''-''' * 100 )
  
          # Predicting Y values
          # storing predicted Y values in 'pre_indexes' variable
          UpperCamelCase :Any										=     predict_y_values(SCREAMING_SNAKE_CASE__  ,						SCREAMING_SNAKE_CASE__  ,						SCREAMING_SNAKE_CASE__  ,						SCREAMING_SNAKE_CASE__ )
          print('''-''' * 100 )
  
          # Calculating Accuracy of the model
          print(F'''Accuracy: {accuracy(SCREAMING_SNAKE_CASE__  ,						SCREAMING_SNAKE_CASE__ )}''' )
          print('''-''' * 100 )
          print(''' DONE '''.center(100  ,						'''+''' ) )
  
          if input('''Press any key to restart or \'q\' for quit: ''' ).strip().lower() == "q":
              print('''\n''' + '''GoodBye!'''.center(100  ,						'''-''' ) + '''\n''' )
              break
          system('''cls''' if name == '''nt''' else '''clear''' )  # noqa: S605
  
  
  if __name__ == "__main__":
   main()
  
  
  
  
  
  
style_context: 
  
  
  
  
  
  
  __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     (       SCREAMING_SNAKE_CASE__						:			List[Any] ):
      UpperCamelCase :List[Any]										=     set()
      for row in edge_array:
          for item in row:
              distinct_edge.add(item[0] )
      return list(SCREAMING_SNAKE_CASE__ )
  
  
  def 						_A     (       SCREAMING_SNAKE_CASE__						:			List[str]  ,						SCREAMING_SNAKE_CASE__						:			str ):
      UpperCamelCase :int										=     ['''0'''] * len(SCREAMING_SNAKE_CASE__ )
      for i, row in enumerate(SCREAMING_SNAKE_CASE__ ):
          for item in row:
              if distinct_edge in item[0]:
                  UpperCamelCase :Tuple										=     '''1'''
                  break
      return "".join(SCREAMING_SNAKE_CASE__ )
  
  
  def 						_A     (       SCREAMING_SNAKE_CASE__						:			Union[str, Any] ):
      UpperCamelCase :Optional[Any]										=     get_distinct_edge(SCREAMING_SNAKE_CASE__ )
      UpperCamelCase :Optional[int]										=     {}
  
      for item in distinct_edge:
          UpperCamelCase :List[str]										=     get_bitcode(SCREAMING_SNAKE_CASE__  ,						SCREAMING_SNAKE_CASE__ )
          # print('bit',bit)
          # bt=''.join(bit)
          UpperCamelCase :str										=     bit.count('''1''' )
          UpperCamelCase :Optional[int]										=     [s, bit]
      # Store [Distinct edge, WT(Bitcode), Bitcode] in descending order
      UpperCamelCase :Optional[int]										=     [
          [k, v[0], v[1]]
          for k, v in sorted(frequency_table.items()  ,						key=lambda SCREAMING_SNAKE_CASE__ : v[1][0]  ,						reverse=SCREAMING_SNAKE_CASE__ )
      ]
      return sorted_frequency_table
  
  
  def 						_A     (       SCREAMING_SNAKE_CASE__						:			int ):
      UpperCamelCase :List[Any]										=     {}
      for _, item in enumerate(SCREAMING_SNAKE_CASE__ ):
          nodes.setdefault(item[2]  ,						[] ).append(item[0] )
      return nodes
  
  
  def 						_A     (       SCREAMING_SNAKE_CASE__						:			Tuple ):
      UpperCamelCase :str										=     {}
      for key, value in nodes.items():
          UpperCamelCase :str										=     value
      return cluster
  
  
  def 						_A     (       SCREAMING_SNAKE_CASE__						:			List[Any] ):
      return [i * 100 / len(SCREAMING_SNAKE_CASE__ ) for i in cluster]
  
  
  def 						_A     (       ):
      print('''\nNodes\n''' )
      for key, value in nodes.items():
          print(SCREAMING_SNAKE_CASE__  ,						SCREAMING_SNAKE_CASE__ )
      print('''\nSupport\n''' )
      print(SCREAMING_SNAKE_CASE__ )
      print('''\n Cluster \n''' )
      for key, value in sorted(cluster.items()  ,						reverse=SCREAMING_SNAKE_CASE__ ):
          print(SCREAMING_SNAKE_CASE__  ,						SCREAMING_SNAKE_CASE__ )
      print('''\n Graph\n''' )
      for key, value in graph.items():
          print(SCREAMING_SNAKE_CASE__  ,						SCREAMING_SNAKE_CASE__ )
      print('''\n Edge List of Frequent subgraphs \n''' )
      for edge_list in freq_subgraph_edge_list:
          print(SCREAMING_SNAKE_CASE__ )
  
  
  def 						_A     (       SCREAMING_SNAKE_CASE__						:			Any  ,						SCREAMING_SNAKE_CASE__						:			str  ,						SCREAMING_SNAKE_CASE__						:			Union[str, Any]  ,						SCREAMING_SNAKE_CASE__						:			Optional[Any] ):
      for i in cluster[ca]:
          UpperCamelCase :Union[str, Any]										=     0
          UpperCamelCase :Dict										=     ca + 1
          while ca < max(cluster.keys() ):
              for j in cluster[ca]:
                  if int(SCREAMING_SNAKE_CASE__  ,						2 ) & int(SCREAMING_SNAKE_CASE__  ,						2 ) == int(SCREAMING_SNAKE_CASE__  ,						2 ):
                      if tuple(nodes[i] ) in graph:
                          graph[tuple(nodes[i] )].append(nodes[j] )
                      else:
                          UpperCamelCase :Union[str, Any]										=     [nodes[j]]
                      count += 1
              if count == 0:
                  UpperCamelCase :int										=     ca + 1
              else:
                  break
  
  
  def 						_A     (       SCREAMING_SNAKE_CASE__						:			List[Any]  ,						SCREAMING_SNAKE_CASE__						:			str ):
      UpperCamelCase :str										=     cluster[max(cluster.keys() )]
      UpperCamelCase :Any										=     '''Header'''
      UpperCamelCase :str										=     {}
      for i in x:
          if (["Header"],) in graph:
              graph[(["Header"],)].append(x[i] )
          else:
              UpperCamelCase :str										=     [x[i]]
      for i in x:
          UpperCamelCase :Dict										=     [['''Header''']]
      UpperCamelCase :Union[str, Any]										=     1
      while i < max(SCREAMING_SNAKE_CASE__ ) - 1:
          create_edge(SCREAMING_SNAKE_CASE__  ,						SCREAMING_SNAKE_CASE__  ,						SCREAMING_SNAKE_CASE__  ,						SCREAMING_SNAKE_CASE__ )
          UpperCamelCase :Optional[int]										=     i + 1
      return graph
  
  
  def 						_A     (       SCREAMING_SNAKE_CASE__						:			List[str]  ,						SCREAMING_SNAKE_CASE__						:			Tuple  ,						SCREAMING_SNAKE_CASE__						:			Optional[int]  ,						SCREAMING_SNAKE_CASE__						:			List[str]=None ):
      UpperCamelCase :Tuple										=     (path or []) + [start]
      if start == end:
          paths.append(SCREAMING_SNAKE_CASE__ )
      for node in graph[start]:
          if tuple(SCREAMING_SNAKE_CASE__ ) not in path:
              my_dfs(SCREAMING_SNAKE_CASE__  ,						tuple(SCREAMING_SNAKE_CASE__ )  ,						SCREAMING_SNAKE_CASE__  ,						SCREAMING_SNAKE_CASE__ )
  
  
  def 						_A     (       SCREAMING_SNAKE_CASE__						:			List[Any]  ,						SCREAMING_SNAKE_CASE__						:			str  ,						SCREAMING_SNAKE_CASE__						:			Union[str, Any] ):
      UpperCamelCase :str										=     int(s / 100 * (len(SCREAMING_SNAKE_CASE__ ) - 1) )
      for i in cluster[k]:
          my_dfs(SCREAMING_SNAKE_CASE__  ,						tuple(cluster[k][i] )  ,						(['''Header'''],) )
  
  
  def 						_A     (       SCREAMING_SNAKE_CASE__						:			str ):
      UpperCamelCase :Dict										=     []
      for edges in paths:
          UpperCamelCase :Tuple										=     []
          for j in range(len(SCREAMING_SNAKE_CASE__ ) - 1 ):
              UpperCamelCase :Dict										=     list(edges[j] )
              for e in temp:
                  UpperCamelCase :Union[str, Any]										=     (e[0], e[1])
                  el.append(SCREAMING_SNAKE_CASE__ )
          freq_sub_el.append(SCREAMING_SNAKE_CASE__ )
      return freq_sub_el
  
  
  def 						_A     (       SCREAMING_SNAKE_CASE__						:			List[str] ):
      for i in range(len(SCREAMING_SNAKE_CASE__ ) ):
          for j in range(len(edge_array[i] ) ):
              UpperCamelCase :Tuple										=     edge_array[i][j].split('''-''' )
              UpperCamelCase :Dict										=     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(60, cluster, graph)
   __snake_case							      =						[]
   __snake_case							      =						freq_subgraphs_edge_list(paths)
   print_all()
  
  
  
  
  
  