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     UpperCAmelCase__		(UpperCamelCase_							,UpperCamelCase_							,UpperCamelCase_       ):
  
  
  
       """simple docstring"""
  
  
  
  
  
  
       seed(1       )
       return [gauss(UpperCamelCase_							,UpperCamelCase_       ) for _ in range(UpperCamelCase_       )]
  def     UpperCAmelCase__		(UpperCamelCase_							,UpperCamelCase_       ):
  
  
  
       """simple docstring"""
  
  
  
  
  
  
       return [k for k in range(UpperCamelCase_       ) for _ in range(instance_count[k]       )]
  def     UpperCAmelCase__		(UpperCamelCase_							,UpperCamelCase_       ):
  
  
  
       """simple docstring"""
  
  
  
  
  
  
       return sum(UpperCamelCase_       ) / instance_count
  def     UpperCAmelCase__		(UpperCamelCase_							,UpperCamelCase_       ):
  
  
  
       """simple docstring"""
  
  
  
  
  
  
       return instance_count / total_count
  def     UpperCAmelCase__		(UpperCamelCase_							,UpperCamelCase_							,UpperCamelCase_       ):
  
  
  
       """simple docstring"""
  
  
  
  
  
  
       snake_case					=       []  # An empty list to store all squared differences
       # iterate over number of elements in items
       for i in range(len(UpperCamelCase_       )       ):
            # 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
       snake_case					=       len(UpperCamelCase_       )  # Number of classes in dataset
       return 1 / (total_count - n_classes) * sum(UpperCamelCase_       )
  def     UpperCAmelCase__		(UpperCamelCase_							,UpperCamelCase_							,UpperCamelCase_							,UpperCamelCase_       ):
  
  
  
       """simple docstring"""
  
  
  
  
  
  
       snake_case					=       []
       # for loop iterates over number of elements in list
       for i in range(len(UpperCamelCase_       )       ):
            # for loop iterates over number of inner items of each element
            for j in range(len(x_items[i]       )       ):
                 snake_case					=       []  # 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(UpperCamelCase_       )       ):
                      # 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(UpperCamelCase_       )
  
       return [result.index(max(UpperCamelCase_       )       ) for result in results]
  def     UpperCAmelCase__		(UpperCamelCase_							,UpperCamelCase_       ):
  
  
  
       """simple docstring"""
  
  
  
  
  
  
       snake_case					=       sum(1 for i, j in zip(UpperCamelCase_							,UpperCamelCase_       ) 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(UpperCamelCase_       )) * 1_00
  
  
  _SCREAMING_SNAKE_CASE    :				Optional[Any]       =					TypeVar("num")
  def     UpperCAmelCase__		(UpperCamelCase_							,UpperCamelCase_							,UpperCamelCase_							,UpperCamelCase_ = lambda UpperCamelCase_       : True							,UpperCamelCase_ = None							,):
  
  
  
       """simple docstring"""
  
  
  
  
  
  
       while True:
            try:
                 snake_case					=       input_type(input(UpperCamelCase_       ).strip() or default       )
                 if condition(UpperCamelCase_       ):
                      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     UpperCAmelCase__		():
  
  
  
       """simple docstring"""
  
  
  
  
  
  
       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
            snake_case					=       valid_input(
                input_type=UpperCamelCase_							,condition=lambda UpperCamelCase_       : x > 0							,input_msg='''Enter the number of classes (Data Groupings): '''							,err_msg='''Number of classes should be positive!'''							,)
  
            print('''-''' * 1_00       )
  
            # Trying to get the value of standard deviation
            snake_case					=       valid_input(
                input_type=UpperCamelCase_							,condition=lambda UpperCamelCase_       : 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('''-''' * 1_00       )
  
            # Trying to get number of instances in classes and theirs means to generate
            # dataset
            snake_case					=       []  # An empty list to store instance counts of classes in dataset
            for i in range(UpperCamelCase_       ):
                 snake_case					=       valid_input(
                     input_type=UpperCamelCase_							,condition=lambda UpperCamelCase_       : x > 0							,input_msg=(F'''Enter The number of instances for class_{i+1}: ''')							,err_msg='''Number of instances should be positive!'''							,)
                 counts.append(UpperCamelCase_       )
            print('''-''' * 1_00       )
  
            # An empty list to store values of user-entered means of classes
            snake_case					=       []
            for a in range(UpperCamelCase_       ):
                 snake_case					=       valid_input(
                     input_type=UpperCamelCase_							,input_msg=(F'''Enter the value of mean for class_{a+1}: ''')							,err_msg='''This is an invalid value.'''							,)
                 user_means.append(UpperCamelCase_       )
            print('''-''' * 1_00       )
  
            print('''Standard deviation: '''							,UpperCamelCase_       )
            # print out the number of instances in classes in separated line
            for i, count in enumerate(UpperCamelCase_							,1       ):
                 print(F'''Number of instances in class_{i} is: {count}'''       )
            print('''-''' * 1_00       )
  
            # print out mean values of classes separated line
            for i, user_mean in enumerate(UpperCamelCase_							,1       ):
                 print(F'''Mean of class_{i} is: {user_mean}'''       )
            print('''-''' * 1_00       )
  
            # Generating training dataset drawn from gaussian distribution
            snake_case					=       [
                gaussian_distribution(user_means[j]							,UpperCamelCase_							,counts[j]       )
                for j in range(UpperCamelCase_       )
            ]
            print('''Generated Normal Distribution: \n'''							,UpperCamelCase_       )
            print('''-''' * 1_00       )
  
            # Generating Ys to detecting corresponding classes
            snake_case					=       y_generator(UpperCamelCase_							,UpperCamelCase_       )
            print('''Generated Corresponding Ys: \n'''							,UpperCamelCase_       )
            print('''-''' * 1_00       )
  
            # Calculating the value of actual mean for each class
            snake_case					=       [calculate_mean(counts[k]							,x[k]       ) for k in range(UpperCamelCase_       )]
            # for loop iterates over number of elements in 'actual_means' list and print
            # out them in separated line
            for i, actual_mean in enumerate(UpperCamelCase_							,1       ):
                 print(F'''Actual(Real) mean of class_{i} is: {actual_mean}'''       )
            print('''-''' * 1_00       )
  
            # Calculating the value of probabilities for each class
            snake_case					=       [
                calculate_probabilities(counts[i]							,sum(UpperCamelCase_       )       ) for i in range(UpperCamelCase_       )
            ]
  
            # for loop iterates over number of elements in 'probabilities' list and print
            # out them in separated line
            for i, probability in enumerate(UpperCamelCase_							,1       ):
                 print(F'''Probability of class_{i} is: {probability}'''       )
            print('''-''' * 1_00       )
  
            # Calculating the values of variance for each class
            snake_case					=       calculate_variance(UpperCamelCase_							,UpperCamelCase_							,sum(UpperCamelCase_       )       )
            print('''Variance: '''							,UpperCamelCase_       )
            print('''-''' * 1_00       )
  
            # Predicting Y values
            # storing predicted Y values in 'pre_indexes' variable
            snake_case					=       predict_y_values(UpperCamelCase_							,UpperCamelCase_							,UpperCamelCase_							,UpperCamelCase_       )
            print('''-''' * 1_00       )
  
            # Calculating Accuracy of the model
            print(F'''Accuracy: {accuracy(UpperCamelCase_							,UpperCamelCase_       )}'''       )
            print('''-''' * 1_00       )
            print(''' DONE '''.center(1_00							,'''+'''       )       )
  
            if input('''Press any key to restart or \'q\' for quit: '''       ).strip().lower() == "q":
                 print('''\n''' + '''GoodBye!'''.center(1_00							,'''-'''       ) + '''\n'''       )
                 break
            system('''cls''' if name == '''nt''' else '''clear'''       )  # noqa: S605
  
  
  if __name__ == "__main__":
   main()
  
  
  
  
  
style_context: 
  
  
  from __future__ import annotations
  
  import random
  from collections.abc import Iterable
  
  class 						A__      :
  
  
  
  
  
  
  
      """simple docstring"""
  
      def __init__( self    ,      __snake_case					):
           snake_case					=       {literal: None for literal in literals}
      def __str__( self					):
           return "{" + " , ".join(self.literals					) + "}"
      def __len__( self					):
           return len(self.literals					)
      def 	a_    ( self    ,      __snake_case					):
           for literal in self.literals:
                snake_case					=       literal[:2]
                if symbol in model:
                     snake_case					=       model[symbol]
                else:
                     continue
                if value is not None:
                     # Complement assignment if literal is in complemented form
                     if literal.endswith('''\''''					):
                          snake_case					=       not value
                snake_case					=       value
  
  
  
  
      def 	a_    ( self    ,      __snake_case					):
           for literal in self.literals:
                snake_case					=       literal.rstrip('''\''''					) if literal.endswith('''\''''					) else literal + '''\''''
                if symbol in self.literals:
                     return True
  
           self.assign(__snake_case					)
           for value in self.literals.values():
                if value in (True, None):
                     return value
           return any(self.literals.values()					)
  
  
  
  
  
  
  class 						A__      :
  
  
  
  
  
  
  
      """simple docstring"""
  
      def __init__( self    ,      __snake_case					):
           snake_case					=       list(__snake_case					)
  
  
  
  
      def __str__( self					):
           return "{" + " , ".join(str(__snake_case					) for clause in self.clauses					) + "}"
  
  
  
  
  
  
  def     UpperCAmelCase__		():
  
  
  
       """simple docstring"""
  
  
  
  
  
  
       snake_case					=       []
       snake_case					=       random.randint(1							,5       )
       snake_case					=       '''A'''
       snake_case					=       0
       while i < no_of_literals:
            snake_case					=       random.randint(1							,5       )
            snake_case					=       base_var + str(UpperCamelCase_       )
            snake_case					=       random.randint(0							,1       )
            if var_complement == 1:
                 var_name += "'"
            if var_name in literals:
                 i -= 1
            else:
                 literals.append(UpperCamelCase_       )
            i += 1
       return Clause(UpperCamelCase_       )
  def     UpperCAmelCase__		():
  
  
  
       """simple docstring"""
  
  
  
  
  
  
       snake_case					=       set()
       snake_case					=       random.randint(1							,10       )
       while len(UpperCamelCase_       ) < no_of_clauses:
            clauses.add(generate_clause()       )
       return Formula(UpperCamelCase_       )
  def     UpperCAmelCase__		(UpperCamelCase_       ):
  
  
  
       """simple docstring"""
  
  
  
  
  
  
       snake_case					=       formula.clauses
       snake_case					=       []
       for clause in formula.clauses:
            for literal in clause.literals:
                 snake_case					=       literal[:2]
                 if symbol not in symbols_set:
                      symbols_set.append(UpperCamelCase_       )
       return clauses, symbols_set
  def     UpperCAmelCase__		(UpperCamelCase_							,UpperCamelCase_							,UpperCamelCase_       ):
  
  
  
       """simple docstring"""
  
  
  
  
  
  
       snake_case					=       []
       snake_case					=       {}
       snake_case					=       []
  
       for clause in clauses:
            if clause.evaluate(UpperCamelCase_       ):
                 continue
            for literal in clause.literals:
                 literals.append(UpperCamelCase_       )
  
       for s in symbols:
            snake_case					=       s + '''\''''
            if (s in literals and sym not in literals) or (
                s not in literals and sym in literals
            ):
                 pure_symbols.append(UpperCamelCase_       )
       for p in pure_symbols:
            snake_case					=       None
       for s in pure_symbols:
            snake_case					=       s + '''\''''
            if s in literals:
                 snake_case					=       True
            elif sym in literals:
                 snake_case					=       False
       return pure_symbols, assignment
  def     UpperCAmelCase__		(UpperCamelCase_							,UpperCamelCase_       ):
  
  
  
       """simple docstring"""
  
  
  
  
  
  
       snake_case					=       []
       for clause in clauses:
            if len(UpperCamelCase_       ) == 1:
                 unit_symbols.append(list(clause.literals.keys()       )[0]       )
            else:
                 snake_case				,						snake_case					=       0, 0
                 for literal, value in clause.literals.items():
                      if value is False:
                           f_count += 1
                      elif value is None:
                           snake_case					=       literal
                           n_count += 1
                 if f_count == len(UpperCamelCase_       ) - 1 and n_count == 1:
                      unit_symbols.append(UpperCamelCase_       )
       snake_case					=       {}
       for i in unit_symbols:
            snake_case					=       i[:2]
            snake_case					=       len(UpperCamelCase_       ) == 2
       snake_case					=       [i[:2] for i in unit_symbols]
  
       return unit_symbols, assignment
  def     UpperCAmelCase__		(UpperCamelCase_							,UpperCamelCase_							,UpperCamelCase_       ):
  
  
  
       """simple docstring"""
  
  
  
  
  
  
       snake_case					=       True
       for clause in clauses:
            snake_case					=       clause.evaluate(UpperCamelCase_       )
            if clause_check is False:
                 return False, None
            elif clause_check is None:
                 snake_case					=       False
                 continue
  
       if check_clause_all_true:
            return True, model
  
       try:
            snake_case				,						snake_case					=       find_pure_symbols(UpperCamelCase_							,UpperCamelCase_							,UpperCamelCase_       )
       except RecursionError:
            print('''raises a RecursionError and is'''       )
            return None, {}
       snake_case					=       None
       if len(UpperCamelCase_       ) > 0:
            snake_case				,						snake_case					=       pure_symbols[0], assignment[pure_symbols[0]]
  
       if p:
            snake_case					=       model
            snake_case					=       value
            snake_case					=       list(UpperCamelCase_       )
            if p in tmp_symbols:
                 tmp_symbols.remove(UpperCamelCase_       )
            return dpll_algorithm(UpperCamelCase_							,UpperCamelCase_							,UpperCamelCase_       )
  
       snake_case				,						snake_case					=       find_unit_clauses(UpperCamelCase_							,UpperCamelCase_       )
       snake_case					=       None
       if len(UpperCamelCase_       ) > 0:
            snake_case				,						snake_case					=       unit_symbols[0], assignment[unit_symbols[0]]
       if p:
            snake_case					=       model
            snake_case					=       value
            snake_case					=       list(UpperCamelCase_       )
            if p in tmp_symbols:
                 tmp_symbols.remove(UpperCamelCase_       )
            return dpll_algorithm(UpperCamelCase_							,UpperCamelCase_							,UpperCamelCase_       )
       snake_case					=       symbols[0]
       snake_case					=       symbols[1:]
       snake_case				,						snake_case					=       model, model
       snake_case				,						snake_case					=       True, False
  
       return dpll_algorithm(UpperCamelCase_							,UpperCamelCase_							,UpperCamelCase_       ) or dpll_algorithm(UpperCamelCase_							,UpperCamelCase_							,UpperCamelCase_       )
  
  
  if __name__ == "__main__":
   import doctest
  
   doctest.testmod()
  
   _SCREAMING_SNAKE_CASE    :				Dict       =					generate_formula()
   print(f'''The formula {formula} is''', end=" ")
  
   _SCREAMING_SNAKE_CASE   ,     _SCREAMING_SNAKE_CASE    :				Any       =					generate_parameters(formula)
   _SCREAMING_SNAKE_CASE   ,     _SCREAMING_SNAKE_CASE    :				Optional[Any]       =					dpll_algorithm(clauses, symbols, {})
  
   if solution:
    print(f'''satisfiable with the assignment {model}.''')
   else:
    print("not satisfiable.")
  
  
  
  
  