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()








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.")




