





from collections.abc import Callable
from math import log
from os import name, system
from random import gauss, seed
from typing import TypeVar


def        __SCREAMING_SNAKE_CASE	(				__lowercase:		Tuple  ,				__lowercase:		str  ,				__lowercase:		Optional[int]):



  '''simple docstring'''






  seed(1)
  return [gauss(lowerCAmelCase_  ,				lowerCAmelCase_) for _ in range(lowerCAmelCase_)]


def        __SCREAMING_SNAKE_CASE	(				__lowercase:		int  ,				__lowercase:		Optional[Any]):



  '''simple docstring'''






  return [k for k in range(lowerCAmelCase_) for _ in range(instance_count[k])]


def        __SCREAMING_SNAKE_CASE	(				__lowercase:		Tuple  ,				__lowercase:		Dict):



  '''simple docstring'''






  return sum(lowerCAmelCase_) / instance_count


def        __SCREAMING_SNAKE_CASE	(				__lowercase:		List[Any]  ,				__lowercase:		Optional[Any]):



  '''simple docstring'''






  return instance_count / total_count


def        __SCREAMING_SNAKE_CASE	(				__lowercase:		Optional[int]  ,				__lowercase:		int  ,				__lowercase:		Dict):



  '''simple docstring'''






  __lowerCAmelCase								=					[]  # An empty list to store all squared differences
  # iterate over number of elements in items
  for i in range(len(lowerCAmelCase_)):
    # 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
  __lowerCAmelCase								=					len(lowerCAmelCase_)  # Number of classes in dataset
  return 1 / (total_count - n_classes) * sum(lowerCAmelCase_)


def        __SCREAMING_SNAKE_CASE	(				__lowercase:		Tuple  ,				__lowercase:		Tuple  ,				__lowercase:		Optional[Any]  ,				__lowercase:		int):



  '''simple docstring'''






  __lowerCAmelCase								=					[]
  # for loop iterates over number of elements in list
  for i in range(len(lowerCAmelCase_)):
    # for loop iterates over number of inner items of each element
    for j in range(len(x_items[i])):
      __lowerCAmelCase								=					[]  # 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(lowerCAmelCase_)):
        # 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(lowerCAmelCase_)

  return [result.index(max(lowerCAmelCase_)) for result in results]


def        __SCREAMING_SNAKE_CASE	(				__lowercase:		str  ,				__lowercase:		Any):



  '''simple docstring'''






  __lowerCAmelCase								=					sum(1 for i, j in zip(lowerCAmelCase_  ,				lowerCAmelCase_) 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(lowerCAmelCase_)) * 1_00


__lowercase				    =      TypeVar("""num""")


def        __SCREAMING_SNAKE_CASE	(				__lowercase:		Optional[int]  ,				__lowercase:		Optional[Any]  ,				__lowercase:		str  ,				__lowercase:		Optional[Any] = lambda __lowercase: True  ,				__lowercase:		str = None  ,				):



  '''simple docstring'''






  while True:
    try:
      __lowerCAmelCase								=					input_type(input(lowerCAmelCase_).strip() or default)
      if condition(lowerCAmelCase_):
        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        __SCREAMING_SNAKE_CASE	(				):



  '''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
    __lowerCAmelCase								=					valid_input(
        input_type=lowerCAmelCase_  ,				condition=lambda __lowercase: 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
    __lowerCAmelCase								=					valid_input(
        input_type=lowerCAmelCase_  ,				condition=lambda __lowercase: 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
    __lowerCAmelCase								=					[]  # An empty list to store instance counts of classes in dataset
    for i in range(lowerCAmelCase_):
      __lowerCAmelCase								=					valid_input(
          input_type=lowerCAmelCase_  ,				condition=lambda __lowercase: x > 0  ,				input_msg=(F'''Enter The number of instances for class_{i+1}: ''')  ,				err_msg='''Number of instances should be positive!'''  ,				)
      counts.append(lowerCAmelCase_)
    print('''-''' * 1_00)

    # An empty list to store values of user-entered means of classes
    __lowerCAmelCase								=					[]
    for a in range(lowerCAmelCase_):
      __lowerCAmelCase								=					valid_input(
          input_type=lowerCAmelCase_  ,				input_msg=(F'''Enter the value of mean for class_{a+1}: ''')  ,				err_msg='''This is an invalid value.'''  ,				)
      user_means.append(lowerCAmelCase_)
    print('''-''' * 1_00)

    print('''Standard deviation: '''  ,				lowerCAmelCase_)
    # print out the number of instances in classes in separated line
    for i, count in enumerate(lowerCAmelCase_  ,				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(lowerCAmelCase_  ,				1):
      print(F'''Mean of class_{i} is: {user_mean}''')
    print('''-''' * 1_00)

    # Generating training dataset drawn from gaussian distribution
    __lowerCAmelCase								=					[
        gaussian_distribution(user_means[j]  ,				lowerCAmelCase_  ,				counts[j])
        for j in range(lowerCAmelCase_)
    ]
    print('''Generated Normal Distribution: \n'''  ,				lowerCAmelCase_)
    print('''-''' * 1_00)

    # Generating Ys to detecting corresponding classes
    __lowerCAmelCase								=					y_generator(lowerCAmelCase_  ,				lowerCAmelCase_)
    print('''Generated Corresponding Ys: \n'''  ,				lowerCAmelCase_)
    print('''-''' * 1_00)

    # Calculating the value of actual mean for each class
    __lowerCAmelCase								=					[calculate_mean(counts[k]  ,				x[k]) for k in range(lowerCAmelCase_)]
    # for loop iterates over number of elements in 'actual_means' list and print
    # out them in separated line
    for i, actual_mean in enumerate(lowerCAmelCase_  ,				1):
      print(F'''Actual(Real) mean of class_{i} is: {actual_mean}''')
    print('''-''' * 1_00)

    # Calculating the value of probabilities for each class
    __lowerCAmelCase								=					[
        calculate_probabilities(counts[i]  ,				sum(lowerCAmelCase_)) for i in range(lowerCAmelCase_)
    ]

    # for loop iterates over number of elements in 'probabilities' list and print
    # out them in separated line
    for i, probability in enumerate(lowerCAmelCase_  ,				1):
      print(F'''Probability of class_{i} is: {probability}''')
    print('''-''' * 1_00)

    # Calculating the values of variance for each class
    __lowerCAmelCase								=					calculate_variance(lowerCAmelCase_  ,				lowerCAmelCase_  ,				sum(lowerCAmelCase_))
    print('''Variance: '''  ,				lowerCAmelCase_)
    print('''-''' * 1_00)

    # Predicting Y values
    # storing predicted Y values in 'pre_indexes' variable
    __lowerCAmelCase								=					predict_y_values(lowerCAmelCase_  ,				lowerCAmelCase_  ,				lowerCAmelCase_  ,				lowerCAmelCase_)
    print('''-''' * 1_00)

    # Calculating Accuracy of the model
    print(F'''Accuracy: {accuracy(lowerCAmelCase_  ,				lowerCAmelCase_)}''')
    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()

UpperCAmelCase				 =   {
    0: """underwear""",
    1: """pants""",
    2: """belt""",
    3: """suit""",
    4: """shoe""",
    5: """socks""",
    6: """shirt""",
    7: """tie""",
    8: """watch""",
}

UpperCAmelCase				 =   [[1, 4], [2, 4], [3], [], [], [4], [2, 7], [3], []]

UpperCAmelCase				 =   [0 for x in range(len(graph))]
UpperCAmelCase				 =   []







def 						UpperCAmelCase							(		lowerCAmelCase_    ,   lowerCAmelCase_							)						->						List[Any]:
     a	:     Tuple						      =    1
     while stack:
          a	:     Optional[Any]						      =    stack.pop()
          print(lowerCAmelCase_    ,   clothes[current_clothing]							)
          order += 1







def 						UpperCAmelCase							(		lowerCAmelCase_    ,   lowerCAmelCase_    ,   lowerCAmelCase_							)						->						Any:
     a	:     Union[str, Any]						      =    1
     for v in graph[u]:
          if not visited[v]:
               depth_first_search(lowerCAmelCase_    ,   lowerCAmelCase_    ,   lowerCAmelCase_							)

     stack.append(lowerCAmelCase_							)







def 						UpperCAmelCase							(		lowerCAmelCase_    ,   lowerCAmelCase_							)						->						Optional[Any]:
     for v in range(len(lowerCAmelCase_							)							):
          if not visited[v]:
               depth_first_search(lowerCAmelCase_    ,   lowerCAmelCase_    ,   lowerCAmelCase_							)


if __name__ == "__main__":
  topological_sort(graph, visited)
  print(stack)
  print_stack(stack, clothes)