"""simple docstring"""






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__    (     __UpperCAmelCase ,					__UpperCAmelCase ,					__UpperCAmelCase				)						->						list:
   seed(1				)
   return [gauss(__UpperCAmelCase ,					__UpperCAmelCase				) for _ in range(__UpperCAmelCase				)]



def SCREAMING_SNAKE_CASE__    (     __UpperCAmelCase ,					__UpperCAmelCase				)						->						list:
   return [k for k in range(__UpperCAmelCase				) for _ in range(instance_count[k]				)]



def SCREAMING_SNAKE_CASE__    (     __UpperCAmelCase ,					__UpperCAmelCase				)						->						float:
   return sum(__UpperCAmelCase				) / instance_count



def SCREAMING_SNAKE_CASE__    (     __UpperCAmelCase ,					__UpperCAmelCase				)						->						float:
   return instance_count / total_count



def SCREAMING_SNAKE_CASE__    (     __UpperCAmelCase ,					__UpperCAmelCase ,					__UpperCAmelCase				)						->						float:
   lowercase__:     Optional[Any]      =   []  # 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
   lowercase__:     List[Any]      =   len(__UpperCAmelCase				)  # Number of classes in dataset
   return 1 / (total_count - n_classes) * sum(__UpperCAmelCase				)



def SCREAMING_SNAKE_CASE__    (     __UpperCAmelCase ,					__UpperCAmelCase ,					__UpperCAmelCase ,					__UpperCAmelCase				)						->						list:
   lowercase__:     str      =   []
   # 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]				)				):
         lowercase__:     int      =   []  # 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 SCREAMING_SNAKE_CASE__    (     __UpperCAmelCase ,					__UpperCAmelCase				)						->						float:
   lowercase__:     Tuple      =   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_0_0


__A         =				TypeVar("num")



def SCREAMING_SNAKE_CASE__    (     __UpperCAmelCase ,					__UpperCAmelCase ,					__UpperCAmelCase ,					__UpperCAmelCase = lambda __UpperCAmelCase				: True ,					__UpperCAmelCase = None ,					)						->						num:
   while True:
      try:
         lowercase__:     str      =   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 SCREAMING_SNAKE_CASE__    (     )						->						str:
   while True:
      print(''' Linear Discriminant Analysis '''.center(5_0 ,					'''*'''				)				)
      print('''*''' * 5_0 ,					'''\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
      lowercase__:     Optional[int]      =   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_0_0				)

      # Trying to get the value of standard deviation
      lowercase__:     Optional[Any]      =   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_0_0				)

      # Trying to get number of instances in classes and theirs means to generate
      # dataset
      lowercase__:     Any      =   []  # An empty list to store instance counts of classes in dataset
      for i in range(__UpperCAmelCase				):
         lowercase__:     Union[str, Any]      =   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_0_0				)

      # An empty list to store values of user-entered means of classes
      lowercase__:     Optional[int]      =   []
      for a in range(__UpperCAmelCase				):
         lowercase__:     List[Any]      =   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_0_0				)

      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_0_0				)

      # 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_0_0				)

      # Generating training dataset drawn from gaussian distribution
      lowercase__:     Tuple      =   [
          gaussian_distribution(user_means[j] ,					__UpperCAmelCase ,					counts[j]				)
          for j in range(__UpperCAmelCase				)
      ]
      print('''Generated Normal Distribution: \n''' ,					__UpperCAmelCase				)
      print('''-''' * 1_0_0				)

      # Generating Ys to detecting corresponding classes
      lowercase__:     int      =   y_generator(__UpperCAmelCase ,					__UpperCAmelCase				)
      print('''Generated Corresponding Ys: \n''' ,					__UpperCAmelCase				)
      print('''-''' * 1_0_0				)

      # Calculating the value of actual mean for each class
      lowercase__:     Optional[int]      =   [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_0_0				)

      # Calculating the value of probabilities for each class
      lowercase__:     Dict      =   [
          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_0_0				)

      # Calculating the values of variance for each class
      lowercase__:     List[str]      =   calculate_variance(__UpperCAmelCase ,					__UpperCAmelCase ,					sum(__UpperCAmelCase				)				)
      print('''Variance: ''' ,					__UpperCAmelCase				)
      print('''-''' * 1_0_0				)

      # Predicting Y values
      # storing predicted Y values in 'pre_indexes' variable
      lowercase__:     Optional[Any]      =   predict_y_values(__UpperCAmelCase ,					__UpperCAmelCase ,					__UpperCAmelCase ,					__UpperCAmelCase				)
      print('''-''' * 1_0_0				)

      # Calculating Accuracy of the model
      print(F"""Accuracy: {accuracy(__UpperCAmelCase ,					__UpperCAmelCase				)}"""				)
      print('''-''' * 1_0_0				)
      print(''' DONE '''.center(1_0_0 ,					'''+'''				)				)

      if input('''Press any key to restart or \'q\' for quit: '''				).strip().lower() == "q":
         print('''\n''' + '''GoodBye!'''.center(1_0_0 ,					'''-'''				) + '''\n'''				)
         break
      system('''cls''' if name == '''nt''' else '''clear'''				)  # noqa: S605


if __name__ == "__main__":
       main()

"""simple docstring"""






def SCREAMING_SNAKE_CASE__    (     __UpperCAmelCase				)						->						Optional[int]:
   lowercase__:     str      =   [7_0_1, 3_0_1, 1_3_2, 5_7, 2_3, 1_0, 4, 1]
   for gap in gaps:
      for i in range(__UpperCAmelCase ,					len(__UpperCAmelCase				)				):
         lowercase__:     Any      =   collection[i]
         lowercase__:     Tuple      =   i
         while j >= gap and collection[j - gap] > insert_value:
            lowercase__:     List[str]      =   collection[j - gap]
            j -= gap
         if j != i:
            lowercase__:     List[str]      =   insert_value
   return collection


if __name__ == "__main__":
       from doctest import testmod

       testmod()
       __A         =				input("Enter numbers separated by a comma:\n").strip()
       __A         =				[int(item) for item in user_input.split(",")]
       print(shell_sort(unsorted))
