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   SCREAMING_SNAKE_CASE__						(							snake_case_,	snake_case_,	snake_case_	)			->							list:
  				seed(1	)
  				return [gauss(snake_case_,	snake_case_	) for _ in range(snake_case_	)]
  
  
  
  def   SCREAMING_SNAKE_CASE__						(							snake_case_,	snake_case_	)			->							list:
  				return [k for k in range(snake_case_	) for _ in range(instance_count[k]	)]
  
  
  
  def   SCREAMING_SNAKE_CASE__						(							snake_case_,	snake_case_	)			->							float:
  				return sum(snake_case_	) / instance_count
  
  
  
  def   SCREAMING_SNAKE_CASE__						(							snake_case_,	snake_case_	)			->							float:
  				return instance_count / total_count
  
  
  
  def   SCREAMING_SNAKE_CASE__						(							snake_case_,	snake_case_,	snake_case_	)			->							float:
  				A__     :							List[Any]   				=[]  # An empty list to store all squared differences
  				# iterate over number of elements in items
  				for i in range(len(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
  				A__     :							Tuple   				=len(snake_case_	)  # Number of classes in dataset
  				return 1 / (total_count - n_classes) * sum(snake_case_	)
  
  
  
  def   SCREAMING_SNAKE_CASE__						(							snake_case_,	snake_case_,	snake_case_,	snake_case_	)			->							list:
  				A__     :							List[Any]   				=[]
  				# for loop iterates over number of elements in list
  				for i in range(len(snake_case_	)	):
  								# for loop iterates over number of inner items of each element
  								for j in range(len(x_items[i]	)	):
  												A__     :							List[str]   				=[]  # 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(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(snake_case_	)
  
  				return [result.index(max(snake_case_	)	) for result in results]
  
  
  
  def   SCREAMING_SNAKE_CASE__						(							snake_case_,	snake_case_	)			->							float:
  				A__     :							Dict   				=sum(1 for i, j in zip(snake_case_,	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(snake_case_	)) * 1_0_0
  
  
  __lowerCamelCase       :       List[Any]				   =			TypeVar("num")
  
  
  
  def   SCREAMING_SNAKE_CASE__						(							snake_case_,	snake_case_,	snake_case_,	snake_case_ = lambda snake_case_	: True,	snake_case_ = None,	)			->							num:
  				while True:
  								try:
  												A__     :							Union[str, Any]   				=input_type(input(snake_case_	).strip() or default	)
  												if condition(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   SCREAMING_SNAKE_CASE__						(							)			->							Optional[int]:
  				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
  								A__     :							Union[str, Any]   				=valid_input(
  								    input_type=snake_case_,	condition=lambda snake_case_	: 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
  								A__     :							Any   				=valid_input(
  								    input_type=snake_case_,	condition=lambda 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('''-''' * 1_0_0	)
  
  								# Trying to get number of instances in classes and theirs means to generate
  								# dataset
  								A__     :							Optional[int]   				=[]  # An empty list to store instance counts of classes in dataset
  								for i in range(snake_case_	):
  												A__     :							int   				=valid_input(
  												    input_type=snake_case_,	condition=lambda 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(snake_case_	)
  								print('''-''' * 1_0_0	)
  
  								# An empty list to store values of user-entered means of classes
  								A__     :							Tuple   				=[]
  								for a in range(snake_case_	):
  												A__     :							Any   				=valid_input(
  												    input_type=snake_case_,	input_msg=(f'Enter the value of mean for class_{a+1}: '),	err_msg='''This is an invalid value.''',	)
  												user_means.append(snake_case_	)
  								print('''-''' * 1_0_0	)
  
  								print('''Standard deviation: ''',	snake_case_	)
  								# print out the number of instances in classes in separated line
  								for i, count in enumerate(snake_case_,	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(snake_case_,	1	):
  												print(f'Mean of class_{i} is: {user_mean}'	)
  								print('''-''' * 1_0_0	)
  
  								# Generating training dataset drawn from gaussian distribution
  								A__     :							Optional[int]   				=[
  								    gaussian_distribution(user_means[j],	snake_case_,	counts[j]	)
  								    for j in range(snake_case_	)
  								]
  								print('''Generated Normal Distribution: \n''',	snake_case_	)
  								print('''-''' * 1_0_0	)
  
  								# Generating Ys to detecting corresponding classes
  								A__     :							Any   				=y_generator(snake_case_,	snake_case_	)
  								print('''Generated Corresponding Ys: \n''',	snake_case_	)
  								print('''-''' * 1_0_0	)
  
  								# Calculating the value of actual mean for each class
  								A__     :							int   				=[calculate_mean(counts[k],	x[k]	) for k in range(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(snake_case_,	1	):
  												print(f'Actual(Real) mean of class_{i} is: {actual_mean}'	)
  								print('''-''' * 1_0_0	)
  
  								# Calculating the value of probabilities for each class
  								A__     :							str   				=[
  								    calculate_probabilities(counts[i],	sum(snake_case_	)	) for i in range(snake_case_	)
  								]
  
  								# for loop iterates over number of elements in 'probabilities' list and print
  								# out them in separated line
  								for i, probability in enumerate(snake_case_,	1	):
  												print(f'Probability of class_{i} is: {probability}'	)
  								print('''-''' * 1_0_0	)
  
  								# Calculating the values of variance for each class
  								A__     :							Any   				=calculate_variance(snake_case_,	snake_case_,	sum(snake_case_	)	)
  								print('''Variance: ''',	snake_case_	)
  								print('''-''' * 1_0_0	)
  
  								# Predicting Y values
  								# storing predicted Y values in 'pre_indexes' variable
  								A__     :							Tuple   				=predict_y_values(snake_case_,	snake_case_,	snake_case_,	snake_case_	)
  								print('''-''' * 1_0_0	)
  
  								# Calculating Accuracy of the model
  								print(f'Accuracy: {accuracy(snake_case_,	snake_case_	)}'	)
  								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()
  
  
  
  
style_context: 
  
  
  from __future__ import annotations
  
  
  
  def   SCREAMING_SNAKE_CASE__						(							snake_case_	)			->							list[int]:
  				A__     :							Optional[int]   				=[0] * len(snake_case_	)
  				for i in range(1,	len(snake_case_	)	):
  								A__     :							List[Any]   				=duration_times[i - 1] + waiting_times[i - 1]
  				return waiting_times
  
  
  
  def   SCREAMING_SNAKE_CASE__						(							snake_case_,	snake_case_	)			->							list[int]:
  				return [
  				    duration_time + waiting_times[i]
  				    for i, duration_time in enumerate(snake_case_	)
  				]
  
  
  
  def   SCREAMING_SNAKE_CASE__						(							snake_case_	)			->							float:
  				return sum(snake_case_	) / len(snake_case_	)
  
  
  
  def   SCREAMING_SNAKE_CASE__						(							snake_case_	)			->							float:
  				return sum(snake_case_	) / len(snake_case_	)
  
  
  if __name__ == "__main__":
  						# process id's
  						__lowerCamelCase       :       List[str]				   =			[1, 2, 3]
  
  						# ensure that we actually have processes
  						if len(processes) == 0:
  												print("Zero amount of processes")
  												raise SystemExit(0)
  
  						# duration time of all processes
  						__lowerCamelCase       :       Dict				   =			[19, 8, 9]
  
  						# ensure we can match each id to a duration time
  						if len(duration_times) != len(processes):
  												print("Unable to match all id's with their duration time")
  												raise SystemExit(0)
  
  						# get the waiting times and the turnaround times
  						__lowerCamelCase       :       int				   =			calculate_waiting_times(duration_times)
  						__lowerCamelCase       :       Optional[int]				   =			calculate_turnaround_times(duration_times, waiting_times)
  
  						# get the average times
  						__lowerCamelCase       :       List[str]				   =			calculate_average_waiting_time(waiting_times)
  						__lowerCamelCase       :       Dict				   =			calculate_average_turnaround_time(turnaround_times)
  
  						# print all the results
  						print("Process ID\tDuration Time\tWaiting Time\tTurnaround Time")
  						for i, process in enumerate(processes):
  												print(
  												    F"{process}\t\t{duration_times[i]}\t\t{waiting_times[i]}\t\t"
  												    F"{turnaround_times[i]}"
  												)
  						print(F"Average waiting time = {average_waiting_time}")
  						print(F"Average turn around time = {average_turnaround_time}")
  
  
  
  