

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





def   __SCREAMING_SNAKE_CASE (SCREAMING_SNAKE_CASE__  ,		SCREAMING_SNAKE_CASE__	):
						return [k for k in range(SCREAMING_SNAKE_CASE__	) for _ in range(instance_count[k]	)]





def   __SCREAMING_SNAKE_CASE (SCREAMING_SNAKE_CASE__  ,		SCREAMING_SNAKE_CASE__	):
						return sum(SCREAMING_SNAKE_CASE__	) / instance_count





def   __SCREAMING_SNAKE_CASE (SCREAMING_SNAKE_CASE__  ,		SCREAMING_SNAKE_CASE__	):
						return instance_count / total_count





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





def   __SCREAMING_SNAKE_CASE (SCREAMING_SNAKE_CASE__  ,		SCREAMING_SNAKE_CASE__  ,		SCREAMING_SNAKE_CASE__  ,		SCREAMING_SNAKE_CASE__	):
						snake_case_       =     []
						# for loop iterates over number of elements in list
						for i in range(len(SCREAMING_SNAKE_CASE__	)	):
												# 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(SCREAMING_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(SCREAMING_SNAKE_CASE__	)

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





def   __SCREAMING_SNAKE_CASE (SCREAMING_SNAKE_CASE__  ,		SCREAMING_SNAKE_CASE__	):
						snake_case_       =     sum(1 for i, j in zip(SCREAMING_SNAKE_CASE__  ,		SCREAMING_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(SCREAMING_SNAKE_CASE__	)) * 100


lowerCAmelCase_	     =     TypeVar('''num''')





def   __SCREAMING_SNAKE_CASE (SCREAMING_SNAKE_CASE__  ,		SCREAMING_SNAKE_CASE__  ,		SCREAMING_SNAKE_CASE__  ,		SCREAMING_SNAKE_CASE__ = lambda SCREAMING_SNAKE_CASE__	: True  ,		SCREAMING_SNAKE_CASE__ = None  ,		):
						while True:
												try:
																		snake_case_       =     input_type(input(SCREAMING_SNAKE_CASE__	).strip() or default	)
																		if condition(SCREAMING_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 ():
						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=SCREAMING_SNAKE_CASE__  ,		condition=lambda SCREAMING_SNAKE_CASE__	: x > 0  ,		input_msg='''Enter the number of classes (Data Groupings): '''  ,		err_msg='''Number of classes should be positive!'''  ,		)

												print('''-''' * 100	)

												# Trying to get the value of standard deviation
												snake_case_       =     valid_input(
												    input_type=SCREAMING_SNAKE_CASE__  ,		condition=lambda SCREAMING_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('''-''' * 100	)

												# 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(SCREAMING_SNAKE_CASE__	):
																		snake_case_       =     valid_input(
																		    input_type=SCREAMING_SNAKE_CASE__  ,		condition=lambda SCREAMING_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(SCREAMING_SNAKE_CASE__	)
												print('''-''' * 100	)

												# An empty list to store values of user-entered means of classes
												snake_case_       =     []
												for a in range(SCREAMING_SNAKE_CASE__	):
																		snake_case_       =     valid_input(
																		    input_type=SCREAMING_SNAKE_CASE__  ,		input_msg=(F'''Enter the value of mean for class_{a+1}: ''')  ,		err_msg='''This is an invalid value.'''  ,		)
																		user_means.append(SCREAMING_SNAKE_CASE__	)
												print('''-''' * 100	)

												print('''Standard deviation: '''  ,		SCREAMING_SNAKE_CASE__	)
												# print out the number of instances in classes in separated line
												for i, count in enumerate(SCREAMING_SNAKE_CASE__  ,		1	):
																		print(F'''Number of instances in class_{i} is: {count}'''	)
												print('''-''' * 100	)

												# print out mean values of classes separated line
												for i, user_mean in enumerate(SCREAMING_SNAKE_CASE__  ,		1	):
																		print(F'''Mean of class_{i} is: {user_mean}'''	)
												print('''-''' * 100	)

												# Generating training dataset drawn from gaussian distribution
												snake_case_       =     [
												    gaussian_distribution(user_means[j]  ,		SCREAMING_SNAKE_CASE__  ,		counts[j]	)
												    for j in range(SCREAMING_SNAKE_CASE__	)
												]
												print('''Generated Normal Distribution: \n'''  ,		SCREAMING_SNAKE_CASE__	)
												print('''-''' * 100	)

												# Generating Ys to detecting corresponding classes
												snake_case_       =     y_generator(SCREAMING_SNAKE_CASE__  ,		SCREAMING_SNAKE_CASE__	)
												print('''Generated Corresponding Ys: \n'''  ,		SCREAMING_SNAKE_CASE__	)
												print('''-''' * 100	)

												# Calculating the value of actual mean for each class
												snake_case_       =     [calculate_mean(counts[k]  ,		x[k]	) for k in range(SCREAMING_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(SCREAMING_SNAKE_CASE__  ,		1	):
																		print(F'''Actual(Real) mean of class_{i} is: {actual_mean}'''	)
												print('''-''' * 100	)

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

												# for loop iterates over number of elements in 'probabilities' list and print
												# out them in separated line
												for i, probability in enumerate(SCREAMING_SNAKE_CASE__  ,		1	):
																		print(F'''Probability of class_{i} is: {probability}'''	)
												print('''-''' * 100	)

												# Calculating the values of variance for each class
												snake_case_       =     calculate_variance(SCREAMING_SNAKE_CASE__  ,		SCREAMING_SNAKE_CASE__  ,		sum(SCREAMING_SNAKE_CASE__	)	)
												print('''Variance: '''  ,		SCREAMING_SNAKE_CASE__	)
												print('''-''' * 100	)

												# Predicting Y values
												# storing predicted Y values in 'pre_indexes' variable
												snake_case_       =     predict_y_values(SCREAMING_SNAKE_CASE__  ,		SCREAMING_SNAKE_CASE__  ,		SCREAMING_SNAKE_CASE__  ,		SCREAMING_SNAKE_CASE__	)
												print('''-''' * 100	)

												# Calculating Accuracy of the model
												print(F'''Accuracy: {accuracy(SCREAMING_SNAKE_CASE__  ,		SCREAMING_SNAKE_CASE__	)}'''	)
												print('''-''' * 100	)
												print(''' DONE '''.center(100  ,		'''+'''	)	)

												if input('''Press any key to restart or \'q\' for quit: '''	).strip().lower() == "q":
																		print('''\n''' + '''GoodBye!'''.center(100  ,		'''-'''	) + '''\n'''	)
																		break
												system('''cls''' if name == '''nt''' else '''clear'''	)  # noqa: S605


if __name__ == "__main__":
					main()


from __future__ import annotations

from random import randrange


def   __SCREAMING_SNAKE_CASE (SCREAMING_SNAKE_CASE__	):
						if len(SCREAMING_SNAKE_CASE__	) < 2:
												return collection
						snake_case_       =     randrange(len(SCREAMING_SNAKE_CASE__	)	)  # Use random element as pivot
						snake_case_       =     collection[pivot_index]
						snake_case_       =     []  # All elements greater than pivot
						snake_case_       =     []  # All elements less than or equal to pivot

						for element in collection[:pivot_index]:
												(greater if element > pivot else lesser).append(SCREAMING_SNAKE_CASE__	)

						for element in collection[pivot_index + 1 :]:
												(greater if element > pivot else lesser).append(SCREAMING_SNAKE_CASE__	)

						return [*quick_sort(SCREAMING_SNAKE_CASE__	), pivot, *quick_sort(SCREAMING_SNAKE_CASE__	)]


if __name__ == "__main__":
					lowerCAmelCase_	     =     input('''Enter numbers separated by a comma:\n''').strip()
					lowerCAmelCase_	     =     [int(item) for item in user_input.split(''',''')]
					print(quick_sort(unsorted))