
"""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      lowerCAmelCase_     (	snake_case_	:    float							,					snake_case_	:    float							,					snake_case_	:    int    )     ->list:
			seed(1    )
			return [gauss(snake_case_							,					snake_case_    ) for _ in range(snake_case_    )]






def      lowerCAmelCase_     (	snake_case_	:    int							,					snake_case_	:    list    )     ->list:
			return [k for k in range(snake_case_    ) for _ in range(instance_count[k]    )]






def      lowerCAmelCase_     (	snake_case_	:    int							,					snake_case_	:    list    )     ->float:
			return sum(snake_case_    ) / instance_count






def      lowerCAmelCase_     (	snake_case_	:    int							,					snake_case_	:    int    )     ->float:
			return instance_count / total_count






def      lowerCAmelCase_     (	snake_case_	:    list							,					snake_case_	:    list							,					snake_case_	:    int    )     ->float:
			lowerCamelCase__			:  List[str]  =[]  # 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
			lowerCamelCase__			:  str  =len(snake_case_    )  # Number of classes in dataset
			return 1 / (total_count - n_classes) * sum(snake_case_    )






def      lowerCAmelCase_     (	snake_case_	:    list							,					snake_case_	:    list							,					snake_case_	:    float							,					snake_case_	:    list    )     ->list:
			lowerCamelCase__			:  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]    )    ):
									lowerCamelCase__			:  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(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      lowerCAmelCase_     (	snake_case_	:    list							,					snake_case_	:    list    )     ->float:
			lowerCamelCase__			:  int  =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			=		TypeVar("""num""")






def      lowerCAmelCase_     (	snake_case_	:    Callable[[object], num]							,					snake_case_	:    str							,					snake_case_	:    str							,					snake_case_	:    Callable[[num], bool] = lambda snake_case_    : True							,					snake_case_	:    str | None = None							,					)     ->num:
			while True:
						try:
									lowerCamelCase__			:  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      lowerCAmelCase_     (	)     ->Any:
			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
						lowerCamelCase__			:  List[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
						lowerCamelCase__			:  List[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
						lowerCamelCase__			:  str  =[]  # An empty list to store instance counts of classes in dataset
						for i in range(snake_case_    ):
									lowerCamelCase__			:  Optional[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
						lowerCamelCase__			:  Dict  =[]
						for a in range(snake_case_    ):
									lowerCamelCase__			:  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
						lowerCamelCase__			:  List[str]  =[
						    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
						lowerCamelCase__			:  Optional[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
						lowerCamelCase__			:  Any  =[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
						lowerCamelCase__			:  Optional[Any]  =[
						    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
						lowerCamelCase__			:  List[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
						lowerCamelCase__			:  str  =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()








"""simple docstring"""


# A Bipartite Graph is a graph whose vertices can be divided into two independent sets,
# U and V such that every edge (u, v) either connects a vertex from U to V or a vertex
# from V to U. In other words, for every edge (u, v), either u belongs to U and v to V,
# or u belongs to V and v to U. We can also say that there is no edge that connects
# vertices of same set.
from queue import Queue






def      lowerCAmelCase_     (	snake_case_	:    List[Any]    )     ->Optional[int]:
			lowerCamelCase__			:  Optional[int]  =Queue()
			lowerCamelCase__			:  Any  =[False] * len(snake_case_    )
			lowerCamelCase__			:  Optional[Any]  =[-1] * len(snake_case_    )

			def bfs():
						while not queue.empty():
									lowerCamelCase__			:  List[Any]  =queue.get()
									lowerCamelCase__			:  int  =True

									for neighbour in graph[u]:
												if neighbour == u:
															return False

												if color[neighbour] == -1:
															lowerCamelCase__			:  Union[str, Any]  =1 - color[u]
															queue.put(snake_case_    )

												elif color[neighbour] == color[u]:
															return False

						return True

			for i in range(len(snake_case_    )    ):
						if not visited[i]:
									queue.put(snake_case_    )
									lowerCamelCase__			:  Tuple  =0
									if bfs() is False:
												return False

			return True


if __name__ == "__main__":
							# Adjacency List of graph
							print(check_bipartite({0: [1, 3], 1: [0, 2], 2: [1, 3], 3: [0, 2]}))