





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







def    UpperCAmelCase				(  _lowerCamelCase   :	Tuple      , _lowerCamelCase   :	List[Any]      , _lowerCamelCase   :	Any  ):





						'''simple docstring'''


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







def    UpperCAmelCase				(  _lowerCamelCase   :	Optional[int]      , _lowerCamelCase   :	Tuple  ):





						'''simple docstring'''


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







def    UpperCAmelCase				(  _lowerCamelCase   :	int      , _lowerCamelCase   :	Optional[int]  ):





						'''simple docstring'''


						return sum(_lowerCamelCase  ) / instance_count







def    UpperCAmelCase				(  _lowerCamelCase   :	Optional[int]      , _lowerCamelCase   :	Any  ):





						'''simple docstring'''


						return instance_count / total_count







def    UpperCAmelCase				(  _lowerCamelCase   :	Dict      , _lowerCamelCase   :	str      , _lowerCamelCase   :	List[Any]  ):





						'''simple docstring'''


						SCREAMING_SNAKE_CASE__  :					Optional[Any] =       []  # 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
						SCREAMING_SNAKE_CASE__  :					str =       len(_lowerCamelCase  )  # Number of classes in dataset
						return 1 / (total_count - n_classes) * sum(_lowerCamelCase  )







def    UpperCAmelCase				(  _lowerCamelCase   :	Tuple      , _lowerCamelCase   :	Tuple      , _lowerCamelCase   :	Optional[int]      , _lowerCamelCase   :	Optional[Any]  ):





						'''simple docstring'''


						SCREAMING_SNAKE_CASE__  :					Union[str, Any] =       []
						# 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]  )  ):
																		SCREAMING_SNAKE_CASE__  :					List[Any] =       []  # 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    UpperCAmelCase				(  _lowerCamelCase   :	List[Any]      , _lowerCamelCase   :	str  ):





						'''simple docstring'''


						SCREAMING_SNAKE_CASE__  :					str =       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  )) * 100


__lowercase							:Optional[Any]							=	TypeVar("num")







def    UpperCAmelCase				(  _lowerCamelCase   :	Optional[int]      , _lowerCamelCase   :	Tuple      , _lowerCamelCase   :	Tuple      , _lowerCamelCase   :	Union[str, Any] = lambda _lowerCamelCase  : True      , _lowerCamelCase   :	int = None      , ):





						'''simple docstring'''


						while True:
												try:
																		SCREAMING_SNAKE_CASE__  :					Any =       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    UpperCAmelCase				(  ):





						'''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
												SCREAMING_SNAKE_CASE__  :					Optional[Any] =       valid_input(
												    input_type=_lowerCamelCase      , condition=lambda _lowerCamelCase  : 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
												SCREAMING_SNAKE_CASE__  :					int =       valid_input(
												    input_type=_lowerCamelCase      , condition=lambda _lowerCamelCase  : 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
												SCREAMING_SNAKE_CASE__  :					Tuple =       []  # An empty list to store instance counts of classes in dataset
												for i in range(_lowerCamelCase  ):
																		SCREAMING_SNAKE_CASE__  :					Optional[Any] =       valid_input(
																		    input_type=_lowerCamelCase      , condition=lambda _lowerCamelCase  : 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("-" * 100  )

												# An empty list to store values of user-entered means of classes
												SCREAMING_SNAKE_CASE__  :					List[Any] =       []
												for a in range(_lowerCamelCase  ):
																		SCREAMING_SNAKE_CASE__  :					Dict =       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("-" * 100  )

												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("-" * 100  )

												# 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("-" * 100  )

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

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

												# Calculating the value of actual mean for each class
												SCREAMING_SNAKE_CASE__  :					Union[str, Any] =       [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("-" * 100  )

												# Calculating the value of probabilities for each class
												SCREAMING_SNAKE_CASE__  :					Any =       [
												    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("-" * 100  )

												# Calculating the values of variance for each class
												SCREAMING_SNAKE_CASE__  :					Optional[Any] =       calculate_variance(_lowerCamelCase      , _lowerCamelCase      , sum(_lowerCamelCase  )  )
												print("Variance: "      , _lowerCamelCase  )
												print("-" * 100  )

												# Predicting Y values
												# storing predicted Y values in 'pre_indexes' variable
												SCREAMING_SNAKE_CASE__  :					Optional[Any] =       predict_y_values(_lowerCamelCase      , _lowerCamelCase      , _lowerCamelCase      , _lowerCamelCase  )
												print("-" * 100  )

												# Calculating Accuracy of the model
												print(f"""Accuracy: {accuracy(_lowerCamelCase      , _lowerCamelCase  )}"""  )
												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 PIL import Image

# Define the first generation of cells
# fmt: off
a 			=							[[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1,
          0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]
def    a__    (	A       ):
   return [int(A       ) for c in F'''{ruleset:08}'''[:8]]
def    a__    (	A		,					A		,					A       ):
   lowercase__    :						List[Any]       =			len(cells[0]       )  # 31
   lowercase__    :						int       =			[]
   for i in range(A       ):
      # Get the neighbors of each cell
      # Handle neighbours outside bounds by using 0 as their value
      lowercase__    :						Optional[Any]       =			0 if i == 0 else cells[time][i - 1]
      lowercase__    :						Dict       =			0 if i == population - 1 else cells[time][i + 1]
      # Define a new cell and add it to the new generation
      lowercase__    :						str       =			7 - int(F'''{left_neighbor}{cells[time][i]}{right_neighbor}'''		,					2       )
      next_generation.append(rule[situation]       )
   return next_generation
def    a__    (	A       ):
   lowercase__    :						Tuple       =			Image.new("""RGB"""		,					(len(cells[0]       ), len(A       ))       )
   lowercase__    :						Optional[Any]       =			img.load()
   # Generates image
   for w in range(img.width       ):
      for h in range(img.height       ):
         lowercase__    :						Union[str, Any]       =			255 - int(255 * cells[h][w]       )
         lowercase__    :						int       =			(color, color, color)
   return img


if __name__ == "__main__":
 a 			=							bin(int(input('Rule:\n').strip()))[2:]
 a 			=							format_ruleset(int(rule_num))
 for time in range(16):
  CELLS.append(new_generation(CELLS, rule, time))
 a 			=							generate_image(CELLS)
 # Uncomment to save the image
 # img.save(f"rule_{rule_num}.png")
 img.show()


