






"""simple docstring"""





from __future__ import annotations

import random

# Maximum size of the population.  Bigger could be faster but is more memory expensive.
__lowerCamelCase							=  2_00
# Number of elements selected in every generation of evolution. The selection takes
# place from best to worst of that generation and must be smaller than N_POPULATION.
__lowerCamelCase							=  50
# Probability that an element of a generation can mutate, changing one of its genes.
# This will guarantee that all genes will be used during evolution.
__lowerCamelCase							=  0.4
# Just a seed to improve randomness required by the algorithm.
random.seed(random.randint(0, 10_00))



def   a    (     __UpperCAmelCase      :    str      ,   __UpperCAmelCase      :    str  )    ->							tuple[str, float]:
						__magic_name__:	Any							=       len([g for position, g in enumerate(__UpperCAmelCase  ) if g == main_target[position]]  )
						return (item, float(__UpperCAmelCase  ))



def   a    (     __UpperCAmelCase      :    str      ,   __UpperCAmelCase      :    str  )    ->							tuple[str, str]:
						__magic_name__:	Tuple							=       random.randint(0      ,   len(__UpperCAmelCase  ) - 1  )
						__magic_name__:	Optional[Any]							=       parent_a[:random_slice] + parent_a[random_slice:]
						__magic_name__:	Optional[Any]							=       parent_a[:random_slice] + parent_a[random_slice:]
						return (child_a, child_a)



def   a    (     __UpperCAmelCase      :    str      ,   __UpperCAmelCase      :    list[str]  )    ->							str:
						__magic_name__:	Union[str, Any]							=       list(__UpperCAmelCase  )
						if random.uniform(0      ,   1  ) < MUTATION_PROBABILITY:
												__magic_name__:	Any							=       random.choice(__UpperCAmelCase  )
						return "".join(__UpperCAmelCase  )



def   a    (     __UpperCAmelCase      :    tuple[str, float]      ,   __UpperCAmelCase      :    list[tuple[str, float]]      ,   __UpperCAmelCase      :    list[str]      ,   )    ->							list[str]:
						__magic_name__:	Union[str, Any]							=       []
						# Generate more children proportionally to the fitness score.
						__magic_name__:	List[str]							=       int(parent_a[1] * 1_0_0  ) + 1
						__magic_name__:	Union[str, Any]							=       1_0 if child_n >= 1_0 else child_n
						for _ in range(__UpperCAmelCase  ):
												__magic_name__:	Union[str, Any]							=       population_score[random.randint(0      ,   __UpperCAmelCase  )][0]

												__magic_name__,			__magic_name__:	List[str]							=       crossover(parent_a[0]      ,   __UpperCAmelCase  )
												# Append new string to the population list.
												pop.append(mutate(__UpperCAmelCase      ,   __UpperCAmelCase  )  )
												pop.append(mutate(__UpperCAmelCase      ,   __UpperCAmelCase  )  )
						return pop



def   a    (     __UpperCAmelCase      :    str      ,   __UpperCAmelCase      :    list[str]      ,   __UpperCAmelCase      :    bool = True  )    ->							tuple[int, int, str]:

						# Verify if N_POPULATION is bigger than N_SELECTED
						if N_POPULATION < N_SELECTED:
												__magic_name__:	Any							=       f'{N_POPULATION} must be bigger than {N_SELECTED}'
												raise ValueError(__UpperCAmelCase  )
						# Verify that the target contains no genes besides the ones inside genes variable.
						__magic_name__:	Dict							=       sorted({c for c in target if c not in genes}  )
						if not_in_genes_list:
												__magic_name__:	List[str]							=       f'{not_in_genes_list} is not in genes list, evolution cannot converge'
												raise ValueError(__UpperCAmelCase  )

						# Generate random starting population.
						__magic_name__:	Optional[Any]							=       []
						for _ in range(__UpperCAmelCase  ):
												population.append("""""".join([random.choice(__UpperCAmelCase  ) for i in range(len(__UpperCAmelCase  )  )]  )  )

						# Just some logs to know what the algorithms is doing.
						__magic_name__,			__magic_name__:	Optional[int]							=       0, 0

						# This loop will end when we find a perfect match for our target.
						while True:
												generation += 1
												total_population += len(__UpperCAmelCase  )

												# Random population created. Now it's time to evaluate.

												# Adding a bit of concurrency can make everything faster,
												#
												# import concurrent.futures
												# population_score: list[tuple[str, float]] = []
												# with concurrent.futures.ThreadPoolExecutor(
												#                                   max_workers=NUM_WORKERS) as executor:
												#     futures = {executor.submit(evaluate, item) for item in population}
												#     concurrent.futures.wait(futures)
												#     population_score = [item.result() for item in futures]
												#
												# but with a simple algorithm like this, it will probably be slower.
												# We just need to call evaluate for every item inside the population.
												__magic_name__:	Tuple							=       [evaluate(__UpperCAmelCase      ,   __UpperCAmelCase  ) for item in population]

												# Check if there is a matching evolution.
												__magic_name__:	List[Any]							=       sorted(__UpperCAmelCase      ,   key=lambda __UpperCAmelCase  : x[1]      ,   reverse=__UpperCAmelCase  )
												if population_score[0][0] == target:
																		return (generation, total_population, population_score[0][0])

												# Print the best result every 10 generation.
												# Just to know that the algorithm is working.
												if debug and generation % 1_0 == 0:
																		print(
																		    f'\nGeneration: {generation}'
																		    f'\nTotal Population:{total_population}'
																		    f'\nBest score: {population_score[0][1]}'
																		    f'\nBest string: {population_score[0][0]}'  )

												# Flush the old population, keeping some of the best evolutions.
												# Keeping this avoid regression of evolution.
												__magic_name__:	int							=       population[: int(N_POPULATION / 3  )]
												population.clear()
												population.extend(__UpperCAmelCase  )
												# Normalize population score to be between 0 and 1.
												__magic_name__:	Dict							=       [
												    (item, score / len(__UpperCAmelCase  )) for item, score in population_score
												]

												# This is selection
												for i in range(__UpperCAmelCase  ):
																		population.extend(select(population_score[int(__UpperCAmelCase  )]      ,   __UpperCAmelCase      ,   __UpperCAmelCase  )  )
																		# Check if the population has already reached the maximum value and if so,
																		# break the cycle.  If this check is disabled, the algorithm will take
																		# forever to compute large strings, but will also calculate small strings in
																		# a far fewer generations.
																		if len(__UpperCAmelCase  ) > N_POPULATION:
																								break


if __name__ == "__main__":
							__lowerCamelCase							=  (
							    'This is a genetic algorithm to evaluate, combine, evolve, and mutate a string!'
							)
							__lowerCamelCase							=  list(
							    ' ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklm'
							    'nopqrstuvwxyz.,;!?+-*#@^\'èéòà€ù=)(&%$£/\\'
							)
							__lowerCamelCase		,					__lowerCamelCase		,					__lowerCamelCase							=  basic(target_str, genes_list)
							print(
							    f'''\nGeneration: {generation}\nTotal Population: {population}\nTarget: {target}'''
							)











"""simple docstring"""





def   a    (     __UpperCAmelCase      :    int      ,   __UpperCAmelCase      :    int  )    ->							int:
						while b:
												__magic_name__,			__magic_name__:	Optional[int]							=       b, a % b
						return a



def   a    (     __UpperCAmelCase      :    int      ,   __UpperCAmelCase      :    int  )    ->							int:
						return a if b == 0 else euclidean_gcd_recursive(__UpperCAmelCase      ,   a % b  )



def   a    (     )    ->							List[Any]:
						print(f'euclidean_gcd(3, 5) = {euclidean_gcd(3      ,   5  )}'  )
						print(f'euclidean_gcd(5, 3) = {euclidean_gcd(5      ,   3  )}'  )
						print(f'euclidean_gcd(1, 3) = {euclidean_gcd(1      ,   3  )}'  )
						print(f'euclidean_gcd(3, 6) = {euclidean_gcd(3      ,   6  )}'  )
						print(f'euclidean_gcd(6, 3) = {euclidean_gcd(6      ,   3  )}'  )

						print(f'euclidean_gcd_recursive(3, 5) = {euclidean_gcd_recursive(3      ,   5  )}'  )
						print(f'euclidean_gcd_recursive(5, 3) = {euclidean_gcd_recursive(5      ,   3  )}'  )
						print(f'euclidean_gcd_recursive(1, 3) = {euclidean_gcd_recursive(1      ,   3  )}'  )
						print(f'euclidean_gcd_recursive(3, 6) = {euclidean_gcd_recursive(3      ,   6  )}'  )
						print(f'euclidean_gcd_recursive(6, 3) = {euclidean_gcd_recursive(6      ,   3  )}'  )


if __name__ == "__main__":
							main()



