



from __future__ import annotations

import random

# Maximum size of the population.  Bigger could be faster but is more memory expensive.
__snake_case     :Optional[int]			       =200
# 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.
__snake_case     :Optional[Any]			       =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.
__snake_case     :int			       =0.4
# Just a seed to improve randomness required by the algorithm.
random.seed(random.randint(0, 1000))






def  lowerCamelCase_	(      lowerCAmelCase__	:	str			,	lowerCAmelCase__	:	str				)       ->							tuple[str, float]:

							'''simple docstring'''






							A      						=    len([g for position, g in enumerate(lowerCAmelCase__				) if g == main_target[position]]				)
							return (item, float(lowerCAmelCase__				))






def  lowerCamelCase_	(      lowerCAmelCase__	:	str			,	lowerCAmelCase__	:	str				)       ->							tuple[str, str]:

							'''simple docstring'''






							A      						=    random.randint(0			,	len(lowerCAmelCase__				) - 1				)
							A      						=    parent_a[:random_slice] + parent_a[random_slice:]
							A      						=    parent_a[:random_slice] + parent_a[random_slice:]
							return (child_a, child_a)






def  lowerCamelCase_	(      lowerCAmelCase__	:	str			,	lowerCAmelCase__	:	list[str]				)       ->							str:

							'''simple docstring'''






							A      						=    list(lowerCAmelCase__				)
							if random.uniform(0			,	1				) < MUTATION_PROBABILITY:
														A      						=    random.choice(lowerCAmelCase__				)
							return "".join(lowerCAmelCase__				)






def  lowerCamelCase_	(      lowerCAmelCase__	:	tuple[str, float]			,	lowerCAmelCase__	:	list[tuple[str, float]]			,	lowerCAmelCase__	:	list[str]			,	)       ->							list[str]:

							'''simple docstring'''






							A      						=    []
							# Generate more children proportionally to the fitness score.
							A      						=    int(parent_a[1] * 100				) + 1
							A      						=    10 if child_n >= 10 else child_n
							for _ in range(lowerCAmelCase__				):
														A      						=    population_score[random.randint(0			,	lowerCAmelCase__				)][0]

														A						,   A      						=    crossover(parent_a[0]			,	lowerCAmelCase__				)
														# Append new string to the population list.
														pop.append(mutate(lowerCAmelCase__			,	lowerCAmelCase__				)				)
														pop.append(mutate(lowerCAmelCase__			,	lowerCAmelCase__				)				)
							return pop






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

							'''simple docstring'''






							if N_POPULATION < N_SELECTED:
														A      						=    F'''{N_POPULATION} must be bigger than {N_SELECTED}'''
														raise ValueError(lowerCAmelCase__				)
							# Verify that the target contains no genes besides the ones inside genes variable.
							A      						=    sorted({c for c in target if c not in genes}				)
							if not_in_genes_list:
														A      						=    F'''{not_in_genes_list} is not in genes list, evolution cannot converge'''
														raise ValueError(lowerCAmelCase__				)

							# Generate random starting population.
							A      						=    []
							for _ in range(lowerCAmelCase__				):
														population.append(''.join([random.choice(lowerCAmelCase__				) for i in range(len(lowerCAmelCase__				)				)]				)				)

							# Just some logs to know what the algorithms is doing.
							A						,   A      						=    0, 0

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

														# 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.
														A      						=    [evaluate(lowerCAmelCase__			,	lowerCAmelCase__				) for item in population]

														# Check if there is a matching evolution.
														A      						=    sorted(lowerCAmelCase__			,	key=lambda lowerCAmelCase__				: x[1]			,	reverse=lowerCAmelCase__				)
														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 % 10 == 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.
														A      						=    population[: int(N_POPULATION / 3				)]
														population.clear()
														population.extend(lowerCAmelCase__				)
														# Normalize population score to be between 0 and 1.
														A      						=    [
														    (item, score / len(lowerCAmelCase__				)) for item, score in population_score
														]

														# This is selection
														for i in range(lowerCAmelCase__				):
																					population.extend(select(population_score[int(lowerCAmelCase__				)]			,	lowerCAmelCase__			,	lowerCAmelCase__				)				)
																					# 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(lowerCAmelCase__				) > N_POPULATION:
																												break


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




from collections.abc import Callable

import numpy as np






def  lowerCamelCase_	(      lowerCAmelCase__	:	Callable			,	lowerCAmelCase__	:	float			,	lowerCAmelCase__	:	float			,	lowerCAmelCase__	:	float			,	lowerCAmelCase__	:	float				)       ->							np.array:

							'''simple docstring'''






							A      						=    int(np.ceil((x_end - xa) / step_size				)				)
							A      						=    np.zeros((n + 1,)				)
							A      						=    ya
							A      						=    xa

							for k in range(lowerCAmelCase__				):
														A      						=    y[k] + step_size * ode_func(lowerCAmelCase__			,	y[k]				)
														A      						=    y[k] + (
														    (step_size / 2) * (ode_func(lowerCAmelCase__			,	y[k]				) + ode_func(x + step_size			,	lowerCAmelCase__				))
														)
														x += step_size

							return y


if __name__ == "__main__":
				import doctest

				doctest.testmod()