from __future__ import annotations

import random

# Maximum size of the population.  Bigger could be faster but is more memory expensive.
lowerCAmelCase_     =	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.
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, 1000))



def      lowerCamelCase_(__SCREAMING_SNAKE_CASE     ,	__SCREAMING_SNAKE_CASE  )->    tuple[str, float]:
							_SCREAMING_SNAKE_CASE		:						Tuple			  =    len([g for position, g in enumerate(__SCREAMING_SNAKE_CASE  ) if g == main_target[position]]  )
							return (item, float(__SCREAMING_SNAKE_CASE  ))



def      lowerCamelCase_(__SCREAMING_SNAKE_CASE     ,	__SCREAMING_SNAKE_CASE  )->    tuple[str, str]:
							_SCREAMING_SNAKE_CASE		:						Union[str, Any]			  =    random.randint(0     ,	len(__SCREAMING_SNAKE_CASE  ) - 1  )
							_SCREAMING_SNAKE_CASE		:						Any			  =    parent_a[:random_slice] + parent_a[random_slice:]
							_SCREAMING_SNAKE_CASE		:						Dict			  =    parent_a[:random_slice] + parent_a[random_slice:]
							return (child_a, child_a)



def      lowerCamelCase_(__SCREAMING_SNAKE_CASE     ,	__SCREAMING_SNAKE_CASE  )->    str:
							_SCREAMING_SNAKE_CASE		:						Any			  =    list(__SCREAMING_SNAKE_CASE  )
							if random.uniform(0     ,	1  ) < MUTATION_PROBABILITY:
														_SCREAMING_SNAKE_CASE		:						Optional[int]			  =    random.choice(__SCREAMING_SNAKE_CASE  )
							return "".join(__SCREAMING_SNAKE_CASE  )



def      lowerCamelCase_(__SCREAMING_SNAKE_CASE     ,	__SCREAMING_SNAKE_CASE     ,	__SCREAMING_SNAKE_CASE     ,	)->    list[str]:
							_SCREAMING_SNAKE_CASE		:						Dict			  =    []
							# Generate more children proportionally to the fitness score.
							_SCREAMING_SNAKE_CASE		:						Any			  =    int(parent_a[1] * 100  ) + 1
							_SCREAMING_SNAKE_CASE		:						str			  =    10 if child_n >= 10 else child_n
							for _ in range(__SCREAMING_SNAKE_CASE  ):
														_SCREAMING_SNAKE_CASE		:						List[str]			  =    population_score[random.randint(0     ,	__SCREAMING_SNAKE_CASE  )][0]

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



def      lowerCamelCase_(__SCREAMING_SNAKE_CASE     ,	__SCREAMING_SNAKE_CASE     ,	__SCREAMING_SNAKE_CASE = True  )->    tuple[int, int, str]:

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

							# Generate random starting population.
							_SCREAMING_SNAKE_CASE		:						List[Any]			  =    []
							for _ in range(__SCREAMING_SNAKE_CASE  ):
														population.append("""""".join([random.choice(__SCREAMING_SNAKE_CASE  ) for i in range(len(__SCREAMING_SNAKE_CASE  )  )]  )  )

							# Just some logs to know what the algorithms is doing.
							_SCREAMING_SNAKE_CASE		:						Union[str, Any]			  =    0, 0

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

														# 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.
														_SCREAMING_SNAKE_CASE		:						Union[str, Any]			  =    [evaluate(__SCREAMING_SNAKE_CASE     ,	__SCREAMING_SNAKE_CASE  ) for item in population]

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

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





from typing import Any

import numpy as np



def      lowerCamelCase_(__SCREAMING_SNAKE_CASE  )->    bool:
							return np.array_equal(__SCREAMING_SNAKE_CASE     ,	matrix.conjugate().T  )



def      lowerCamelCase_(__SCREAMING_SNAKE_CASE     ,	__SCREAMING_SNAKE_CASE  )->    Any:
							_SCREAMING_SNAKE_CASE		:						Optional[int]			  =    v.conjugate().T
							_SCREAMING_SNAKE_CASE		:						Optional[int]			  =    v_star.dot(__SCREAMING_SNAKE_CASE  )
							assert isinstance(__SCREAMING_SNAKE_CASE     ,	np.ndarray  )
							return (v_star_dot.dot(__SCREAMING_SNAKE_CASE  )) / (v_star.dot(__SCREAMING_SNAKE_CASE  ))



def      lowerCamelCase_()->    None:
							_SCREAMING_SNAKE_CASE		:						Optional[Any]			  =    np.array([[2, 2 + 1j, 4], [2 - 1j, 3, 1j], [4, -1j, 1]]  )
							_SCREAMING_SNAKE_CASE		:						int			  =    np.array([[1], [2], [3]]  )
							assert is_hermitian(__SCREAMING_SNAKE_CASE  ), F"""{a} is not hermitian."""
							print(rayleigh_quotient(__SCREAMING_SNAKE_CASE     ,	__SCREAMING_SNAKE_CASE  )  )

							_SCREAMING_SNAKE_CASE		:						int			  =    np.array([[1, 2, 4], [2, 3, -1], [4, -1, 1]]  )
							assert is_hermitian(__SCREAMING_SNAKE_CASE  ), F"""{a} is not hermitian."""
							assert rayleigh_quotient(__SCREAMING_SNAKE_CASE     ,	__SCREAMING_SNAKE_CASE  ) == float(3  )


if __name__ == "__main__":
			import doctest

			doctest.testmod()
			tests()


