
"""simple docstring"""




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			(			__a,				__a     ):
		SCREAMING_SNAKE_CASE_    			=			len([g for position, g in enumerate(__a     ) if g == main_target[position]]     )
		return (item, float(__a     ))



def 							_lowerCamelCase			(			__a,				__a     ):
		SCREAMING_SNAKE_CASE_    			=			random.randint(0,				len(__a     ) - 1     )
		SCREAMING_SNAKE_CASE_    			=			parent_a[:random_slice] + parent_a[random_slice:]
		SCREAMING_SNAKE_CASE_    			=			parent_a[:random_slice] + parent_a[random_slice:]
		return (child_a, child_a)



def 							_lowerCamelCase			(			__a,				__a     ):
		SCREAMING_SNAKE_CASE_    			=			list(__a     )
		if random.uniform(0,				1     ) < MUTATION_PROBABILITY:
				SCREAMING_SNAKE_CASE_    			=			random.choice(__a     )
		return "".join(__a     )



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

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



def 							_lowerCamelCase			(			__a,				__a,				__a = True     ):

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

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

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

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

				# 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_    			=			[evaluate(__a,				__a     ) for item in population]

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

				# This is selection
				for i in range(__a     ):
						population.extend(select(population_score[int(__a     )],				__a,				__a     )     )
						# 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(__a     ) > 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 __future__ import annotations

from collections.abc import Callable



def 							_lowerCamelCase			(			__a,				__a,				__a,				__a = 100,				):
		SCREAMING_SNAKE_CASE_    			=			x_start
		SCREAMING_SNAKE_CASE_    			=			fnc(__a     )
		SCREAMING_SNAKE_CASE_    			=			0.0
		for _ in range(__a     ):
				# Approximates small segments of curve as linear and solve
				# for trapezoidal area
				SCREAMING_SNAKE_CASE_    			=			(x_end - x_start) / steps + xa
				SCREAMING_SNAKE_CASE_    			=			fnc(__a     )
				area += abs(fxa + fxa     ) * (xa - xa) / 2
				# Increment step
				SCREAMING_SNAKE_CASE_    			=			xa
				SCREAMING_SNAKE_CASE_    			=			fxa
		return area


if __name__ == "__main__":



						def 							_lowerCamelCase			(			__a     ):
								return x**3 + x**2

						print('f(x) = x^3 + x^2')
						print('The area between the curve, x = -5, x = 5 and the x axis is:')
						lowerCAmelCase__				=					10
						while i <= 100000:
												print(f'''with {i} steps: {trapezoidal_area(f, -5, 5, i)}''')
												i *= 10