

from __future__ import annotations







def 						lowerCamelCase__      ( __A    :int | float | str	,__A    :int | float | str		):


       """simple docstring"""




       if nth_term == "":
              return [""]
       __snake_case       	=							int(__A		)
       __snake_case       	=							int(__A		)
       __snake_case       	=							[]
       for temp in range(int(__A		)		):
              series.append(F'1 / {pow(temp + 1	,int(__A		)		)}' if series else """1"""		)
       return series


if __name__ == "__main__":
    import doctest

    doctest.testmod()

    UpperCamelCase__		 =     int(input('''Enter the last number (nth term) of the P-Series'''))
    UpperCamelCase__		 =     int(input('''Enter the power for  P-Series'''))
    print('''Formula of P-Series => 1+1/2^p+1/3^p ..... 1/n^p''')
    print(p_series(nth_term, power))




from __future__ import annotations

import random

# Maximum size of the population.  Bigger could be faster but is more memory expensive.
UpperCamelCase__		 =     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.
UpperCamelCase__		 =     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.
UpperCamelCase__		 =     0.4
# Just a seed to improve randomness required by the algorithm.
random.seed(random.randint(0, 1000))







def 						lowerCamelCase__      ( __A    :str	,__A    :str		):


       """simple docstring"""




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







def 						lowerCamelCase__      ( __A    :str	,__A    :str		):


       """simple docstring"""




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







def 						lowerCamelCase__      ( __A    :str	,__A    :list[str]		):


       """simple docstring"""




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







def 						lowerCamelCase__      ( __A    :tuple[str, float]	,__A    :list[tuple[str, float]]	,__A    :list[str]	,):


       """simple docstring"""




       __snake_case       	=							[]
       # Generate more children proportionally to the fitness score.
       __snake_case       	=							int(parent_a[1] * 1_0_0		) + 1
       __snake_case       	=							1_0 if child_n >= 1_0 else child_n
       for _ in range(__A		):
              __snake_case       	=							population_score[random.randint(0	,__A		)][0]

              __snake_case	,    __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    :str	,__A    :list[str]	,__A    :bool = True		):


       """simple docstring"""




       if N_POPULATION < N_SELECTED:
              __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.
       __snake_case       	=							sorted({c for c in target if c not in genes}		)
       if not_in_genes_list:
              __snake_case       	=							F'{not_in_genes_list} is not in genes list, evolution cannot converge'
              raise ValueError(__A		)

       # Generate random starting population.
       __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.
       __snake_case	,    __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.
              __snake_case       	=							[evaluate(__A	,__A		) for item in population]

              # Check if there is a matching evolution.
              __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 % 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.
              __snake_case       	=							population[: int(N_POPULATION / 3		)]
              population.clear()
              population.extend(__A		)
              # Normalize population score to be between 0 and 1.
              __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__":
    UpperCamelCase__		 =     (
        '''This is a genetic algorithm to evaluate, combine, evolve, and mutate a string!'''
    )
    UpperCamelCase__		 =     list(
        ''' ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklm'''
        '''nopqrstuvwxyz.,;!?+-*#@^\'èéòà€ù=)(&%$£/\\'''
    )
    UpperCamelCase__ ,UpperCamelCase__ ,UpperCamelCase__		 =     basic(target_str, genes_list)
    print(
        F'\nGeneration: {generation}\nTotal Population: {population}\nTarget: {target}'
    )

