






'''simple docstring'''
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 		__SCREAMING_SNAKE_CASE					(  _UpperCamelCase						,		_UpperCamelCase							):


   """simple docstring"""




   lowercase_	:    Tuple           =     len([g for position, g in enumerate(_UpperCamelCase							) if g == main_target[position]]							)
   return (item, float(_UpperCamelCase							))




def 		__SCREAMING_SNAKE_CASE					(  _UpperCamelCase						,		_UpperCamelCase							):


   """simple docstring"""




   lowercase_	:    Union[str, Any]           =     random.randint(0						,		len(_UpperCamelCase							) - 1							)
   lowercase_	:    Any           =     parent_a[:random_slice] + parent_a[random_slice:]
   lowercase_	:    Optional[Any]           =     parent_a[:random_slice] + parent_a[random_slice:]
   return (child_a, child_a)




def 		__SCREAMING_SNAKE_CASE					(  _UpperCamelCase						,		_UpperCamelCase							):


   """simple docstring"""




   lowercase_	:    Tuple           =     list(_UpperCamelCase							)
   if random.uniform(0						,		1							) < MUTATION_PROBABILITY:
      lowercase_	:    Optional[Any]           =     random.choice(_UpperCamelCase							)
   return "".join(_UpperCamelCase							)




def 		__SCREAMING_SNAKE_CASE					(  _UpperCamelCase						,		_UpperCamelCase						,		_UpperCamelCase						,		):


   """simple docstring"""




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

      lowercase_    ,		lowercase_	:    Dict           =     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 		__SCREAMING_SNAKE_CASE					(  _UpperCamelCase						,		_UpperCamelCase						,		_UpperCamelCase = True							):


   """simple docstring"""




   if N_POPULATION < N_SELECTED:
      lowercase_	:    Optional[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.
   lowercase_	:    Union[str, Any]           =     sorted({c for c in target if c not in genes}							)
   if not_in_genes_list:
      lowercase_	:    Optional[Any]           =     F"""{not_in_genes_list} is not in genes list, evolution cannot converge"""
      raise ValueError(_UpperCamelCase							)

   # Generate random starting population.
   lowercase_	:    Dict           =     []
   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.
   lowercase_    ,		lowercase_	:    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.
      lowercase_	:    List[Any]           =     [evaluate(_UpperCamelCase						,		_UpperCamelCase							) for item in population]

      # Check if there is a matching evolution.
      lowercase_	:    Union[str, 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 % 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.
      lowercase_	:    Union[str, Any]           =     population[: int(N_POPULATION / 3							)]
      population.clear()
      population.extend(_UpperCamelCase							)
      # Normalize population score to be between 0 and 1.
      lowercase_	:    Union[str, Any]           =     [
          (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__":
 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}"""
 )












'''simple docstring'''
import heapq




def 		__SCREAMING_SNAKE_CASE					(  _UpperCamelCase							):


   """simple docstring"""




   lowercase_	:    list[list]           =     []

   # for each node and his adjacency list add them and the rank of the node to queue
   # using heapq module the queue will be filled like a Priority Queue
   # heapq works with a min priority queue, so I used -1*len(v) to build it
   for key, value in graph.items():
      # O(log(n))
      heapq.heappush(_UpperCamelCase						,		[-1 * len(_UpperCamelCase							), (key, value)]							)

   # chosen_vertices = set of chosen vertices
   lowercase_	:    Optional[Any]           =     set()

   # while queue isn't empty and there are still edges
   #   (queue[0][0] is the rank of the node with max rank)
   while queue and queue[0][0] != 0:
      # extract vertex with max rank from queue and add it to chosen_vertices
      lowercase_	:    Any           =     heapq.heappop(_UpperCamelCase							)[1][0]
      chosen_vertices.add(_UpperCamelCase							)

      # Remove all arcs adjacent to argmax
      for elem in queue:
         # if v haven't adjacent node, skip
         if elem[0] == 0:
            continue
         # if argmax is reachable from elem
         # remove argmax from elem's adjacent list and update his rank
         if argmax in elem[1][1]:
            lowercase_	:    str           =     elem[1][1].index(_UpperCamelCase							)
            del elem[1][1][index]
            elem[0] += 1
        # re-order the queue
      heapq.heapify(_UpperCamelCase							)
   return chosen_vertices


if __name__ == "__main__":
 import doctest

 doctest.testmod()

 UpperCamelCase__ =			{0: [1, 3], 1: [0, 3], 2: [0, 3, 4], 3: [0, 1, 2], 4: [2, 3]}
 print(f"""Minimum vertex cover:\n{greedy_min_vertex_cover(graph)}""")




