



'''simple docstring'''






from __future__ import annotations

import random

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


def 				snake_case_  (      _lowerCAmelCase						:		str     ,   _lowerCAmelCase						:		str						)   ->     tuple[str, float]:
							UpperCAmelCase				: str											=	len([g for position, g in enumerate(_lowerCAmelCase						) if g == main_target[position]]						)
							return (item, float(_lowerCAmelCase						))


def 				snake_case_  (      _lowerCAmelCase						:		str     ,   _lowerCAmelCase						:		str						)   ->     tuple[str, str]:
							UpperCAmelCase				: str											=	random.randint(0     ,   len(_lowerCAmelCase						) - 1						)
							UpperCAmelCase				: Dict											=	parent_a[:random_slice] + parent_a[random_slice:]
							UpperCAmelCase				: Tuple											=	parent_a[:random_slice] + parent_a[random_slice:]
							return (child_a, child_a)


def 				snake_case_  (      _lowerCAmelCase						:		str     ,   _lowerCAmelCase						:		list[str]						)   ->     str:
							UpperCAmelCase				: Optional[int]											=	list(_lowerCAmelCase						)
							if random.uniform(0     ,   1						) < MUTATION_PROBABILITY:
														UpperCAmelCase				: str											=	random.choice(_lowerCAmelCase						)
							return "".join(_lowerCAmelCase						)


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

														UpperCAmelCase				: Optional[int]											=	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 				snake_case_  (      _lowerCAmelCase						:		str     ,   _lowerCAmelCase						:		list[str]     ,   _lowerCAmelCase						:		bool = True						)   ->     tuple[int, int, str]:

							# Verify if N_POPULATION is bigger than N_SELECTED
							if N_POPULATION < N_SELECTED:
														UpperCAmelCase				: Optional[Any]											=	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.
							UpperCAmelCase				: Optional[int]											=	sorted({c for c in target if c not in genes}						)
							if not_in_genes_list:
														UpperCAmelCase				: str											=	f"""{not_in_genes_list} is not in genes list, evolution cannot converge"""
														raise ValueError(_lowerCAmelCase						)

							# Generate random starting population.
							UpperCAmelCase				: int											=	[]
							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.
							UpperCAmelCase				: Dict											=	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.
														UpperCAmelCase				: Optional[int]											=	[evaluate(_lowerCAmelCase     ,   _lowerCAmelCase						) for item in population]

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










'''simple docstring'''






def 				snake_case_  (      _lowerCAmelCase						:		Tuple     ,   _lowerCAmelCase						:		Tuple     ,   _lowerCAmelCase						:		int     ,   _lowerCAmelCase						:		Tuple						)   ->     Union[str, Any]:
							# Return True if there is node that has not iterated.
							UpperCAmelCase				: Optional[Any]											=	[False] * len(_lowerCAmelCase						)
							UpperCAmelCase				: Dict											=	[]
							queue.append(_lowerCAmelCase						)
							UpperCAmelCase				: str											=	True

							while queue:
														UpperCAmelCase				: Optional[int]											=	queue.pop(0						)
														for ind in range(len(graph[u]						)						):
																					if visited[ind] is False and graph[u][ind] > 0:
																												queue.append(_lowerCAmelCase						)
																												UpperCAmelCase				: Union[str, Any]											=	True
																												UpperCAmelCase				: Optional[int]											=	u

							return visited[t]


def 				snake_case_  (      _lowerCAmelCase						:		Union[str, Any]     ,   _lowerCAmelCase						:		List[str]     ,   _lowerCAmelCase						:		List[str]						)   ->     Any:
							# This array is filled by BFS and to store path
							UpperCAmelCase				: Dict											=	[-1] * (len(_lowerCAmelCase						))
							UpperCAmelCase				: Any											=	0
							while bfs(_lowerCAmelCase     ,   _lowerCAmelCase     ,   _lowerCAmelCase     ,   _lowerCAmelCase						):
														UpperCAmelCase				: List[str]											=	float('''Inf'''						)
														UpperCAmelCase				: str											=	sink

														while s != source:
																					# Find the minimum value in select path
																					UpperCAmelCase				: int											=	min(_lowerCAmelCase     ,   graph[parent[s]][s]						)
																					UpperCAmelCase				: Tuple											=	parent[s]

														max_flow += path_flow
														UpperCAmelCase				: Optional[Any]											=	sink

														while v != source:
																					UpperCAmelCase				: Dict											=	parent[v]
																					graph[u][v] -= path_flow
																					graph[v][u] += path_flow
																					UpperCAmelCase				: Dict											=	parent[v]
							return max_flow


UpperCamelCase__:     Tuple										=    [
    [0, 16, 13, 0, 0, 0],
    [0, 0, 10, 12, 0, 0],
    [0, 4, 0, 0, 14, 0],
    [0, 0, 9, 0, 0, 20],
    [0, 0, 0, 7, 0, 4],
    [0, 0, 0, 0, 0, 0],
]

UpperCamelCase__			,      UpperCamelCase__:     int										=    0, 5




print(ford_fulkerson(graph, source, sink))





