import math as m





def      __lowercase  (		lowerCamelCase      :  Optional[int]						,						lowerCamelCase      :  str						,						lowerCamelCase      :  List[str]=0.0_0_1			):
 return (f(a + h			) - f(a - h			)) / (2 * h)





def      __lowercase  (		lowerCamelCase      :  Optional[Any]						,						lowerCamelCase      :  Union[str, Any]=0						,						lowerCamelCase      :  List[str]=100						,						lowerCamelCase      :  List[Any]=0.0_0_0_1						,						lowerCamelCase      :  Optional[Any]=1e-6						,						lowerCamelCase      :  str=False			):
 UpperCamelCase_      :		Optional[Any]				=      xa  # set the initial guess
 UpperCamelCase_      :		str				=      [a]
 UpperCamelCase_      :		Optional[Any]				=      abs(f(lowerCamelCase			)			)
 UpperCamelCase_      :		Dict				=      lambda lowerCamelCase			: calc_derivative(lowerCamelCase						,						lowerCamelCase						,						h=lowerCamelCase			)  # noqa: E731  Derivative of f(x)
 for _ in range(lowerCamelCase			):
  if fa(lowerCamelCase			) == 0:
   raise ValueError('No converging solution found'			)
  UpperCamelCase_      :		Optional[Any]				=      a - f(lowerCamelCase			) / fa(lowerCamelCase			)  # Calculate the next estimate
  if logsteps:
   steps.append(lowerCamelCase			)
  if error < maxerror:
   break
 else:
  raise ValueError('Iteration limit reached, no converging solution found'			)
 if logsteps:
  # If logstep is true, then log intermediate steps
  return a, error, steps
 return a, error


if __name__ == "__main__":
   from matplotlib import pyplot as plt

   a_					      = lambda x: m.tanh(x) ** 2 - m.exp(3 * x)  # noqa: E731
   a_      ,				a_      ,				a_					      = newton_raphson(
       f, xa=10, maxiter=1_000, step=1E-6, logsteps=True
   )
   plt.plot([abs(f(x)) for x in steps])
   plt.xlabel('step')
   plt.ylabel('error')
   plt.show()
   print(F"""solution = {{{solution:f}}}, error = {{{error:f}}}""")




from __future__ import annotations

from collections import deque
from queue import Queue
from timeit import timeit

a_					      = {
    'A': ['B', 'C'],
    'B': ['A', 'D', 'E'],
    'C': ['A', 'F'],
    'D': ['B'],
    'E': ['B', 'F'],
    'F': ['C', 'E'],
}





def      __lowercase  (		lowerCamelCase      :  dict						,						lowerCamelCase      :  str			):
 UpperCamelCase_      :		Tuple				=      {start}
 UpperCamelCase_      :		Optional[Any]				=      [start]
 UpperCamelCase_      :		Queue				=      Queue()
 queue.put(lowerCamelCase			)
 while not queue.empty():
  UpperCamelCase_      :		Union[str, Any]				=      queue.get()
  for w in graph[v]:
   if w not in explored:
    explored.add(lowerCamelCase			)
    result.append(lowerCamelCase			)
    queue.put(lowerCamelCase			)
 return result





def      __lowercase  (		lowerCamelCase      :  dict						,						lowerCamelCase      :  str			):
 UpperCamelCase_      :		Dict				=      {start}
 UpperCamelCase_      :		Optional[int]				=      [start]
 UpperCamelCase_      :		Union[str, Any]				=      deque([start]			)
 while queue:
  UpperCamelCase_      :		Optional[int]				=      queue.popleft()
  for child in graph[v]:
   if child not in visited:
    visited.add(lowerCamelCase			)
    result.append(lowerCamelCase			)
    queue.append(lowerCamelCase			)
 return result





def      __lowercase  (		lowerCamelCase      :  str			):
 UpperCamelCase_      :		str				=      F"from __main__ import G, {name}"
 UpperCamelCase_      :		int				=      10000
 UpperCamelCase_      :		Optional[Any]				=      timeit(F"{name}(G, 'A')"						,						setup=lowerCamelCase						,						number=lowerCamelCase			)
 print(F"{name:<35} finished {number} runs in {res:.5f} seconds"			)


if __name__ == "__main__":
   import doctest

   doctest.testmod()

   benchmark_function('breadth_first_search')
   benchmark_function('breadth_first_search_with_deque')
   # breadth_first_search                finished 10000 runs in 0.20999 seconds
   # breadth_first_search_with_deque     finished 10000 runs in 0.01421 seconds



