
"""simple docstring"""
from collections.abc import Callable

import numpy as np





def    _lowerCAmelCase    (     lowerCamelCase__							:							Any,						lowerCamelCase__							:							Any,						lowerCamelCase__							:							Optional[int],						lowerCamelCase__							:							Dict,						lowerCamelCase__							:							Optional[Any]				)  ->    np.array:
  _SCREAMING_SNAKE_CASE   :				str							    = int(np.ceil((x_end - xa) / step_size				)				)
  _SCREAMING_SNAKE_CASE   :				Optional[Any]							    = np.zeros((n + 1,)				)
  _SCREAMING_SNAKE_CASE   :				Union[str, Any]							    = ya
  _SCREAMING_SNAKE_CASE   :				Tuple							    = xa

  for k in range(lowerCamelCase__				):
    _SCREAMING_SNAKE_CASE   :				int							    = y[k] + step_size * ode_func(lowerCamelCase__,						y[k]				)
    _SCREAMING_SNAKE_CASE   :				Tuple							    = y[k] + (
        (step_size / 2) * (ode_func(lowerCamelCase__,						y[k]				) + ode_func(x + step_size,						lowerCamelCase__				))
    )
    x += step_size

  return y


if __name__ == "__main__":
      import doctest

      doctest.testmod()





"""simple docstring"""
from __future__ import annotations

lowercase_       :						List[str]     					=	'''#'''
class 			UpperCamelCase      :
     def __init__(     self				):




       """simple docstring"""


       _SCREAMING_SNAKE_CASE   :				dict							    = {}
     def 				__SCREAMING_SNAKE_CASE							(     self  ,     snake_case__				):




       """simple docstring"""


       _SCREAMING_SNAKE_CASE   :				str							    = self._trie
       for char in text:
         if char not in trie:
           _SCREAMING_SNAKE_CASE   :				List[str]							    = {}
         _SCREAMING_SNAKE_CASE   :				List[str]							    = trie[char]
       _SCREAMING_SNAKE_CASE   :				Optional[Any]							    = True
     def 				__SCREAMING_SNAKE_CASE							(     self  ,     snake_case__				):




       """simple docstring"""


       _SCREAMING_SNAKE_CASE   :				Optional[Any]							    = self._trie
       for char in prefix:
         if char in trie:
           _SCREAMING_SNAKE_CASE   :				str							    = trie[char]
         else:
           return []
       return self._elements(snake_case__				)




     def 				__SCREAMING_SNAKE_CASE							(     self  ,     snake_case__				):




       """simple docstring"""


       _SCREAMING_SNAKE_CASE   :				str							    = []
       for c, v in d.items():
         _SCREAMING_SNAKE_CASE   :				int							    = [" "] if c == END else [(c + s) for s in self._elements(snake_case__				)]
         result.extend(snake_case__				)
       return tuple(snake_case__				)
lowercase_       :						Union[str, Any]     					=	Trie()
lowercase_       :						Optional[Any]     					=	('''depart''', '''detergent''', '''daring''', '''dog''', '''deer''', '''deal''')
for word in words:
      trie.insert_word(word)





def    _lowerCAmelCase    (     lowerCamelCase__							:							str				)  ->    tuple:
  _SCREAMING_SNAKE_CASE   :				Dict							    = trie.find_word(lowerCamelCase__				)
  return tuple(string + word for word in suffixes				)





def    _lowerCAmelCase    (     )  ->    None:
  print(autocomplete_using_trie("de"				)				)


if __name__ == "__main__":
      import doctest

      doctest.testmod()
      main()



