




"""simple docstring"""

class        lowercase      :

				'''simple docstring'''





				def __init__(							self   :					Optional[int]       ):



					"""simple docstring"""

					A_  :				dict[str, TrieNode]	   =		{}  # Mapping from char to TrieNode
					A_  :				str	   =		False







				def 					a_  (							self   :					Tuple      ,     _lowerCamelCase   :					list[str]       ):



					"""simple docstring"""

					for word in words:
						self.insert(_lowerCamelCase       )







				def 					a_  (							self   :					str      ,     _lowerCamelCase   :					str       ):



					"""simple docstring"""

					A_  :				List[str]	   =		self
					for char in word:
						if char not in curr.nodes:
							A_  :				str	   =		TrieNode()
						A_  :				List[Any]	   =		curr.nodes[char]
					A_  :				List[Any]	   =		True







				def 					a_  (							self   :					str      ,     _lowerCamelCase   :					str       ):



					"""simple docstring"""

					A_  :				str	   =		self
					for char in word:
						if char not in curr.nodes:
							return False
						A_  :				int	   =		curr.nodes[char]
					return curr.is_leaf







				def 					a_  (							self   :					int      ,     _lowerCamelCase   :					str       ):



					"""simple docstring"""

					def _delete(_lowerCamelCase   :					TrieNode      ,     _lowerCamelCase   :					str      ,     _lowerCamelCase   :					int       ) -> bool:
						if index == len(_lowerCamelCase       ):
							# If word does not exist
							if not curr.is_leaf:
								return False
							A_  :				str	   =		False
							return len(curr.nodes       ) == 0
						A_  :				Union[str, Any]	   =		word[index]
						A_  :				Optional[int]	   =		curr.nodes.get(_lowerCamelCase       )
						# If char not in current trie node
						if not char_node:
							return False
						# Flag to check if node can be deleted
						A_  :				List[Any]	   =		_delete(_lowerCamelCase      ,     _lowerCamelCase      ,     index + 1       )
						if delete_curr:
							del curr.nodes[char]
							return len(curr.nodes       ) == 0
						return delete_curr

					_delete(self      ,     _lowerCamelCase      ,     0       )

def 		lowercase_      (		_UpperCAmelCase  ,      _UpperCAmelCase	):




	"""simple docstring"""






	if node.is_leaf:
		print(_UpperCAmelCase  ,      end=''' '''	)

	for key, value in node.nodes.items():
		print_words(_UpperCAmelCase  ,      word + key	)

def 		lowercase_      (		):




	"""simple docstring"""






	A_  :				List[Any]	   =		'''banana bananas bandana band apple all beast'''.split()
	A_  :				List[Any]	   =		TrieNode()
	root.insert_many(_UpperCAmelCase	)
	# print_words(root, "")
	assert all(root.find(_UpperCAmelCase	) for word in words	)
	assert root.find('''banana'''	)
	assert not root.find('''bandanas'''	)
	assert not root.find('''apps'''	)
	assert root.find('''apple'''	)
	assert root.find('''all'''	)
	root.delete('''all'''	)
	assert not root.find('''all'''	)
	root.delete('''banana'''	)
	assert not root.find('''banana'''	)
	assert root.find('''bananas'''	)
	return True

def 		lowercase_      (		_UpperCAmelCase  ,      _UpperCAmelCase	):




	"""simple docstring"""






	print(str(_UpperCAmelCase	)  ,      '''works!''' if passes else '''doesn\'t work :('''	)

def 		lowercase_      (		):




	"""simple docstring"""






	assert test_trie()

def 		lowercase_      (		):




	"""simple docstring"""






	print_results('''Testing trie functionality'''  ,      test_trie()	)


if __name__ == "__main__":
		main()











"""simple docstring"""

from typing import Any

import numpy as np

def 		lowercase_      (		_UpperCAmelCase	):




	"""simple docstring"""






	return np.array_equal(_UpperCAmelCase  ,      matrix.conjugate().T	)

def 		lowercase_      (		_UpperCAmelCase  ,      _UpperCAmelCase	):




	"""simple docstring"""






	A_  :				Tuple	   =		v.conjugate().T
	A_  :				Tuple	   =		v_star.dot(_UpperCAmelCase	)
	assert isinstance(_UpperCAmelCase  ,      np.ndarray	)
	return (v_star_dot.dot(_UpperCAmelCase	)) / (v_star.dot(_UpperCAmelCase	))

def 		lowercase_      (		):




	"""simple docstring"""






	A_  :				Optional[Any]	   =		np.array([[2, 2 + 1J, 4], [2 - 1J, 3, 1J], [4, -1J, 1]]	)
	A_  :				str	   =		np.array([[1], [2], [3]]	)
	assert is_hermitian(_UpperCAmelCase	), f"""{a} is not hermitian."""
	print(rayleigh_quotient(_UpperCAmelCase  ,      _UpperCAmelCase	)	)

	A_  :				int	   =		np.array([[1, 2, 4], [2, 3, -1], [4, -1, 1]]	)
	assert is_hermitian(_UpperCAmelCase	), f"""{a} is not hermitian."""
	assert rayleigh_quotient(_UpperCAmelCase  ,      _UpperCAmelCase	) == float(3	)


if __name__ == "__main__":
		import doctest

		doctest.testmod()
		tests()





