
'''simple docstring'''

class       UpperCAmelCase					:





		"""simple docstring"""





		def __init__(     self	,       _snake_case = ""	,       _snake_case = False  )					->     None:
				# Mapping from the first character of the prefix of the node
				_UpperCamelCase							:			Dict     =   {}

				# A node will be a leaf if the tree contains its word
				_UpperCamelCase							:			Any     =   is_leaf

				_UpperCamelCase							:			Any     =   prefix
		def _lowercase	(     self	,       _snake_case  )					->     tuple[str, str, str]:
				_UpperCamelCase							:			Optional[int]     =   0
				for q, w in zip(self.prefix	,       _snake_case  ):
						if q != w:
								break

						x += 1

				return self.prefix[:x], self.prefix[x:], word[x:]
		def _lowercase	(     self	,       _snake_case  )					->     None:
				for word in words:
						self.insert(_snake_case  )
		def _lowercase	(     self	,       _snake_case  )					->     None:
				# Case 1: If the word is the prefix of the node
				# Solution: We set the current node as leaf
				if self.prefix == word:
						_UpperCamelCase							:			Optional[int]     =   True

				# Case 2: The node has no edges that have a prefix to the word
				# Solution: We create an edge from the current node to a new one
				# containing the word
				elif word[0] not in self.nodes:
						_UpperCamelCase							:			List[Any]     =   RadixNode(prefix=_snake_case	,       is_leaf=_snake_case  )

				else:
						_UpperCamelCase							:			Optional[Any]     =   self.nodes[word[0]]
						_UpperCamelCase,				_UpperCamelCase,				_UpperCamelCase							:			List[Any]     =   incoming_node.match(
						    _snake_case  )

						# Case 3: The node prefix is equal to the matching
						# Solution: We insert remaining word on the next node
						if remaining_prefix == "":
								self.nodes[matching_string[0]].insert(_snake_case  )

						# Case 4: The word is greater equal to the matching
						# Solution: Create a node in between both nodes, change
						# prefixes and add the new node for the remaining word
						else:
								_UpperCamelCase							:			str     =   remaining_prefix

								_UpperCamelCase							:			int     =   self.nodes[matching_string[0]]
								_UpperCamelCase							:			List[str]     =   RadixNode(_snake_case	,       _snake_case  )
								_UpperCamelCase							:			int     =   aux_node

								if remaining_word == "":
										_UpperCamelCase							:			int     =   True
								else:
										self.nodes[matching_string[0]].insert(_snake_case  )
		def _lowercase	(     self	,       _snake_case  )					->     bool:
				_UpperCamelCase							:			Any     =   self.nodes.get(word[0]	,       _snake_case  )
				if not incoming_node:
						return False
				else:
						_UpperCamelCase,				_UpperCamelCase,				_UpperCamelCase							:			Any     =   incoming_node.match(
						    _snake_case  )
						# If there is remaining prefix, the word can't be on the tree
						if remaining_prefix != "":
								return False
						# This applies when the word and the prefix are equal
						elif remaining_word == "":
								return incoming_node.is_leaf
						# We have word remaining so we check the next node
						else:
								return incoming_node.find(_snake_case  )
		def _lowercase	(     self	,       _snake_case  )					->     bool:
				_UpperCamelCase							:			Union[str, Any]     =   self.nodes.get(word[0]	,       _snake_case  )
				if not incoming_node:
						return False
				else:
						_UpperCamelCase,				_UpperCamelCase,				_UpperCamelCase							:			Optional[int]     =   incoming_node.match(
						    _snake_case  )
						# If there is remaining prefix, the word can't be on the tree
						if remaining_prefix != "":
								return False
						# We have word remaining so we check the next node
						elif remaining_word != "":
								return incoming_node.delete(_snake_case  )
						else:
								# If it is not a leaf, we don't have to delete
								if not incoming_node.is_leaf:
										return False
								else:
										# We delete the nodes if no edges go from it
										if len(incoming_node.nodes  ) == 0:
												del self.nodes[word[0]]
												# We merge the current node with its only child
												if len(self.nodes  ) == 1 and not self.is_leaf:
														_UpperCamelCase							:			List[str]     =   list(self.nodes.values()  )[0]
														_UpperCamelCase							:			Tuple     =   merging_node.is_leaf
														self.prefix += merging_node.prefix
														_UpperCamelCase							:			Optional[int]     =   merging_node.nodes
                    # If there is more than 1 edge, we just mark it as non-leaf
										elif len(incoming_node.nodes  ) > 1:
												_UpperCamelCase							:			Union[str, Any]     =   False
										# If there is 1 edge, we merge it with its child
										else:
												_UpperCamelCase							:			Union[str, Any]     =   list(incoming_node.nodes.values()  )[0]
												_UpperCamelCase							:			Optional[int]     =   merging_node.is_leaf
												incoming_node.prefix += merging_node.prefix
												_UpperCamelCase							:			Optional[Any]     =   merging_node.nodes

										return True




		def _lowercase	(     self	,       _snake_case = 0  )					->     None:
				if self.prefix != "":
						print('''-''' * height	,       self.prefix	,       '''  (leaf)''' if self.is_leaf else ''''''  )

				for value in self.nodes.values():
						value.print_tree(height + 1  )







def     snake_case__						(   )			->   List[Any]:
		_UpperCamelCase							:			str     =   '''banana bananas bandana band apple all beast'''.split()
		_UpperCamelCase							:			Dict     =   RadixNode()
		root.insert_many(a_						)

		assert all(root.find(a_						) for word in words						)
		assert not root.find('''bandanas'''						)
		assert not root.find('''apps'''						)
		root.delete('''all'''						)
		assert not root.find('''all'''						)
		root.delete('''banana'''						)
		assert not root.find('''banana'''						)
		assert root.find('''bananas'''						)

		return True







def     snake_case__						(   )			->   Optional[int]:
		assert test_trie()







def     snake_case__						(   )			->   str:
		_UpperCamelCase							:			Any     =   RadixNode()
		_UpperCamelCase							:			Dict     =   '''banana bananas bandanas bandana band apple all beast'''.split()
		root.insert_many(a_						)

		print('''Words:'''      ,a_						)
		print('''Tree:'''						)
		root.print_tree()


if __name__ == "__main__":
	main()













import unittest

import numpy as np





def 		__UpperCAmelCase     (	a_				,	a_				,	a_				,	a_ = None				,	):
							snake_case_           =				np.shape(a_)
							snake_case_           =				np.shape(a_)
							snake_case_           =				np.shape(a_)

							if shape_a[0] != shape_b[0]:
														snake_case_           =				(
														    'Expected the same number of rows for A and B. '
														    f'''Instead found A of size {shape_a} and B of size {shape_b}'''
														)
														raise ValueError(a_)

							if shape_b[1] != shape_c[1]:
														snake_case_           =				(
														    'Expected the same number of columns for B and C. '
														    f'''Instead found B of size {shape_b} and C of size {shape_c}'''
														)
														raise ValueError(a_)

							snake_case_           =				pseudo_inv
							if a_inv is None:
														try:
																					snake_case_           =				np.linalg.inv(a_)
														except np.linalg.LinAlgError:
																					raise ValueError(
																					    'Input matrix A is not invertible. Cannot compute Schur complement.')

							return mat_c - mat_b.T @ a_inv @ mat_b




class 					UpperCamelCase_ (     unittest.TestCase							):



	'''simple docstring'''




	def 				_UpperCamelCase     (			self   )			->       None:
								snake_case_           =				np.array([[1, 2, 1], [2, 1, 2], [3, 2, 4]]   )
								snake_case_           =				np.array([[0, 3], [3, 0], [2, 3]]   )
								snake_case_           =				np.array([[2, 1], [6, 3]]   )

								snake_case_           =				schur_complement(a			,     a			,     a   )

								snake_case_           =				np.block([[a, b], [b.T, c]]   )

								snake_case_           =				np.linalg.det(a   )
								snake_case_           =				np.linalg.det(a   )
								snake_case_           =				np.linalg.det(a   )

								self.assertAlmostEqual(a			,     det_a * det_s   )




	def 				_UpperCamelCase     (			self   )			->       None:
								snake_case_           =				np.array([[1, 2, 1], [2, 1, 2], [3, 2, 4]]   )
								snake_case_           =				np.array([[0, 3], [3, 0], [2, 3]]   )
								snake_case_           =				np.array([[2, 1], [6, 3]]   )

								with self.assertRaises(a   ):
															schur_complement(a			,     a			,     a   )






	def 				_UpperCamelCase     (			self   )			->       None:
								snake_case_           =				np.array([[1, 2, 1], [2, 1, 2], [3, 2, 4]]   )
								snake_case_           =				np.array([[0, 3], [3, 0], [2, 3]]   )
								snake_case_           =				np.array([[2, 1, 3], [6, 3, 5]]   )

								with self.assertRaises(a   ):
															schur_complement(a			,     a			,     a   )


if __name__ == "__main__":
	import doctest

	doctest.testmod()
	unittest.main()





