

class 			lowercase    :




				def __init__( self				,       snake_case = ""				,       snake_case = False	):
											# Mapping from the first character of the prefix of the node
											snake_case_          =   {}

											# A node will be a leaf if the tree contains its word
											snake_case_          =   is_leaf

											snake_case_          =   prefix




				def    a							( self				,       snake_case	):
											snake_case_          =   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    a							( self				,       snake_case	):
											for word in words:
																		self.insert(snake_case	)




				def    a							( self				,       snake_case	):
											# Case 1: If the word is the prefix of the node
											# Solution: We set the current node as leaf
											if self.prefix == word:
																		snake_case_          =   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:
																		snake_case_          =   RadixNode(prefix=snake_case				,       is_leaf=snake_case	)

											else:
																		snake_case_          =   self.nodes[word[0]]
																		snake_case_    ,   snake_case_    ,   snake_case_          =   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:
																									snake_case_          =   remaining_prefix

																									snake_case_          =   self.nodes[matching_string[0]]
																									snake_case_          =   RadixNode(snake_case				,       snake_case	)
																									snake_case_          =   aux_node

																									if remaining_word == "":
																																snake_case_          =   True
																									else:
																																self.nodes[matching_string[0]].insert(snake_case	)




				def    a							( self				,       snake_case	):
											snake_case_          =   self.nodes.get(word[0]				,       snake_case	)
											if not incoming_node:
																		return False
											else:
																		snake_case_    ,   snake_case_    ,   snake_case_          =   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    a							( self				,       snake_case	):
											snake_case_          =   self.nodes.get(word[0]				,       snake_case	)
											if not incoming_node:
																		return False
											else:
																		snake_case_    ,   snake_case_    ,   snake_case_          =   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:
																																														snake_case_          =   list(self.nodes.values()	)[0]
																																														snake_case_          =   merging_node.is_leaf
																																														self.prefix += merging_node.prefix
																																														snake_case_          =   merging_node.nodes
                    # If there is more than 1 edge, we just mark it as non-leaf
																																elif len(incoming_node.nodes	) > 1:
																																							snake_case_          =   False
																																# If there is 1 edge, we merge it with its child
																																else:
																																							snake_case_          =   list(incoming_node.nodes.values()	)[0]
																																							snake_case_          =   merging_node.is_leaf
																																							incoming_node.prefix += merging_node.prefix
																																							snake_case_          =   merging_node.nodes

																																return True




				def    a							( self				,       snake_case = 0	):
											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  __lowerCamelCase     (			):







							'''simple docstring'''






							snake_case_          =   'banana bananas bandana band apple all beast'.split()
							snake_case_          =   RadixNode()
							root.insert_many(UpperCamelCase__				)

							assert all(root.find(UpperCamelCase__				) 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  __lowerCamelCase     (			):







							'''simple docstring'''






							assert test_trie()





def  __lowerCamelCase     (			):







							'''simple docstring'''






							snake_case_          =   RadixNode()
							snake_case_          =   'banana bananas bandanas bandana band apple all beast'.split()
							root.insert_many(UpperCamelCase__				)

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


if __name__ == "__main__":
					main()







def  __lowerCamelCase     (			UpperCamelCase__       ,							UpperCamelCase__       ,							UpperCamelCase__       ,							UpperCamelCase__				):







							'''simple docstring'''






							global f  # a global dp table for knapsack
							if f[i][j] < 0:
														if j < wt[i - 1]:
																					snake_case_          =   mf_knapsack(i - 1       ,							UpperCamelCase__       ,							UpperCamelCase__       ,							UpperCamelCase__				)
														else:
																					snake_case_          =   max(
																					    mf_knapsack(i - 1       ,							UpperCamelCase__       ,							UpperCamelCase__       ,							UpperCamelCase__				)       ,							mf_knapsack(i - 1       ,							UpperCamelCase__       ,							UpperCamelCase__       ,							j - wt[i - 1]				) + val[i - 1]       ,							)
														snake_case_          =   val
							return f[i][j]





def  __lowerCamelCase     (			UpperCamelCase__       ,							UpperCamelCase__       ,							UpperCamelCase__       ,							UpperCamelCase__				):







							'''simple docstring'''






							snake_case_          =   [[0] * (w + 1) for _ in range(n + 1				)]

							for i in range(1       ,							n + 1				):
														for w_ in range(1       ,							w + 1				):
																					if wt[i - 1] <= w_:
																												snake_case_          =   max(val[i - 1] + dp[i - 1][w_ - wt[i - 1]]       ,							dp[i - 1][w_]				)
																					else:
																												snake_case_          =   dp[i - 1][w_]

							return dp[n][w_], dp





def  __lowerCamelCase     (			UpperCamelCase__       ,							UpperCamelCase__       ,							UpperCamelCase__				):







							'''simple docstring'''






							if not (isinstance(UpperCamelCase__       ,							(list, tuple)				) and isinstance(UpperCamelCase__       ,							(list, tuple)				)):
														raise ValueError(
														    'Both the weights and values vectors must be either lists or tuples'				)

							snake_case_          =   len(UpperCamelCase__				)
							if num_items != len(UpperCamelCase__				):
														snake_case_          =   (
														    'The number of weights must be the same as the number of values.\n'
														    F'''But got {num_items} weights and {len(UpperCamelCase__				)} values'''
														)
														raise ValueError(UpperCamelCase__				)
							for i in range(UpperCamelCase__				):
														if not isinstance(wt[i]       ,							UpperCamelCase__				):
																					snake_case_          =   (
																					    'All weights must be integers but got weight of '
																					    F'''type {type(wt[i]				)} at index {i}'''
																					)
																					raise TypeError(UpperCamelCase__				)

							snake_case_    ,   snake_case_          =   knapsack(UpperCamelCase__       ,							UpperCamelCase__       ,							UpperCamelCase__       ,							UpperCamelCase__				)
							snake_case_          =   set()
							_construct_solution(UpperCamelCase__       ,							UpperCamelCase__       ,							UpperCamelCase__       ,							UpperCamelCase__       ,							UpperCamelCase__				)

							return optimal_val, example_optional_set





def  __lowerCamelCase     (			UpperCamelCase__       ,							UpperCamelCase__       ,							UpperCamelCase__       ,							UpperCamelCase__       ,							UpperCamelCase__				):







							'''simple docstring'''






							if i > 0 and j > 0:
														if dp[i - 1][j] == dp[i][j]:
																					_construct_solution(UpperCamelCase__       ,							UpperCamelCase__       ,							i - 1       ,							UpperCamelCase__       ,							UpperCamelCase__				)
														else:
																					optimal_set.add(UpperCamelCase__				)
																					_construct_solution(UpperCamelCase__       ,							UpperCamelCase__       ,							i - 1       ,							j - wt[i - 1]       ,							UpperCamelCase__				)


if __name__ == "__main__":
					_UpperCAmelCase		:       int						    =	[3, 2, 4, 4]
					_UpperCAmelCase		:       Tuple						    =	[4, 3, 2, 3]
					_UpperCAmelCase		:       Dict						    =	4
					_UpperCAmelCase		:       int						    =	6
					_UpperCAmelCase		:       Union[str, Any]						    =	[[0] * (w + 1)] + [[0] + [-1] * (w + 1) for _ in range(n + 1)]
					_UpperCAmelCase    ,						_UpperCAmelCase		:       Optional[int]						    =	knapsack(w, wt, val, n)
					print(optimal_solution)
					print(mf_knapsack(n, wt, val, w))  # switched the n and w

					# testing the dynamic programming problem with example
					# the optimal subset for the above example are items 3 and 4
					_UpperCAmelCase    ,						_UpperCAmelCase		:       Optional[int]						    =	knapsack_with_example_solution(w, wt, val)
					assert optimal_solution == 8
					assert optimal_subset == {3, 4}
					print("""optimal_value = """, optimal_solution)
					print("""An optimal subset corresponding to the optimal value""", optimal_subset)




