


'''simple docstring'''



def   lowerCamelCase							(_SCREAMING_SNAKE_CASE				:       int						,				_SCREAMING_SNAKE_CASE				:       Union[str, Any]						,				_SCREAMING_SNAKE_CASE				:       Dict						,				_SCREAMING_SNAKE_CASE				:       Tuple       ):
					global f  # a global dp table for knapsack
					if f[i][j] < 0:
										if j < wt[i - 1]:
															__a      :	List[str]    =  mf_knapsack(i - 1						,				_SCREAMING_SNAKE_CASE						,				_SCREAMING_SNAKE_CASE						,				_SCREAMING_SNAKE_CASE       )
										else:
															__a      :	Tuple    =  max(
															    mf_knapsack(i - 1						,				_SCREAMING_SNAKE_CASE						,				_SCREAMING_SNAKE_CASE						,				_SCREAMING_SNAKE_CASE       )						,				mf_knapsack(i - 1						,				_SCREAMING_SNAKE_CASE						,				_SCREAMING_SNAKE_CASE						,				j - wt[i - 1]       ) + val[i - 1]						,				)
										__a      :	Any    =  val
					return f[i][j]






def   lowerCamelCase							(_SCREAMING_SNAKE_CASE				:       List[Any]						,				_SCREAMING_SNAKE_CASE				:       Optional[Any]						,				_SCREAMING_SNAKE_CASE				:       List[str]						,				_SCREAMING_SNAKE_CASE				:       str       ):
					__a      :	int    =  [[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_:
																				__a      :	str    =  max(val[i - 1] + dp[i - 1][w_ - wt[i - 1]]						,				dp[i - 1][w_]       )
															else:
																				__a      :	Union[str, Any]    =  dp[i - 1][w_]

					return dp[n][w_], dp






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

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

					__a      :	List[str]    =  knapsack(_SCREAMING_SNAKE_CASE						,				_SCREAMING_SNAKE_CASE						,				_SCREAMING_SNAKE_CASE						,				_SCREAMING_SNAKE_CASE       )
					__a      :	set    =  set()
					_construct_solution(_SCREAMING_SNAKE_CASE						,				_SCREAMING_SNAKE_CASE						,				_SCREAMING_SNAKE_CASE						,				_SCREAMING_SNAKE_CASE						,				_SCREAMING_SNAKE_CASE       )

					return optimal_val, example_optional_set






def   lowerCamelCase							(_SCREAMING_SNAKE_CASE				:       list						,				_SCREAMING_SNAKE_CASE				:       list						,				_SCREAMING_SNAKE_CASE				:       int						,				_SCREAMING_SNAKE_CASE				:       int						,				_SCREAMING_SNAKE_CASE				:       set       ):
					# for the current item i at a maximum weight j to be part of an optimal subset,
					# the optimal value at (i, j) must be greater than the optimal value at (i-1, j).
					# where i - 1 means considering only the previous items at the given maximum weight
					if i > 0 and j > 0:
										if dp[i - 1][j] == dp[i][j]:
															_construct_solution(_SCREAMING_SNAKE_CASE						,				_SCREAMING_SNAKE_CASE						,				i - 1						,				_SCREAMING_SNAKE_CASE						,				_SCREAMING_SNAKE_CASE       )
										else:
															optimal_set.add(_SCREAMING_SNAKE_CASE       )
															_construct_solution(_SCREAMING_SNAKE_CASE						,				_SCREAMING_SNAKE_CASE						,				i - 1						,				j - wt[i - 1]						,				_SCREAMING_SNAKE_CASE       )


if __name__ == "__main__":
	__lowercase     :						Tuple	=     [3, 2, 4, 4]
	__lowercase     :						Any	=     [4, 3, 2, 3]
	__lowercase     :						Optional[Any]	=     4
	__lowercase     :						List[Any]	=     6
	__lowercase     :						List[Any]	=     [[0] * (w + 1)] + [[0] + [-1] * (w + 1) for _ in range(n + 1)]
	__lowercase     :						List[str]	=     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
	__lowercase     :						Union[str, Any]	=     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)







'''simple docstring'''



from __future__ import annotations

from dataclasses import dataclass





@dataclass
class 							__UpperCamelCase    :
	A_           =   42
	A_           =   None
	A_           =   None






def   lowerCamelCase							(_SCREAMING_SNAKE_CASE				:       TreeNode | None       ):

					# Validation
					def is_valid_tree(_SCREAMING_SNAKE_CASE				:       TreeNode | None       ) -> bool:
										if node is None:
															return True

										if not isinstance(_SCREAMING_SNAKE_CASE						,				_SCREAMING_SNAKE_CASE       ):
															return False

										try:
															float(node.data       )
										except (TypeError, ValueError):
															return False

										return is_valid_tree(node.left       ) and is_valid_tree(node.right       )

					if not is_valid_tree(_SCREAMING_SNAKE_CASE       ):
										raise ValueError(
										    'Each node should be type of TreeNode and data should be float.'       )

					def is_binary_search_tree_recursive_check(
					    _SCREAMING_SNAKE_CASE				:       TreeNode | None						,				_SCREAMING_SNAKE_CASE				:       float						,				_SCREAMING_SNAKE_CASE				:       float       ) -> bool:

										if node is None:
															return True

										return (
										    left_bound < node.data < right_bound
										    and is_binary_search_tree_recursive_check(node.left						,				_SCREAMING_SNAKE_CASE						,				node.data       )
										    and is_binary_search_tree_recursive_check(
										        node.right						,				node.data						,				_SCREAMING_SNAKE_CASE       )
										)

					return is_binary_search_tree_recursive_check(_SCREAMING_SNAKE_CASE						,				-float('inf'       )						,				float('inf'       )       )


if __name__ == "__main__":
	import doctest

	doctest.testmod()



