


from __future__ import annotations

from abc import abstractmethod
from collections.abc import Iterable
from typing import Generic, Protocol, TypeVar







class 					__lowercase					(       a_     ):



		"""simple docstring"""

		@abstractmethod
		def __lt__(   self		,			A  )     ->   bool:







					'''simple docstring'''







					pass







		@abstractmethod
		def __gt__(   self		,			A  )     ->   bool:







					'''simple docstring'''







					pass







		@abstractmethod
		def __eq__(   self		,			A  )     ->   bool:







					'''simple docstring'''







					pass






UpperCAmelCase      :						List[str]    =		TypeVar("T", bound=Comparable)







class 					__lowercase					(       Generic[T]     ):



		"""simple docstring"""

		def __init__(   self  )     ->   None:







					'''simple docstring'''







					lowerCamelCase								=     []
					lowerCamelCase								=     0







		def __repr__(   self  )     ->   str:







					'''simple docstring'''







					return str(self.h  )







		def 				__A      (   self		,			A  )     ->   int | None:







					'''simple docstring'''







					if child_idx > 0:
								return (child_idx - 1) // 2
					return None







		def 				__A      (   self		,			A  )     ->   int | None:







					'''simple docstring'''







					lowerCamelCase								=     2 * parent_idx + 1
					if left_child_index < self.heap_size:
								return left_child_index
					return None







		def 				__A      (   self		,			A  )     ->   int | None:







					'''simple docstring'''







					lowerCamelCase								=     2 * parent_idx + 2
					if right_child_index < self.heap_size:
								return right_child_index
					return None







		def 				__A      (   self		,			A  )     ->   None:







					'''simple docstring'''







					if index < self.heap_size:
								lowerCamelCase								=     index
								lowerCamelCase								=     self.left_child_idx(A  )
								lowerCamelCase								=     self.right_child_idx(A  )
								# check which child is larger than its parent
								if left_child is not None and self.h[left_child] > self.h[violation]:
											lowerCamelCase								=     left_child
								if right_child is not None and self.h[right_child] > self.h[violation]:
											lowerCamelCase								=     right_child
								# if violation indeed exists
								if violation != index:
											# swap to fix the violation
											lowerCamelCase		,		lowerCamelCase								=     self.h[index], self.h[violation]
											# fix the subsequent violation recursively if any
											self.max_heapify(A  )







		def 				__A      (   self		,			A  )     ->   None:







					'''simple docstring'''







					lowerCamelCase								=     list(A  )
					lowerCamelCase								=     len(self.h  )
					if self.heap_size > 1:
								# max_heapify from right to left but exclude leaves (last level)
								for i in range(self.heap_size // 2 - 1		,			-1		,			-1  ):
											self.max_heapify(A  )







		def 				__A      (   self  )     ->   T:







					'''simple docstring'''







					if self.heap_size >= 2:
								lowerCamelCase								=     self.h[0]
								lowerCamelCase								=     self.h.pop(-1  )
								self.heap_size -= 1
								self.max_heapify(0  )
								return me
					elif self.heap_size == 1:
								self.heap_size -= 1
								return self.h.pop(-1  )
					else:
								raise Exception("""Empty heap"""  )







		def 				__A      (   self		,			A  )     ->   None:







					'''simple docstring'''







					self.h.append(A  )
					lowerCamelCase								=     (self.heap_size - 1) // 2
					self.heap_size += 1
					while idx >= 0:
								self.max_heapify(A  )
								lowerCamelCase								=     (idx - 1) // 2







		def 				__A      (   self  )     ->   None:







					'''simple docstring'''







					lowerCamelCase								=     self.heap_size
					for j in range(size - 1		,			0		,			-1  ):
								lowerCamelCase		,		lowerCamelCase								=     self.h[j], self.h[0]
								self.heap_size -= 1
								self.max_heapify(0  )
					lowerCamelCase								=     size


if __name__ == "__main__":
		import doctest

		# run doc test
		doctest.testmod()

		# demo
		for unsorted in [
		    [0],
		    [2],
		    [3, 5],
		    [5, 3],
		    [5, 5],
		    [0, 0, 0, 0],
		    [1, 1, 1, 1],
		    [2, 2, 3, 5],
		    [0, 2, 2, 3, 5],
		    [2, 5, 3, 0, 2, 3, 0, 3],
		    [6, 1, 2, 7, 9, 3, 4, 5, 10, 8],
		    [1_03, 9, 1, 7, 11, 15, 25, 2_01, 2_09, 1_07, 5],
		    [-45, -2, -5],
		]:
				print(f"""unsorted array: {unsorted}""")

				UpperCAmelCase      :						Heap[int]    =		Heap()
				heap.build_max_heap(unsorted)
				print(f"""after build heap: {heap}""")

				print(f"""max value: {heap.extract_max()}""")
				print(f"""after max value removed: {heap}""")

				heap.insert(1_00)
				print(f"""after new value 100 inserted: {heap}""")

				heap.heap_sort()
				print(f"""heap-sorted array: {heap}\n""")





from __future__ import annotations

from collections.abc import Callable
from typing import Generic, TypeVar

UpperCAmelCase      :						List[str]    =		TypeVar("T")
UpperCAmelCase      :						Dict    =		TypeVar("U")







class 					__lowercase					(       Generic[T, U]     ):



		"""simple docstring"""

		def __init__(   self		,			A		,			A  )     ->   Any:







					'''simple docstring'''







					lowerCamelCase								=     key
					lowerCamelCase								=     val
					lowerCamelCase								=     0
					lowerCamelCase								=     None
					lowerCamelCase								=     None







		def __repr__(   self  )     ->   str:







					'''simple docstring'''







					return "Node: key: {}, val: {}, freq: {}, has next: {}, has prev: {}".format(
					    self.key		,			self.val		,			self.freq		,			self.next is not None		,			self.prev is not None  )







class 					__lowercase					(       Generic[T, U]     ):



		"""simple docstring"""

		def __init__(   self  )     ->   None:







					'''simple docstring'''







					lowerCamelCase								=     DoubleLinkedListNode(A		,			A  )
					lowerCamelCase								=     DoubleLinkedListNode(A		,			A  )
					lowerCamelCase		,		lowerCamelCase								=     self.rear, self.head







		def __repr__(   self  )     ->   str:







					'''simple docstring'''







					lowerCamelCase								=     ["""DoubleLinkedList"""]
					lowerCamelCase								=     self.head
					while node.next is not None:
								rep.append(str(A  )  )
								lowerCamelCase								=     node.next
					rep.append(str(self.rear  )  )
					return ",\n    ".join(A  )







		def 				__A      (   self		,			A  )     ->   None:







					'''simple docstring'''







					lowerCamelCase								=     self.rear.prev

					# All nodes other than self.head are guaranteed to have non-None previous
					assert previous is not None

					lowerCamelCase								=     node
					lowerCamelCase								=     previous
					lowerCamelCase								=     node
					lowerCamelCase								=     self.rear
					node.freq += 1
					self._position_node(A  )







		def 				__A      (   self		,			A  )     ->   None:







					'''simple docstring'''







					while node.prev is not None and node.prev.freq > node.freq:
								# swap node with previous node
								lowerCamelCase								=     node.prev

								lowerCamelCase								=     previous_node.prev
								lowerCamelCase								=     node.prev
								lowerCamelCase								=     previous_node
								lowerCamelCase								=     node







		def 				__A      (   self		,			A  )     ->   DoubleLinkedListNode[T, U] | None:







					'''simple docstring'''







					if node.prev is None or node.next is None:
								return None

					lowerCamelCase								=     node.next
					lowerCamelCase								=     node.prev
					lowerCamelCase								=     None
					lowerCamelCase								=     None
					return node







class 					__lowercase					(       Generic[T, U]     ):



		"""simple docstring"""

		UpperCamelCase    :				dict[Callable[[T], U], LFUCache[T, U]] 					=		{}







		def __init__(   self		,			A  )     ->   Union[str, Any]:







					'''simple docstring'''







					lowerCamelCase								=     DoubleLinkedList()
					lowerCamelCase								=     capacity
					lowerCamelCase								=     0
					lowerCamelCase								=     0
					lowerCamelCase								=     0
					lowerCamelCase								=     {}







		def __repr__(   self  )     ->   str:







					'''simple docstring'''







					return (
					    F'CacheInfo(hits={self.hits}, misses={self.miss}, '
					    F'capacity={self.capacity}, current_size={self.num_keys})'
					)







		def __contains__(   self		,			A  )     ->   bool:







					'''simple docstring'''







					return key in self.cache







		def 				__A      (   self		,			A  )     ->   U | None:







					'''simple docstring'''







					if key in self.cache:
								self.hits += 1
								lowerCamelCase								=     self.cache[key]
								lowerCamelCase								=     self.list.remove(self.cache[key]  )
								assert node == value_node

								# node is guaranteed not None because it is in self.cache
								assert node is not None
								self.list.add(A  )
								return node.val
					self.miss += 1
					return None







		def 				__A      (   self		,			A		,			A  )     ->   None:







					'''simple docstring'''







					if key not in self.cache:
								if self.num_keys >= self.capacity:
											# delete first node when over capacity
											lowerCamelCase								=     self.list.head.next

											# guaranteed to have a non-None first node when num_keys > 0
											# explain to type checker via assertions
											assert first_node is not None
											assert first_node.key is not None
											assert self.list.remove(A  ) is not None
											# first_node guaranteed to be in list

											del self.cache[first_node.key]
											self.num_keys -= 1
								lowerCamelCase								=     DoubleLinkedListNode(A		,			A  )
								self.list.add(self.cache[key]  )
								self.num_keys += 1

					else:
								lowerCamelCase								=     self.list.remove(self.cache[key]  )
								assert node is not None  # node guaranteed to be in list
								lowerCamelCase								=     value
								self.list.add(A  )







		@classmethod
		def 				__A      (   cls		,			A = 1_28  )     ->   Callable[[Callable[[T], U]], Callable[..., U]]:







					'''simple docstring'''







					def cache_decorator_inner(A  ) -> Callable[..., U]:
								def cache_decorator_wrapper(*A  ) -> U:
											if func not in cls.decorator_function_to_instance_map:
														lowerCamelCase								=     LFUCache(A  )

											lowerCamelCase								=     cls.decorator_function_to_instance_map[func].get(args[0]  )
											if result is None:
														lowerCamelCase								=     func(*A  )
														cls.decorator_function_to_instance_map[func].put(args[0]		,			A  )
											return result

								def cache_info() -> LFUCache[T, U]:
											return cls.decorator_function_to_instance_map[func]

								setattr(A		,			"""cache_info"""		,			A  )  # noqa: B010

								return cache_decorator_wrapper

					return cache_decorator_inner


if __name__ == "__main__":
		import doctest

		doctest.testmod()

