


from __future__ import annotations

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


class        __lowerCamelCase      (				_lowerCAmelCase ):


				"""simple docstring"""







				@abstractmethod
				def __lt__(				self     :    T	,							lowerCamelCase_     :    T					):
								pass






				@abstractmethod
				def __gt__(				self     :    T	,							lowerCamelCase_     :    T					):
								pass






				@abstractmethod
				def __eq__(				self     :    T	,							lowerCamelCase_     :    object					):
								pass
__SCREAMING_SNAKE_CASE	:							List[Any]           =  TypeVar('''T''', bound=Comparable)


class        __lowerCamelCase      (				Generic[T] ):


				"""simple docstring"""







				def __init__(				self     :    List[Any]					):
								_lowerCAmelCase  						=[]
								_lowerCAmelCase  						=0






				def __repr__(				self     :    List[str]					):
								return str(self.h					)






				def        lowerCAmelCase__			(				self     :    List[str]	,							lowerCamelCase_     :    int					):



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






				def        lowerCAmelCase__			(				self     :    Any	,							lowerCamelCase_     :    int					):
								_lowerCAmelCase  						=2 * parent_idx + 1
								if left_child_index < self.heap_size:
												return left_child_index
								return None






				def        lowerCAmelCase__			(				self     :    Tuple	,							lowerCamelCase_     :    int					):
								_lowerCAmelCase  						=2 * parent_idx + 2
								if right_child_index < self.heap_size:
												return right_child_index
								return None






				def        lowerCAmelCase__			(				self     :    Optional[Any]	,							lowerCamelCase_     :    int					):



								if index < self.heap_size:
												_lowerCAmelCase  						=index
												_lowerCAmelCase  						=self.left_child_idx(__UpperCAmelCase					)
												_lowerCAmelCase  						=self.right_child_idx(__UpperCAmelCase					)
												# 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  						=self.h[index], self.h[violation]
																# fix the subsequent violation recursively if any
																self.max_heapify(__UpperCAmelCase					)






				def        lowerCAmelCase__			(				self     :    List[str]	,							lowerCamelCase_     :    Iterable[T]					):
								_lowerCAmelCase  						=list(__UpperCAmelCase					)
								_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(__UpperCAmelCase					)






				def        lowerCAmelCase__			(				self     :    Union[str, Any]					):



								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        lowerCAmelCase__			(				self     :    Any	,							lowerCamelCase_     :    T					):
								self.h.append(__UpperCAmelCase					)
								_lowerCAmelCase  						=(self.heap_size - 1) // 2
								self.heap_size += 1
								while idx >= 0:
												self.max_heapify(__UpperCAmelCase					)
												_lowerCAmelCase  						=(idx - 1) // 2






				def        lowerCAmelCase__			(				self     :    Tuple					):
								_lowerCAmelCase  						=self.heap_size
								for j in range(size - 1	,							0	,							-1					):
												_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],
		    [103, 9, 1, 7, 11, 15, 25, 201, 209, 107, 5],
		    [-45, -2, -5],
		]:
				print(F'unsorted array: {unsorted}')

				__SCREAMING_SNAKE_CASE	:							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(100)
				print(F'after new value 100 inserted: {heap}')

				heap.heap_sort()
				print(F'heap-sorted array: {heap}\n')


"""simple docstring"""




def 				__a       (			_lowercase							, _lowercase						):







					"""simple docstring"""





					if not root or root not in binary_tree_mirror_dictionary:
										return
					lowerCamelCase__				,						lowerCamelCase__		:   Tuple  				=					binary_tree_mirror_dictionary[root][:2]
					lowerCamelCase__		:   Optional[Any]  				=					[right_child, left_child]
					binary_tree_mirror_dict(_lowercase							, _lowercase						)
					binary_tree_mirror_dict(_lowercase							, _lowercase						)



def 				__a       (			_lowercase							, _lowercase = 1						):







					"""simple docstring"""





					if not binary_tree:
										raise ValueError('''binary tree cannot be empty'''						)
					if root not in binary_tree:
										lowerCamelCase__		:   Dict  				=					f"""root {root} is not present in the binary_tree"""
										raise ValueError(_lowercase						)
					lowerCamelCase__		:   Optional[Any]  				=					dict(_lowercase						)
					binary_tree_mirror_dict(_lowercase							, _lowercase						)
					return binary_tree_mirror_dictionary


if __name__ == "__main__":
					UpperCAmelCase       :    Any									=			{1: [2, 3], 2: [4, 5], 3: [6, 7], 7: [8, 9]}
					print(f'''Binary tree: {binary_tree}''')
					UpperCAmelCase       :    List[Any]									=			binary_tree_mirror(binary_tree, 5)
					print(f'''Binary tree mirror: {binary_tree_mirror_dictionary}''')






