


from __future__ import annotations

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




class 					_UpperCamelCase (      lowerCamelCase__	):







							'''simple docstring'''







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







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







							@abstractmethod
							def __eq__(		self  :				T		,				SCREAMING_SNAKE_CASE_  :				object		):
													pass




lowercase_								=    TypeVar('T', bound=Comparable)




class 					_UpperCamelCase (      Generic[T]	):







							'''simple docstring'''







							def __init__(		self  :				Any		):
													_a     =			[]
													_a     =			0







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







							def 		_UpperCAmelCase	(		self  :				Optional[int]		,				SCREAMING_SNAKE_CASE_  :				int		):
													if child_idx > 0:
																			return (child_idx - 1) // 2
													return None







							def 		_UpperCAmelCase	(		self  :				int		,				SCREAMING_SNAKE_CASE_  :				int		):
													_a     =			2 * parent_idx + 1
													if left_child_index < self.heap_size:
																			return left_child_index
													return None







							def 		_UpperCAmelCase	(		self  :				Any		,				SCREAMING_SNAKE_CASE_  :				int		):
													_a     =			2 * parent_idx + 2
													if right_child_index < self.heap_size:
																			return right_child_index
													return None







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







							def 		_UpperCAmelCase	(		self  :				Dict		,				SCREAMING_SNAKE_CASE_  :				Iterable[T]		):
													_a     =			list(SCREAMING_SNAKE_CASE_		)
													_a     =			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(SCREAMING_SNAKE_CASE_		)







							def 		_UpperCAmelCase	(		self  :				Optional[Any]		):
													if self.heap_size >= 2:
																			_a     =			self.h[0]
																			_a     =			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 		_UpperCAmelCase	(		self  :				int		,				SCREAMING_SNAKE_CASE_  :				T		):
													self.h.append(SCREAMING_SNAKE_CASE_		)
													_a     =			(self.heap_size - 1) // 2
													self.heap_size += 1
													while idx >= 0:
																			self.max_heapify(SCREAMING_SNAKE_CASE_		)
																			_a     =			(idx - 1) // 2







							def 		_UpperCAmelCase	(		self  :				int		):
													_a     =			self.heap_size
													for j in range(size - 1		,				0		,				-1		):
																			_a ,	_a     =			self.h[j], self.h[0]
																			self.heap_size -= 1
																			self.max_heapify(0		)
													_a     =			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}""")

				lowercase_								=    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 math import pi


def 							SCREAMING_SNAKE_CASE					(  _UpperCAmelCase				)    ->  float:
						return degree / (180 / pi)


if __name__ == "__main__":
		from doctest import testmod

		testmod()


