code: 
  
  
  
  
  '''simple docstring'''
  
  
  
  
  
  
  
  from __future__ import annotations
  
  from abc import abstractmethod
  from collections.abc import Iterable
  from typing import Generic, Protocol, TypeVar
  
  
  
  
  
  class   lowerCamelCase_							( UpperCAmelCase_							):
  
  
  
  
  					'''simple docstring'''
  
  
  
  
  
  
  					@abstractmethod
  					def __lt__(					self,						__UpperCamelCase				):
  							pass
  
  
  
  
  
  
  					@abstractmethod
  					def __gt__(					self,						__UpperCamelCase				):
  							pass
  
  
  
  
  
  
  					@abstractmethod
  					def __eq__(					self,						__UpperCamelCase				):
  							pass
  
  
  
  
  _lowerCamelCase							:		Tuple										=						TypeVar('T', bound=Comparable)
  
  
  
  
  
  class   lowerCamelCase_							( Generic[T]							):
  
  
  
  
  					'''simple docstring'''
  
  
  
  
  
  
  					def __init__(					self				):
  							_snake_case			 = []
  							_snake_case			 = 0
  
  
  
  
  
  
  					def __repr__(					self				):
  							return str(self.h				)
  
  
  
  
  
  
  					def        __SCREAMING_SNAKE_CASE			(					self,						__UpperCamelCase				):
  							if child_idx > 0:
  									return (child_idx - 1) // 2
  							return None
  
  
  
  
  
  
  					def        __SCREAMING_SNAKE_CASE			(					self,						__UpperCamelCase				):
  							_snake_case			 = 2 * parent_idx + 1
  							if left_child_index < self.heap_size:
  									return left_child_index
  							return None
  
  
  
  
  
  
  					def        __SCREAMING_SNAKE_CASE			(					self,						__UpperCamelCase				):
  							_snake_case			 = 2 * parent_idx + 2
  							if right_child_index < self.heap_size:
  									return right_child_index
  							return None
  
  
  
  
  
  
  					def        __SCREAMING_SNAKE_CASE			(					self,						__UpperCamelCase				):
  							if index < self.heap_size:
  									_snake_case			 = index
  									_snake_case			 = self.left_child_idx(__UpperCamelCase				)
  									_snake_case			 = 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]:
  											_snake_case			 = left_child
  									if right_child is not None and self.h[right_child] > self.h[violation]:
  											_snake_case			 = right_child
  									# if violation indeed exists
  									if violation != index:
  											# swap to fix the violation
  											_snake_case ,					_snake_case			 = self.h[index], self.h[violation]
  											# fix the subsequent violation recursively if any
  											self.max_heapify(__UpperCamelCase				)
  
  
  
  
  
  
  					def        __SCREAMING_SNAKE_CASE			(					self,						__UpperCamelCase				):
  							_snake_case			 = list(__UpperCamelCase				)
  							_snake_case			 = 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        __SCREAMING_SNAKE_CASE			(					self				):
  							if self.heap_size >= 2:
  									_snake_case			 = self.h[0]
  									_snake_case			 = 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        __SCREAMING_SNAKE_CASE			(					self,						__UpperCamelCase				):
  							self.h.append(__UpperCamelCase				)
  							_snake_case			 = (self.heap_size - 1) // 2
  							self.heap_size += 1
  							while idx >= 0:
  									self.max_heapify(__UpperCamelCase				)
  									_snake_case			 = (idx - 1) // 2
  
  
  
  
  
  
  					def        __SCREAMING_SNAKE_CASE			(					self				):
  							_snake_case			 = self.heap_size
  							for j in range(size - 1,						0,						-1				):
  									_snake_case ,					_snake_case			 = self.h[j], self.h[0]
  									self.heap_size -= 1
  									self.max_heapify(0				)
  							_snake_case			 = 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}''')
  
  												_lowerCamelCase							:		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''')
  
  
  
  
  
  
style_context: 
  
  
  
  
  '''simple docstring'''
  
  
  
  
  
  
  
  from __future__ import annotations
  
  from collections.abc import Iterable, Iterator
  from typing import Any, Generic, TypeVar
  
  _lowerCamelCase							:		List[str]										=						TypeVar('T', bound=bool)
  
  
  
  
  
  class   lowerCamelCase_							( Generic[T]							):
  
  
  
  
  					'''simple docstring'''
  
  
  
  
  
  
  					def __init__(					self,						__UpperCamelCase				):
  							_snake_case			 = value
  							_snake_case			 = None
  							_snake_case			 = None
  
  
  
  
  
  
  					@property
  					def        __SCREAMING_SNAKE_CASE			(					self				):
  							return self._value
  
  
  
  
  
  
  					@staticmethod
  					def        __SCREAMING_SNAKE_CASE			(					__UpperCamelCase,						__UpperCamelCase				):
  							if not roota:
  									return roota
  
  							if not roota:
  									return roota
  
  							if roota.value > roota.value:
  									_snake_case ,					_snake_case			 = roota, roota
  
  							_snake_case			 = roota
  							_snake_case			 = roota.right
  							_snake_case			 = roota.left
  							_snake_case			 = SkewNode.merge(__UpperCamelCase,						__UpperCamelCase				)
  
  							return result
  
  
  
  
  
  class   lowerCamelCase_							( Generic[T]							):
  
  
  
  
  					'''simple docstring'''
  
  
  
  
  
  
  					def __init__(					self,						__UpperCamelCase = ()				):
  							_snake_case			 = None
  							if data:
  									for item in data:
  											self.insert(__UpperCamelCase				)
  
  
  
  
  
  
  					def __bool__(					self				):
  							return self._root is not None
  
  
  
  
  
  
  					def __iter__(					self				):
  							_snake_case			 = []
  							while self:
  									result.append(self.pop()				)
  
  							# Pushing items back to the heap not to clear it.
  							for item in result:
  									self.insert(__UpperCamelCase				)
  
  							return iter(__UpperCamelCase				)
  
  
  
  
  
  
  					def        __SCREAMING_SNAKE_CASE			(					self,						__UpperCamelCase				):
  							_snake_case			 = SkewNode.merge(self._root,						SkewNode(__UpperCamelCase				)				)
  
  
  
  
  
  
  					def        __SCREAMING_SNAKE_CASE			(					self				):
  							_snake_case			 = self.top()
  							_snake_case			 = (
  							    SkewNode.merge(self._root.left,						self._root.right				) if self._root else None
  							)
  
  							return result
  
  
  
  
  
  
  					def        __SCREAMING_SNAKE_CASE			(					self				):
  							if not self._root:
  									raise IndexError("Can't get top element for the empty heap."				)
  							return self._root.value
  
  
  
  
  
  
  					def        __SCREAMING_SNAKE_CASE			(					self				):
  							_snake_case			 = None
  
  
  if __name__ == "__main__":
  						import doctest
  
  						doctest.testmod()
  
  
  
  
  
  