code: 
  
  
  
  
  
  
  from __future__ import annotations
  
  from abc import abstractmethod
  from collections.abc import Iterable
  from typing import Generic, Protocol, TypeVar
  
  
  
  
  
  
  
  class 							UpperCAmelCase_     (		a_		):
  
  
  
  
       @abstractmethod
       def __lt__(							self  ,	_lowerCAmelCase		):
            pass
  
  
  
  
       @abstractmethod
       def __gt__(							self  ,	_lowerCAmelCase		):
            pass
  
  
  
  
       @abstractmethod
       def __eq__(							self  ,	_lowerCAmelCase		):
            pass
  
  
  
  SCREAMING_SNAKE_CASE__		:       int   							=							TypeVar("""T""", bound=Comparable)
  
  
  
  
  
  
  
  class 							UpperCAmelCase_     (		Generic[T]		):
  
  
  
  
       def __init__(							self		):
            UpperCAmelCase__			:     list[T]										= []
            UpperCAmelCase__			:     int										= 0
  
  
  
  
       def __repr__(							self		):
            return str(self.h		)
  
  
  
  
       def      __UpperCAmelCase     (							self  ,	_lowerCAmelCase		):
            if child_idx > 0:
                 return (child_idx - 1) // 2
            return None
  
  
  
  
       def      __UpperCAmelCase     (							self  ,	_lowerCAmelCase		):
            UpperCAmelCase__			:     Any										= 2 * parent_idx + 1
            if left_child_index < self.heap_size:
                 return left_child_index
            return None
  
  
  
  
       def      __UpperCAmelCase     (							self  ,	_lowerCAmelCase		):
            UpperCAmelCase__			:     List[Any]										= 2 * parent_idx + 2
            if right_child_index < self.heap_size:
                 return right_child_index
            return None
  
  
  
  
       def      __UpperCAmelCase     (							self  ,	_lowerCAmelCase		):
            if index < self.heap_size:
                 UpperCAmelCase__			:     int										= index
                 UpperCAmelCase__			:     int										= self.left_child_idx(_snake_case		)
                 UpperCAmelCase__			:     int										= self.right_child_idx(_snake_case		)
                 # check which child is larger than its parent
                 if left_child is not None and self.h[left_child] > self.h[violation]:
                      UpperCAmelCase__			:     Optional[Any]										= left_child
                 if right_child is not None and self.h[right_child] > self.h[violation]:
                      UpperCAmelCase__			:     int										= right_child
                 # if violation indeed exists
                 if violation != index:
                      # swap to fix the violation
                      UpperCAmelCase__			:     Any										= self.h[index], self.h[violation]
                      # fix the subsequent violation recursively if any
                      self.max_heapify(_snake_case		)
  
  
  
  
       def      __UpperCAmelCase     (							self  ,	_lowerCAmelCase		):
            UpperCAmelCase__			:     Optional[int]										= list(_snake_case		)
            UpperCAmelCase__			:     Union[str, Any]										= 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(_snake_case		)
  
  
  
  
       def      __UpperCAmelCase     (							self		):
            if self.heap_size >= 2:
                 UpperCAmelCase__			:     Optional[Any]										= self.h[0]
                 UpperCAmelCase__			:     Optional[int]										= 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  ,	_lowerCAmelCase		):
            self.h.append(_snake_case		)
            UpperCAmelCase__			:     Tuple										= (self.heap_size - 1) // 2
            self.heap_size += 1
            while idx >= 0:
                 self.max_heapify(_snake_case		)
                 UpperCAmelCase__			:     List[Any]										= (idx - 1) // 2
  
  
  
  
       def      __UpperCAmelCase     (							self		):
            UpperCAmelCase__			:     List[str]										= self.heap_size
            for j in range(size - 1  ,	0  ,	-1		):
                 UpperCAmelCase__			:     str										= self.h[j], self.h[0]
                 self.heap_size -= 1
                 self.max_heapify(0		)
            UpperCAmelCase__			:     List[str]										= 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}''')
  
          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(1_00)
          print(f'''after new value 100 inserted: {heap}''')
  
          heap.heap_sort()
          print(f'''heap-sorted array: {heap}\n''')
  
  
  
  
  
  
  
style_context: 
  
  
  
  
  
  
  from ..utils import requires_backends
  
  
  SCREAMING_SNAKE_CASE__		:       int   							=							None
  
  
  
  
  
  
  
  class 							UpperCAmelCase_     :
  
  
  
  
       def __init__(							self  ,	*_lowerCAmelCase  ,	**_lowerCAmelCase		):
            requires_backends(self  ,	["""detectron2"""]		)
  
  
  
  
       @classmethod
       def      __UpperCAmelCase     (							cls  ,	*_lowerCAmelCase  ,	**_lowerCAmelCase		):
            requires_backends(cls  ,	["""detectron2"""]		)
  
  
  
  
  
  
  