






from __future__ import annotations

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




class 	lowerCamelCase__				(							UpperCAmelCase ):






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


       """simple docstring"""






       pass






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


       """simple docstring"""






       pass






      @abstractmethod
      def __eq__(self					:    T		,		_snake_case					:    object		)       ->   bool:


       """simple docstring"""






       pass


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




class 	lowerCamelCase__				(							Generic[T] ):






      def __init__(self					:    Tuple		)       ->   None:


       """simple docstring"""






       lowerCamelCase_							:    list[T]							=     []
       lowerCamelCase_							:    int							=     0






      def __repr__(self					:    int		)       ->   str:


       """simple docstring"""






       return str(self.h		)






      def      UpperCAmelCase_     (self					:    int		,		_snake_case					:    int		)       ->   int | None:


       """simple docstring"""






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






      def      UpperCAmelCase_     (self					:    Optional[Any]		,		_snake_case					:    int		)       ->   int | None:


       """simple docstring"""






       lowerCamelCase_							:    Union[str, Any]							=     2 * parent_idx + 1
       if left_child_index < self.heap_size:
        return left_child_index
       return None






      def      UpperCAmelCase_     (self					:    Optional[Any]		,		_snake_case					:    int		)       ->   int | None:


       """simple docstring"""






       lowerCamelCase_							:    Optional[int]							=     2 * parent_idx + 2
       if right_child_index < self.heap_size:
        return right_child_index
       return None






      def      UpperCAmelCase_     (self					:    List[str]		,		_snake_case					:    int		)       ->   None:


       """simple docstring"""






       if index < self.heap_size:
        lowerCamelCase_							:    int							=     index
        lowerCamelCase_							:    Tuple							=     self.left_child_idx(_snake_case		)
        lowerCamelCase_							:    Union[str, Any]							=     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]:
         lowerCamelCase_							:    Optional[int]							=     left_child
        if right_child is not None and self.h[right_child] > self.h[violation]:
         lowerCamelCase_							:    Tuple							=     right_child
        # if violation indeed exists
        if violation != index:
         # swap to fix the violation
         lowerCamelCase_		,      lowerCamelCase_							:    Tuple							=     self.h[index], self.h[violation]
         # fix the subsequent violation recursively if any
         self.max_heapify(_snake_case		)






      def      UpperCAmelCase_     (self					:    int		,		_snake_case					:    Iterable[T]		)       ->   None:


       """simple docstring"""






       lowerCamelCase_							:    Tuple							=     list(_snake_case		)
       lowerCamelCase_							:    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					:    Any		)       ->   T:


       """simple docstring"""






       if self.heap_size >= 2:
        lowerCamelCase_							:    List[str]							=     self.h[0]
        lowerCamelCase_							:    Union[str, Any]							=     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		,		_snake_case					:    T		)       ->   None:


       """simple docstring"""






       self.h.append(_snake_case		)
       lowerCamelCase_							:    Tuple							=     (self.heap_size - 1) // 2
       self.heap_size += 1
       while idx >= 0:
        self.max_heapify(_snake_case		)
        lowerCamelCase_							:    Optional[Any]							=     (idx - 1) // 2






      def      UpperCAmelCase_     (self					:    List[str]		)       ->   None:


       """simple docstring"""






       lowerCamelCase_							:    Optional[int]							=     self.heap_size
       for j in range(size - 1		,		0		,		-1		):
        lowerCamelCase_		,      lowerCamelCase_							:    Any							=     self.h[j], self.h[0]
        self.heap_size -= 1
        self.max_heapify(0		)
       lowerCamelCase_							:    Optional[int]							=     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, 1_0, 8],
           [1_0_3, 9, 1, 7, 1_1, 1_5, 2_5, 2_0_1, 2_0_9, 1_0_7, 5],
           [-4_5, -2, -5],
       ]:
              print(f'''unsorted array: {unsorted}''')

              UpperCamelCase											=      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_0_0)
              print(f'''after new value 100 inserted: {heap}''')

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








def       _a   (							lowerCamelCase__				)  ->      int:
 return int(lowerCamelCase__				) if x - int(lowerCamelCase__				) >= 0 else int(lowerCamelCase__				) - 1


if __name__ == "__main__":
       import doctest

       doctest.testmod()
