


from __future__ import annotations

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

class   lowerCamelCase						(	SCREAMING_SNAKE_CASE  ):

       @abstractmethod
       def __lt__(      self						,    a__       ):






        '''simple docstring'''






        pass

       @abstractmethod
       def __gt__(      self						,    a__       ):






        '''simple docstring'''






        pass



       @abstractmethod
       def __eq__(      self						,    a__       ):






        '''simple docstring'''






        pass







a					:				Dict       =      TypeVar('T', bound=Comparable)

class   lowerCamelCase						(	Generic[T]  ):

       def __init__(      self       ):






        '''simple docstring'''






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

       def __repr__(      self       ):






        '''simple docstring'''






        return str(self.h       )

       def 					UpperCAmelCase					(      self						,    a__       ):






        '''simple docstring'''






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

       def 					UpperCAmelCase					(      self						,    a__       ):






        '''simple docstring'''






        snake_case :			Tuple							=   2 * parent_idx + 1
        if left_child_index < self.heap_size:
         return left_child_index
        return None

       def 					UpperCAmelCase					(      self						,    a__       ):






        '''simple docstring'''






        snake_case :			List[Any]							=   2 * parent_idx + 2
        if right_child_index < self.heap_size:
         return right_child_index
        return None

       def 					UpperCAmelCase					(      self						,    a__       ):






        '''simple docstring'''






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

       def 					UpperCAmelCase					(      self						,    a__       ):






        '''simple docstring'''






        snake_case :			str							=   list(a__       )
        snake_case :			Optional[int]							=   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(a__       )

       def 					UpperCAmelCase					(      self       ):






        '''simple docstring'''






        if self.heap_size >= 2:
         snake_case :			List[str]							=   self.h[0]
         snake_case :			List[str]							=   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						,    a__       ):






        '''simple docstring'''






        self.h.append(a__       )
        snake_case :			Dict							=   (self.heap_size - 1) // 2
        self.heap_size += 1
        while idx >= 0:
         self.max_heapify(a__       )
         snake_case :			Any							=   (idx - 1) // 2



       def 					UpperCAmelCase					(      self       ):






        '''simple docstring'''






        snake_case :			str							=   self.heap_size
        for j in range(size - 1						,    0						,    -1       ):
         snake_case :			int							=   self.h[j], self.h[0]
         self.heap_size -= 1
         self.max_heapify(0       )
        snake_case :			Optional[Any]							=   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}''')

    a					:				Any       =      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   _lowerCAmelCase		(				UpperCAmelCase__							:       int = 4_0_0_0_0_0_0   )		->int:
						A__    :	int			=	1
						A__    :	List[str]			=	2
						A__    :	Union[str, Any]			=	0
						while j <= n:
												if j % 2 == 0:
																		total += j
												A__	,	A__    :	str			=	j, i + j

						return total


if __name__ == "__main__":
						print(F'{solution() = }')






