




from __future__ import annotations

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







class 		__UpperCAmelCase(		A_			):





     """simple docstring"""



     @abstractmethod
     def __lt__(   self			:							str    ,					A			:							Optional[Any]     )      ->      Dict:






         """simple docstring"""
         pass

     @abstractmethod
     def __gt__(   self			:							int    ,					A			:							int     )      ->      str:






         """simple docstring"""
         pass






     @abstractmethod
     def __eq__(   self			:							Dict    ,					A			:							List[Any]     )      ->      Optional[Any]:






         """simple docstring"""
         pass






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







class 		__UpperCAmelCase(		Generic[T]			):





     """simple docstring"""



     def __init__(   self			:							Any     )      ->      Dict:






         """simple docstring"""
         a__  			=							[]
         a__  			=							0

     def __repr__(   self			:							Optional[int]     )      ->      Dict:






         """simple docstring"""
         return str(self.h     )

     def 					__SCREAMING_SNAKE_CASE		(   self			:							str    ,					A			:							Optional[Any]     )      ->      int:






         """simple docstring"""



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

     def 					__SCREAMING_SNAKE_CASE		(   self			:							Union[str, Any]    ,					A			:							int     )      ->      Union[str, Any]:






         """simple docstring"""
         a__  			=							2 * parent_idx + 1
         if left_child_index < self.heap_size:
             return left_child_index
         return None

     def 					__SCREAMING_SNAKE_CASE		(   self			:							List[str]    ,					A			:							Optional[Any]     )      ->      str:






         """simple docstring"""
         a__  			=							2 * parent_idx + 2
         if right_child_index < self.heap_size:
             return right_child_index
         return None

     def 					__SCREAMING_SNAKE_CASE		(   self			:							Optional[int]    ,					A			:							Optional[Any]     )      ->      Optional[int]:






         """simple docstring"""



         if index < self.heap_size:
             a__  			=							index
             a__  			=							self.left_child_idx(__lowerCamelCase     )
             a__  			=							self.right_child_idx(__lowerCamelCase     )
             # 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__  			=							self.h[index], self.h[violation]
                 # fix the subsequent violation recursively if any
                 self.max_heapify(__lowerCamelCase     )

     def 					__SCREAMING_SNAKE_CASE		(   self			:							int    ,					A			:							List[str]     )      ->      Dict:






         """simple docstring"""
         a__  			=							list(__lowerCamelCase     )
         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(__lowerCamelCase     )

     def 					__SCREAMING_SNAKE_CASE		(   self			:							Tuple     )      ->      Dict:






         """simple docstring"""



         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 					__SCREAMING_SNAKE_CASE		(   self			:							Optional[int]    ,					A			:							List[Any]     )      ->      Dict:






         """simple docstring"""
         self.h.append(__lowerCamelCase     )
         a__  			=							(self.heap_size - 1) // 2
         self.heap_size += 1
         while idx >= 0:
             self.max_heapify(__lowerCamelCase     )
             a__  			=							(idx - 1) // 2






     def 					__SCREAMING_SNAKE_CASE		(   self			:							Dict     )      ->      Any:






         """simple docstring"""
         a__  			=							self.heap_size
         for j in range(size - 1    ,					0    ,					-1     ):
             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}")

  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")







"""simple docstring"""







import pytest

from datasets.utils.version import Version




@pytest.mark.parametrize(
    'other, expected_equality'  ,       [
        (Version('1.0.0'						), True),
        ('1.0.0', True),
        (Version('2.0.0'						), False),
        ('2.0.0', False),
        ('1', False),
        ('a', False),
        (1, False),
        (None, False),
    ]  ,       )
def 						_lowercase				(  _SCREAMING_SNAKE_CASE				:				Tuple  ,       _SCREAMING_SNAKE_CASE				:				Any						)    ->     List[str]:







     '''simple docstring'''


     __A					:					Tuple								=		Version('1.0.0'						)
     assert (version == other) is expected_equality
     assert (version != other) is not expected_equality
     assert (hash(_SCREAMING_SNAKE_CASE						) == hash(_SCREAMING_SNAKE_CASE						)) is expected_equality



