"""simple docstring"""






from __future__ import annotations

from abc import abstractmethod
from collections.abc import Iterable
from typing import Generic, Protocol, TypeVar
class 							snake_case			(					__UpperCAmelCase							):




					"""simple docstring"""

					@abstractmethod
					def __lt__(							self  :      T       ,lowerCamelCase__  :      T     ):
									pass







					@abstractmethod
					def __gt__(							self  :      T       ,lowerCamelCase__  :      T     ):
									pass







					@abstractmethod
					def __eq__(							self  :      T       ,lowerCamelCase__  :      object     ):
									pass






lowerCAmelCase__    :    Optional[int]			=      TypeVar('T', bound=Comparable)
class 							snake_case			(					Generic[T]							):




					"""simple docstring"""

					def __init__(							self  :      str     ):
									UpperCAmelCase__			 =				[]
									UpperCAmelCase__			 =				0







					def __repr__(							self  :      Optional[Any]     ):
									return str(self.h     )







					def 						__lowerCAmelCase		(							self  :      Dict       ,lowerCamelCase__  :      int     ):
									if child_idx > 0:
													return (child_idx - 1) // 2
									return None







					def 						__lowerCAmelCase		(							self  :      int       ,lowerCamelCase__  :      int     ):
									UpperCAmelCase__			 =				2 * parent_idx + 1
									if left_child_index < self.heap_size:
													return left_child_index
									return None







					def 						__lowerCAmelCase		(							self  :      Optional[Any]       ,lowerCamelCase__  :      int     ):
									UpperCAmelCase__			 =				2 * parent_idx + 2
									if right_child_index < self.heap_size:
													return right_child_index
									return None







					def 						__lowerCAmelCase		(							self  :      List[Any]       ,lowerCamelCase__  :      int     ):
									if index < self.heap_size:
													UpperCAmelCase__			 =				index
													UpperCAmelCase__			 =				self.left_child_idx(lowerCamelCase__     )
													UpperCAmelCase__			 =				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]:
																	UpperCAmelCase__			 =				left_child
													if right_child is not None and self.h[right_child] > self.h[violation]:
																	UpperCAmelCase__			 =				right_child
													# if violation indeed exists
													if violation != index:
																	# swap to fix the violation
																	UpperCAmelCase__ ,      UpperCAmelCase__			 =				self.h[index], self.h[violation]
																	# fix the subsequent violation recursively if any
																	self.max_heapify(lowerCamelCase__     )







					def 						__lowerCAmelCase		(							self  :      Any       ,lowerCamelCase__  :      Iterable[T]     ):
									UpperCAmelCase__			 =				list(lowerCamelCase__     )
									UpperCAmelCase__			 =				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 						__lowerCAmelCase		(							self  :      Union[str, Any]     ):
									if self.heap_size >= 2:
													UpperCAmelCase__			 =				self.h[0]
													UpperCAmelCase__			 =				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 						__lowerCAmelCase		(							self  :      List[Any]       ,lowerCamelCase__  :      T     ):
									self.h.append(lowerCamelCase__     )
									UpperCAmelCase__			 =				(self.heap_size - 1) // 2
									self.heap_size += 1
									while idx >= 0:
													self.max_heapify(lowerCamelCase__     )
													UpperCAmelCase__			 =				(idx - 1) // 2







					def 						__lowerCAmelCase		(							self  :      Optional[Any]     ):
									UpperCAmelCase__			 =				self.heap_size
									for j in range(size - 1       ,0       ,-1     ):
													UpperCAmelCase__ ,      UpperCAmelCase__			 =				self.h[j], self.h[0]
													self.heap_size -= 1
													self.max_heapify(0     )
									UpperCAmelCase__			 =				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""")




"""simple docstring"""






import os
import unittest

import pytest
from parameterized import parameterized

from transformers.testing_utils import require_torch, require_torch_gpu, slow, torch_device


# skipping in unittest tests

lowerCAmelCase__    :    Union[str, Any]			=      [(1,)]



def     a_		(   ):
				UpperCAmelCase__			 =				bool(os.getenv('RUN_SLOW'   ,     0			)			)
				if run_slow:
								assert True
				else:
								assert False, "should have been skipped"



def     a_		(   ):
				UpperCAmelCase__			 =				bool(os.getenv('RUN_SLOW'   ,     0			)			)
				if run_slow and torch_device == "cuda":
								assert True
				else:
								assert False, "should have been skipped"
@require_torch
class 							snake_case			(					unittest.TestCase							):




					"""simple docstring"""

					@slow
					@require_torch_gpu
					def 						__lowerCAmelCase		(							self  :      Optional[Any]     ):
									check_slow_torch_cuda()







					@require_torch_gpu
					@slow
					def 						__lowerCAmelCase		(							self  :      Any     ):
									check_slow_torch_cuda()







					@parameterized.expand(lowerCamelCase__     )
					@slow
					def 						__lowerCAmelCase		(							self  :      Union[str, Any]       ,lowerCamelCase__  :      str=None     ):
									check_slow()






@slow
@require_torch_gpu
def     a_		(   ):
				check_slow_torch_cuda()



@require_torch_gpu
@slow
def     a_		(   ):
				check_slow_torch_cuda()



@slow
@pytest.mark.parametrize('param'   ,     [1]			)
def     a_		(   lowerCamelCase			):
				check_slow()







@pytest.mark.parametrize('param'   ,     [1]			)
@slow
def     a_		(   lowerCamelCase			):
				check_slow()



