code: from __future__ import annotations
  
  from abc import abstractmethod
  from collections.abc import Iterable
  from typing import Generic, Protocol, TypeVar
  
  
  
  
  
  
  
  class 					__lowercase					(       a_     ):
  
  
  
  		"""simple docstring"""
  
  		@abstractmethod
  		def __lt__(   self		,			A  )     ->   bool:
  
  
  
  
  
  
  
  					'''simple docstring'''
  
  
  
  
  
  
  
  					pass
  
  
  
  
  
  
  
  		@abstractmethod
  		def __gt__(   self		,			A  )     ->   bool:
  
  
  
  
  
  
  
  					'''simple docstring'''
  
  
  
  
  
  
  
  					pass
  
  
  
  
  
  
  
  		@abstractmethod
  		def __eq__(   self		,			A  )     ->   bool:
  
  
  
  
  
  
  
  					'''simple docstring'''
  
  
  
  
  
  
  
  					pass
  
  
  
  
  
  
  UpperCAmelCase      :						List[str]    =		TypeVar("T", bound=Comparable)
  
  
  
  
  
  
  
  class 					__lowercase					(       Generic[T]     ):
  
  
  
  		"""simple docstring"""
  
  		def __init__(   self  )     ->   None:
  
  
  
  
  
  
  
  					'''simple docstring'''
  
  
  
  
  
  
  
  					lowerCamelCase								=     []
  					lowerCamelCase								=     0
  
  
  
  
  
  
  
  		def __repr__(   self  )     ->   str:
  
  
  
  
  
  
  
  					'''simple docstring'''
  
  
  
  
  
  
  
  					return str(self.h  )
  
  
  
  
  
  
  
  		def 				__A      (   self		,			A  )     ->   int | None:
  
  
  
  
  
  
  
  					'''simple docstring'''
  
  
  
  
  
  
  
  					if child_idx > 0:
  								return (child_idx - 1) // 2
  					return None
  
  
  
  
  
  
  
  		def 				__A      (   self		,			A  )     ->   int | None:
  
  
  
  
  
  
  
  					'''simple docstring'''
  
  
  
  
  
  
  
  					lowerCamelCase								=     2 * parent_idx + 1
  					if left_child_index < self.heap_size:
  								return left_child_index
  					return None
  
  
  
  
  
  
  
  		def 				__A      (   self		,			A  )     ->   int | None:
  
  
  
  
  
  
  
  					'''simple docstring'''
  
  
  
  
  
  
  
  					lowerCamelCase								=     2 * parent_idx + 2
  					if right_child_index < self.heap_size:
  								return right_child_index
  					return None
  
  
  
  
  
  
  
  		def 				__A      (   self		,			A  )     ->   None:
  
  
  
  
  
  
  
  					'''simple docstring'''
  
  
  
  
  
  
  
  					if index < self.heap_size:
  								lowerCamelCase								=     index
  								lowerCamelCase								=     self.left_child_idx(A  )
  								lowerCamelCase								=     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]:
  											lowerCamelCase								=     left_child
  								if right_child is not None and self.h[right_child] > self.h[violation]:
  											lowerCamelCase								=     right_child
  								# if violation indeed exists
  								if violation != index:
  											# swap to fix the violation
  											lowerCamelCase		,		lowerCamelCase								=     self.h[index], self.h[violation]
  											# fix the subsequent violation recursively if any
  											self.max_heapify(A  )
  
  
  
  
  
  
  
  		def 				__A      (   self		,			A  )     ->   None:
  
  
  
  
  
  
  
  					'''simple docstring'''
  
  
  
  
  
  
  
  					lowerCamelCase								=     list(A  )
  					lowerCamelCase								=     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 				__A      (   self  )     ->   T:
  
  
  
  
  
  
  
  					'''simple docstring'''
  
  
  
  
  
  
  
  					if self.heap_size >= 2:
  								lowerCamelCase								=     self.h[0]
  								lowerCamelCase								=     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 				__A      (   self		,			A  )     ->   None:
  
  
  
  
  
  
  
  					'''simple docstring'''
  
  
  
  
  
  
  
  					self.h.append(A  )
  					lowerCamelCase								=     (self.heap_size - 1) // 2
  					self.heap_size += 1
  					while idx >= 0:
  								self.max_heapify(A  )
  								lowerCamelCase								=     (idx - 1) // 2
  
  
  
  
  
  
  
  		def 				__A      (   self  )     ->   None:
  
  
  
  
  
  
  
  					'''simple docstring'''
  
  
  
  
  
  
  
  					lowerCamelCase								=     self.heap_size
  					for j in range(size - 1		,			0		,			-1  ):
  								lowerCamelCase		,		lowerCamelCase								=     self.h[j], self.h[0]
  								self.heap_size -= 1
  								self.max_heapify(0  )
  					lowerCamelCase								=     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}""")
  
  				UpperCAmelCase      :						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: 
  
  
  import abc
  import copy
  import dataclasses
  from dataclasses import dataclass
  from typing import ClassVar, Dict, Type, TypeVar
  
  from ..features import Features
  
  
  UpperCAmelCase      :						List[Any]    =		TypeVar("T", bound="TaskTemplate")
  
  
  
  
  
  
  
  @dataclass(frozen=a_     )
  class 					__lowercase					(       abc.ABC     ):
  
  
  
  		"""simple docstring"""
  
  		UpperCamelCase    :				str
  		UpperCamelCase    :				ClassVar[Features]
  		UpperCamelCase    :				ClassVar[Features]
  
  
  
  
  
  
  
  		def 				__A      (   self		,			A  )     ->   T:
  
  
  
  
  
  
  
  					'''simple docstring'''
  
  
  
  
  
  
  
  					return copy.deepcopy(self  )
  
  
  
  
  
  
  
  		@property
  		def 				__A      (   self  )     ->   Features:
  
  
  
  
  
  
  
  					'''simple docstring'''
  
  
  
  
  
  
  
  					return Features(**self.input_schema		,			**self.label_schema  )
  
  
  
  
  
  
  
  		@property
  		@abc.abstractmethod
  		def 				__A      (   self  )     ->   Dict[str, str]:
  
  
  
  
  
  
  
  					'''simple docstring'''
  
  
  
  
  
  
  
  					raise NotImplementedError
  
  
  
  
  
  
  
  		@classmethod
  		def 				__A      (   cls		,			A  )     ->   T:
  
  
  
  
  
  
  
  					'''simple docstring'''
  
  
  
  
  
  
  
  					lowerCamelCase								=     {f.name for f in dataclasses.fields(cls  )}
  					return cls(**{k: v for k, v in template_dict.items() if k in field_names}  )
  
  