




'''simple docstring'''







from __future__ import annotations

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





class   lowerCamelCase_							( UpperCAmelCase_							):




					'''simple docstring'''






					@abstractmethod
					def __lt__(					self,						__UpperCamelCase				):
							pass






					@abstractmethod
					def __gt__(					self,						__UpperCamelCase				):
							pass






					@abstractmethod
					def __eq__(					self,						__UpperCamelCase				):
							pass




_lowerCamelCase							:		Tuple										=						TypeVar('T', bound=Comparable)





class   lowerCamelCase_							( Generic[T]							):




					'''simple docstring'''






					def __init__(					self				):
							_snake_case			 = []
							_snake_case			 = 0






					def __repr__(					self				):
							return str(self.h				)






					def        __SCREAMING_SNAKE_CASE			(					self,						__UpperCamelCase				):
							if child_idx > 0:
									return (child_idx - 1) // 2
							return None






					def        __SCREAMING_SNAKE_CASE			(					self,						__UpperCamelCase				):
							_snake_case			 = 2 * parent_idx + 1
							if left_child_index < self.heap_size:
									return left_child_index
							return None






					def        __SCREAMING_SNAKE_CASE			(					self,						__UpperCamelCase				):
							_snake_case			 = 2 * parent_idx + 2
							if right_child_index < self.heap_size:
									return right_child_index
							return None






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






					def        __SCREAMING_SNAKE_CASE			(					self,						__UpperCamelCase				):
							_snake_case			 = list(__UpperCamelCase				)
							_snake_case			 = 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(__UpperCamelCase				)






					def        __SCREAMING_SNAKE_CASE			(					self				):
							if self.heap_size >= 2:
									_snake_case			 = self.h[0]
									_snake_case			 = 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,						__UpperCamelCase				):
							self.h.append(__UpperCamelCase				)
							_snake_case			 = (self.heap_size - 1) // 2
							self.heap_size += 1
							while idx >= 0:
									self.max_heapify(__UpperCamelCase				)
									_snake_case			 = (idx - 1) // 2






					def        __SCREAMING_SNAKE_CASE			(					self				):
							_snake_case			 = self.heap_size
							for j in range(size - 1,						0,						-1				):
									_snake_case ,					_snake_case			 = self.h[j], self.h[0]
									self.heap_size -= 1
									self.max_heapify(0				)
							_snake_case			 = 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'''







from __future__ import annotations

from collections.abc import Iterable, Iterator
from typing import Any, Generic, TypeVar

_lowerCamelCase							:		List[str]										=						TypeVar('T', bound=bool)





class   lowerCamelCase_							( Generic[T]							):




					'''simple docstring'''






					def __init__(					self,						__UpperCamelCase				):
							_snake_case			 = value
							_snake_case			 = None
							_snake_case			 = None






					@property
					def        __SCREAMING_SNAKE_CASE			(					self				):
							return self._value






					@staticmethod
					def        __SCREAMING_SNAKE_CASE			(					__UpperCamelCase,						__UpperCamelCase				):
							if not roota:
									return roota

							if not roota:
									return roota

							if roota.value > roota.value:
									_snake_case ,					_snake_case			 = roota, roota

							_snake_case			 = roota
							_snake_case			 = roota.right
							_snake_case			 = roota.left
							_snake_case			 = SkewNode.merge(__UpperCamelCase,						__UpperCamelCase				)

							return result





class   lowerCamelCase_							( Generic[T]							):




					'''simple docstring'''






					def __init__(					self,						__UpperCamelCase = ()				):
							_snake_case			 = None
							if data:
									for item in data:
											self.insert(__UpperCamelCase				)






					def __bool__(					self				):
							return self._root is not None






					def __iter__(					self				):
							_snake_case			 = []
							while self:
									result.append(self.pop()				)

							# Pushing items back to the heap not to clear it.
							for item in result:
									self.insert(__UpperCamelCase				)

							return iter(__UpperCamelCase				)






					def        __SCREAMING_SNAKE_CASE			(					self,						__UpperCamelCase				):
							_snake_case			 = SkewNode.merge(self._root,						SkewNode(__UpperCamelCase				)				)






					def        __SCREAMING_SNAKE_CASE			(					self				):
							_snake_case			 = self.top()
							_snake_case			 = (
							    SkewNode.merge(self._root.left,						self._root.right				) if self._root else None
							)

							return result






					def        __SCREAMING_SNAKE_CASE			(					self				):
							if not self._root:
									raise IndexError("Can't get top element for the empty heap."				)
							return self._root.value






					def        __SCREAMING_SNAKE_CASE			(					self				):
							_snake_case			 = None


if __name__ == "__main__":
						import doctest

						doctest.testmod()





