




from __future__ import annotations

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

class 		lowercase_       (	lowerCAmelCase__				):




					@abstractmethod
					def __lt__(   self:		T,     _lowercase:		T):


									'''simple docstring'''


									pass




					@abstractmethod
					def __gt__(   self:		T,     _lowercase:		T):


									'''simple docstring'''


									pass







					@abstractmethod
					def __eq__(   self:		T,     _lowercase:		object):


									'''simple docstring'''


									pass





__A						:		Any          =						TypeVar("T", bound=Comparable)

class 		lowercase_       (	Generic[T]				):




					def __init__(   self:		Tuple):


									'''simple docstring'''


									__lowerCAmelCase					=  []
									__lowerCAmelCase					=  0




					def __repr__(   self:		int):


									'''simple docstring'''


									return str(self.h)




					def     _lowercase						(   self:		int,     _lowercase:		int):


									'''simple docstring'''


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




					def     _lowercase						(   self:		Optional[Any],     _lowercase:		int):


									'''simple docstring'''


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




					def     _lowercase						(   self:		Optional[Any],     _lowercase:		int):


									'''simple docstring'''


									__lowerCAmelCase					=  2 * parent_idx + 2
									if right_child_index < self.heap_size:
													return right_child_index
									return None




					def     _lowercase						(   self:		List[str],     _lowercase:		int):


									'''simple docstring'''


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




					def     _lowercase						(   self:		int,     _lowercase:		Iterable[T]):


									'''simple docstring'''


									__lowerCAmelCase					=  list(_snake_case)
									__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(_snake_case)




					def     _lowercase						(   self:		Any):


									'''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     _lowercase						(   self:		int,     _lowercase:		T):


									'''simple docstring'''


									self.h.append(_snake_case)
									__lowerCAmelCase					=  (self.heap_size - 1) // 2
									self.heap_size += 1
									while idx >= 0:
													self.max_heapify(_snake_case)
													__lowerCAmelCase					=  (idx - 1) // 2







					def     _lowercase						(   self:		List[str]):


									'''simple docstring'''


									__lowerCAmelCase					=  self.heap_size
									for j in range(size - 1,     0,     -1):
													__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],
	    [103, 9, 1, 7, 11, 15, 25, 201, 209, 107, 5],
	    [-45, -2, -5],
	]:
		print(f"""unsorted array: {unsorted}""")

		__A						:		Tuple          =						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""")













def       _a   (							lowerCamelCase__				)  ->      int:
 return int(lowerCamelCase__				) if x - int(lowerCamelCase__				) >= 0 else int(lowerCamelCase__				) - 1


if __name__ == "__main__":
       import doctest

       doctest.testmod()
