




from __future__ import annotations

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






class    __lowerCAmelCase			(	UpperCAmelCase__			):







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




         """simple docstring"""


         pass







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




         """simple docstring"""


         pass







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




         """simple docstring"""


         pass




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






class    __lowerCAmelCase			(	Generic[T]			):







   def __init__(	self   :      Optional[int]				):




         """simple docstring"""


         _UpperCAmelCase													=					[]
         _UpperCAmelCase													=					0







   def __repr__(	self   :      Dict				):




         """simple docstring"""


         return str(self.h				)







   def UpperCamelCase      (	self   :      Optional[Any]   ,   snake_case__   :      int				):




         """simple docstring"""


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







   def UpperCamelCase      (	self   :      Tuple   ,   snake_case__   :      int				):




         """simple docstring"""


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







   def UpperCamelCase      (	self   :      Union[str, Any]   ,   snake_case__   :      int				):




         """simple docstring"""


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







   def UpperCamelCase      (	self   :      Dict   ,   snake_case__   :      int				):




         """simple docstring"""


         if index < self.heap_size:
               _UpperCAmelCase													=					index
               _UpperCAmelCase													=					self.left_child_idx(snake_case__				)
               _UpperCAmelCase													=					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]:
                     _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(snake_case__				)







   def UpperCamelCase      (	self   :      Tuple   ,   snake_case__   :      Iterable[T]				):




         """simple docstring"""


         _UpperCAmelCase													=					list(snake_case__				)
         _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(snake_case__				)







   def UpperCamelCase      (	self   :      Tuple				):




         """simple docstring"""


         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 UpperCamelCase      (	self   :      str   ,   snake_case__   :      T				):




         """simple docstring"""


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







   def UpperCamelCase      (	self   :      Any				):




         """simple docstring"""


         _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],
        [1_03, 9, 1, 7, 11, 15, 25, 2_01, 2_09, 1_07, 5],
        [-45, -2, -5],
    ]:
        print(f"""unsorted array: {unsorted}""")

        lowercase_     :    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""")










from __future__ import annotations


def 							__SCREAMING_SNAKE_CASE  (      snake_case_						):

						'''simple docstring'''


						if len(snake_case_						) == 0:
												raise ValueError("find_max() arg is an empty sequence"						)
						_UpperCAmelCase													=					nums[0]
						for x in nums:
												if x > max_num:
																		_UpperCAmelCase													=					x
						return max_num


if __name__ == "__main__":
				import doctest

				doctest.testmod(verbose=True)




