






"""simple docstring"""
from __future__ import annotations

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



class 						a_ (      snake_case_					):







      '''simple docstring'''

      @abstractmethod
      def __lt__(self,	lowerCamelCase_   ):

       '''simple docstring'''



       pass




      @abstractmethod
      def __gt__(self,	lowerCamelCase_   ):

       '''simple docstring'''



       pass





      @abstractmethod
      def __eq__(self,	lowerCamelCase_   ):

       '''simple docstring'''



       pass


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



class 						a_ (      Generic[T]					):







      '''simple docstring'''

      def __init__(self   ):

       '''simple docstring'''



       lowerCamelCase__	:     list[T]								=		[]
       lowerCamelCase__	:     int								=		0




      def __repr__(self   ):

       '''simple docstring'''



       return str(self.h   )




      def      a__				(self,	lowerCamelCase_   ):

       '''simple docstring'''



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




      def      a__				(self,	lowerCamelCase_   ):

       '''simple docstring'''



       lowerCamelCase__	:     List[str]								=		2 * parent_idx + 1
       if left_child_index < self.heap_size:
        return left_child_index
       return None




      def      a__				(self,	lowerCamelCase_   ):

       '''simple docstring'''



       lowerCamelCase__	:     Optional[int]								=		2 * parent_idx + 2
       if right_child_index < self.heap_size:
        return right_child_index
       return None




      def      a__				(self,	lowerCamelCase_   ):

       '''simple docstring'''



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




      def      a__				(self,	lowerCamelCase_   ):

       '''simple docstring'''



       lowerCamelCase__	:     Tuple								=		list(lowerCamelCase_   )
       lowerCamelCase__	:     Tuple								=		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      a__				(self   ):

       '''simple docstring'''



       if self.heap_size >= 2:
        lowerCamelCase__	:     Dict								=		self.h[0]
        lowerCamelCase__	:     List[str]								=		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,	lowerCamelCase_   ):

       '''simple docstring'''



       self.h.append(lowerCamelCase_   )
       lowerCamelCase__	:     Any								=		(self.heap_size - 1) // 2
       self.heap_size += 1
       while idx >= 0:
        self.max_heapify(lowerCamelCase_   )
        lowerCamelCase__	:     Optional[Any]								=		(idx - 1) // 2





      def      a__				(self   ):

       '''simple docstring'''



       lowerCamelCase__	:     List[str]								=		self.heap_size
       for j in range(size - 1,	0,	-1   ):
        lowerCamelCase__							,	lowerCamelCase__	:     Optional[Any]								=		self.h[j], self.h[0]
        self.heap_size -= 1
        self.max_heapify(0   )
       lowerCamelCase__	:     Dict								=		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}")

            A_     :					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")









"""simple docstring"""
class 						a_ :







      '''simple docstring'''

      def __init__(self,	lowerCamelCase_   ):

       '''simple docstring'''



       lowerCamelCase__	:     Dict								=		data
       lowerCamelCase__	:     BinaryTreeNode | None								=		None
       lowerCamelCase__	:     BinaryTreeNode | None								=		None






def 			lowerCamelCase_    (		_lowerCamelCase     ,  _lowerCamelCase							):
 if node is None:
  lowerCamelCase__	:     List[str]								=		BinaryTreeNode(_lowerCamelCase							)
  return node

 # binary search tree is not empty,
 # so we will insert it into the tree
 # if new_value is less than value of data in node,
 #  add it to left subtree and proceed recursively
 if new_value < node.data:
  lowerCamelCase__	:     str								=		insert(node.left_child     ,  _lowerCamelCase							)
 else:
  # if new_value is greater than value of data in node,
  #  add it to right subtree and proceed recursively
  lowerCamelCase__	:     str								=		insert(node.right_child     ,  _lowerCamelCase							)
 return node






def 			lowerCamelCase_    (		_lowerCamelCase							):  # if node is None,return
 if node:
  lowerCamelCase__	:     Any								=		inorder(node.left_child							)
  lowerCamelCase__	:     Tuple								=		[*inorder_array, node.data]
  lowerCamelCase__	:     List[Any]								=		inorder_array + inorder(node.right_child							)
 else:
  lowerCamelCase__	:     Any								=		[]
 return inorder_array






def 			lowerCamelCase_    (		):
 lowerCamelCase__	:     Tuple								=		insert(_lowerCamelCase     ,  15							)
 insert(_lowerCamelCase     ,  10							)
 insert(_lowerCamelCase     ,  25							)
 insert(_lowerCamelCase     ,  6							)
 insert(_lowerCamelCase     ,  14							)
 insert(_lowerCamelCase     ,  20							)
 insert(_lowerCamelCase     ,  60							)
 return root






def 			lowerCamelCase_    (		):
 # main function
 lowerCamelCase__	:     List[Any]								=		make_tree()
 print('Printing values of binary search tree in Inorder Traversal.'							)
 inorder(_lowerCamelCase							)


if __name__ == "__main__":
      import doctest

      doctest.testmod()
      main()

