




from collections.abc import Iterable
from typing import Any







class 						lowercase							:

     def __init__(  self		,     _a = None				)						->							Dict:
           _A							:     Any			=						value
           _A							:     Node | None			=						None  # Added in order to delete a node easier
           _A							:     Node | None			=						None
           _A							:     Node | None			=						None



     def __repr__(  self				)						->							str:
           from pprint import pformat

           if self.left is None and self.right is None:
                 return str(self.value				)
           return pformat({F'''{self.value}''': (self.left, self.right)}		,     indent=1				)







class 						lowercase							:

     def __init__(  self		,     _a = None				)						->							Optional[Any]:
           _A							:     Dict			=						root

     def __str__(  self				)						->							str:
           return str(self.root				)

     def 					a__	(  self		,     _a		,     _a				)						->							None:
           if new_children is not None:  # reset its kids
                 _A							:     Tuple			=						node.parent
           if node.parent is not None:  # reset its parent
                 if self.is_right(_a				):  # If it is the right children
                       _A							:     Dict			=						new_children
                 else:
                       _A							:     int			=						new_children
           else:
                 _A							:     List[str]			=						new_children

     def 					a__	(  self		,     _a				)						->							bool:
           if node.parent and node.parent.right:
                 return node == node.parent.right
           return False

     def 					a__	(  self				)						->							bool:
           return self.root is None

     def 					a__	(  self		,     _a				)						->							None:
           _A							:     List[Any]			=						Node(_a				)  # create a new Node
           if self.empty():  # if Tree is empty
                 _A							:     Union[str, Any]			=						new_node  # set its root
           else:  # Tree is not empty
                 _A							:     int			=						self.root  # from root
                 if parent_node is None:
                       return
                 while True:  # While we don't get to a leaf
                       if value < parent_node.value:  # We go left
                             if parent_node.left is None:
                                   _A							:     List[Any]			=						new_node  # We insert the new node in a leaf
                                   break
                             else:
                                   _A							:     Union[str, Any]			=						parent_node.left
                       else:
                             if parent_node.right is None:
                                   _A							:     List[Any]			=						new_node
                                   break
                             else:
                                   _A							:     int			=						parent_node.right
                 _A							:     Optional[int]			=						parent_node

     def 					a__	(  self		,     *_a				)						->							None:
           for value in values:
                 self.__insert(_a				)

     def 					a__	(  self		,     _a				)						->							Node | None:
           if self.empty():
                 raise IndexError("""Warning: Tree is empty! please use another."""				)
           else:
                 _A							:     Union[str, Any]			=						self.root
                 # use lazy evaluation here to avoid NoneType Attribute error
                 while node is not None and node.value is not value:
                       _A							:     int			=						node.left if value < node.value else node.right
                 return node

     def 					a__	(  self		,     _a = None				)						->							Node | None:
           if node is None:
                 if self.root is None:
                       return None
                 _A							:     Union[str, Any]			=						self.root

           if not self.empty():
                 while node.right is not None:
                       _A							:     str			=						node.right
           return node

     def 					a__	(  self		,     _a = None				)						->							Node | None:
           if node is None:
                 _A							:     Dict			=						self.root
           if self.root is None:
                 return None
           if not self.empty():
                 _A							:     str			=						self.root
                 while node.left is not None:
                       _A							:     int			=						node.left
           return node

     def 					a__	(  self		,     _a				)						->							None:
           _A							:     Tuple			=						self.search(_a				)  # Look for the node with that label
           if node is not None:
                 if node.left is None and node.right is None:  # If it has no children
                       self.__reassign_nodes(_a		,     _a				)
                 elif node.left is None:  # Has only right children
                       self.__reassign_nodes(_a		,     node.right				)
                 elif node.right is None:  # Has only left children
                       self.__reassign_nodes(_a		,     node.left				)
                 else:
                       _A							:     Tuple			=						self.get_max(
                           node.left				)  # Gets the max value of the left branch
                       self.remove(tmp_node.value				)  # type: ignore
                       _A							:     Union[str, Any]			=						(
                           tmp_node.value  # type: ignore
                       )  # Assigns the value to the node to delete and keep tree structure

     def 					a__	(  self		,     _a				)						->							Iterable:
           if node is not None:
                 yield node  # Preorder Traversal
                 yield from self.preorder_traverse(node.left				)
                 yield from self.preorder_traverse(node.right				)

     def 					a__	(  self		,     _a=None				)						->							Any:
           if traversal_function is None:
                 return self.preorder_traverse(self.root				)
           else:
                 return traversal_function(self.root				)

     def 					a__	(  self		,     _a		,     _a				)						->							None:
           if node:
                 self.inorder(_a		,     node.left				)
                 arr.append(node.value				)
                 self.inorder(_a		,     node.right				)



     def 					a__	(  self		,     _a		,     _a				)						->							int:
           _A							:     list[int]			=						[]
           self.inorder(_a		,     _a				)  # append all values to list using inorder traversal
           return arr[k - 1]







def 				lowerCAmelCase_	(     snake_case_     ):
      _A							:     List[Any]			=						[]
      if curr_node is not None:
            _A							:     Union[str, Any]			=						postorder(curr_node.left     ) + postorder(curr_node.right     ) + [curr_node]
      return node_list







def 				lowerCAmelCase_	(     ):
      _A							:     int			=						(8, 3, 6, 1, 10, 14, 13, 4, 7)
      _A							:     List[Any]			=						BinarySearchTree()
      for i in testlist:
            t.insert(snake_case_     )

      # Prints all the elements of the list in order traversal
      print(snake_case_     )

      if t.search(6     ) is not None:
            print("""The value 6 exists"""     )
      else:
            print("""The value 6 doesn't exist"""     )

      if t.search(-1     ) is not None:
            print("""The value -1 exists"""     )
      else:
            print("""The value -1 doesn't exist"""     )

      if not t.empty():
            print("""Max Value: """,t.get_max().value     )  # type: ignore
            print("""Min Value: """,t.get_min().value     )  # type: ignore

      for i in testlist:
            t.remove(snake_case_     )
            print(snake_case_     )


if __name__ == "__main__":
  import doctest

  doctest.testmod(verbose=True)


"""simple docstring"""






def SCREAMING_SNAKE_CASE__			(   __UpperCAmelCase       ,    __UpperCAmelCase )  ->  List[str]:
   lowercase__:   Optional[Any]					=      0
   lowercase__:   List[Any]					=      len(__UpperCAmelCase ) - 1

   while left <= right:
      # avoid divided by 0 during interpolation
      if sorted_collection[left] == sorted_collection[right]:
         if sorted_collection[left] == item:
            return left
         else:
            return None

      lowercase__:   Tuple					=      left + ((item - sorted_collection[left]) * (right - left)) // (
          sorted_collection[right] - sorted_collection[left]
      )

      # out of range check
      if point < 0 or point >= len(__UpperCAmelCase ):
         return None

      lowercase__:   Optional[int]					=      sorted_collection[point]
      if current_item == item:
         return point
      else:
         if point < left:
            lowercase__:   List[Any]					=      left
            lowercase__:   int					=      point
         elif point > right:
            lowercase__:   Dict					=      right
            lowercase__:   List[str]					=      point
         else:
            if item < current_item:
               lowercase__:   int					=      point - 1
            else:
               lowercase__:   int					=      point + 1
   return None



def SCREAMING_SNAKE_CASE__			(   __UpperCAmelCase       ,    __UpperCAmelCase       ,    __UpperCAmelCase       ,    __UpperCAmelCase )  ->  List[str]:

   # avoid divided by 0 during interpolation
   if sorted_collection[left] == sorted_collection[right]:
      if sorted_collection[left] == item:
         return left
      else:
         return None

   lowercase__:   Optional[int]					=      left + ((item - sorted_collection[left]) * (right - left)) // (
       sorted_collection[right] - sorted_collection[left]
   )

   # out of range check
   if point < 0 or point >= len(__UpperCAmelCase ):
      return None

   if sorted_collection[point] == item:
      return point
   elif point < left:
      return interpolation_search_by_recursion(__UpperCAmelCase       ,    __UpperCAmelCase       ,    __UpperCAmelCase       ,    __UpperCAmelCase )
   elif point > right:
      return interpolation_search_by_recursion(__UpperCAmelCase       ,    __UpperCAmelCase       ,    __UpperCAmelCase       ,    __UpperCAmelCase )
   else:
      if sorted_collection[point] > item:
         return interpolation_search_by_recursion(
             __UpperCAmelCase       ,    __UpperCAmelCase       ,    __UpperCAmelCase       ,    point - 1 )
      else:
         return interpolation_search_by_recursion(
             __UpperCAmelCase       ,    __UpperCAmelCase       ,    point + 1       ,    __UpperCAmelCase )



def SCREAMING_SNAKE_CASE__			(   __UpperCAmelCase )  ->  List[Any]:
   if collection != sorted(__UpperCAmelCase ):
      raise ValueError('''Collection must be ascending sorted''' )
   return True


if __name__ == "__main__":
       import sys
       __A			   = 0
       if debug == 1:
              __A			   = [1_0, 3_0, 4_0, 4_5, 5_0, 6_6, 7_7, 9_3]
              try:
                     __assert_sorted(collection)
              except ValueError:
                     sys.exit("Sequence must be ascending sorted to apply interpolation search")
              __A			   = 6_7

       __A			   = interpolation_search(collection, target)
       if result is not None:
              print(f'''{target} found at positions: {result}''')
       else:
              print("Not found")
