data_structures.binary_tree.floor_and_ceiling
=============================================

.. py:module:: data_structures.binary_tree.floor_and_ceiling

.. autoapi-nested-parse::

   In a binary search tree (BST):
   * The floor of key 'k' is the maximum value that is smaller than or equal to 'k'.
   * The ceiling of key 'k' is the minimum value that is greater than or equal to 'k'.

   Reference:
   https://bit.ly/46uB0a2

   Author : Arunkumar
   Date : 14th October 2023



Classes
-------

.. autoapisummary::

   data_structures.binary_tree.floor_and_ceiling.Node


Functions
---------

.. autoapisummary::

   data_structures.binary_tree.floor_and_ceiling.floor_ceiling


Module Contents
---------------

.. py:class:: Node

   .. py:method:: __iter__() -> collections.abc.Iterator[int]


   .. py:method:: __len__() -> int


   .. py:attribute:: key
      :type:  int


   .. py:attribute:: left
      :type:  Node | None
      :value: None



   .. py:attribute:: right
      :type:  Node | None
      :value: None



.. py:function:: floor_ceiling(root: Node | None, key: int) -> tuple[int | None, int | None]

   Find the floor and ceiling values for a given key in a Binary Search Tree (BST).

   Args:
       root: The root of the binary search tree.
       key: The key for which to find the floor and ceiling.

   Returns:
       A tuple containing the floor and ceiling values, respectively.

   Examples:
       >>> root = Node(10)
       >>> root.left = Node(5)
       >>> root.right = Node(20)
       >>> root.left.left = Node(3)
       >>> root.left.right = Node(7)
       >>> root.right.left = Node(15)
       >>> root.right.right = Node(25)
       >>> tuple(root)
       (3, 5, 7, 10, 15, 20, 25)
       >>> floor_ceiling(root, 8)
       (7, 10)
       >>> floor_ceiling(root, 14)
       (10, 15)
       >>> floor_ceiling(root, -1)
       (None, 3)
       >>> floor_ceiling(root, 30)
       (25, None)