diff --git a/data_structures/binary_tree/floor_and_ceiling.py b/data_structures/binary_tree/floor_and_ceiling.py new file mode 100644 index 000000000000..f8a1adbd967b --- /dev/null +++ b/data_structures/binary_tree/floor_and_ceiling.py @@ -0,0 +1,87 @@ +""" +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 +""" +from __future__ import annotations + +from collections.abc import Iterator +from dataclasses import dataclass + + +@dataclass +class Node: + key: int + left: Node | None = None + right: Node | None = None + + def __iter__(self) -> Iterator[int]: + if self.left: + yield from self.left + yield self.key + if self.right: + yield from self.right + + def __len__(self) -> int: + return sum(1 for _ in self) + + +def 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) + """ + floor_val = None + ceiling_val = None + + while root: + if root.key == key: + floor_val = root.key + ceiling_val = root.key + break + + if key < root.key: + ceiling_val = root.key + root = root.left + else: + floor_val = root.key + root = root.right + + return floor_val, ceiling_val + + +if __name__ == "__main__": + import doctest + + doctest.testmod()