Floor and ceil in Binary search tree added

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()