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89 lines
2.1 KiB
Python
89 lines
2.1 KiB
Python
"""
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In a binary search tree (BST):
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* The floor of key 'k' is the maximum value that is smaller than or equal to 'k'.
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* The ceiling of key 'k' is the minimum value that is greater than or equal to 'k'.
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Reference:
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https://bit.ly/46uB0a2
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Author : Arunkumar
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Date : 14th October 2023
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"""
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from __future__ import annotations
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from collections.abc import Iterator
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from dataclasses import dataclass
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@dataclass
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class Node:
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key: int
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left: Node | None = None
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right: Node | None = None
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def __iter__(self) -> Iterator[int]:
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if self.left:
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yield from self.left
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yield self.key
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if self.right:
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yield from self.right
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def __len__(self) -> int:
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return sum(1 for _ in self)
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def floor_ceiling(root: Node | None, key: int) -> tuple[int | None, int | None]:
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"""
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Find the floor and ceiling values for a given key in a Binary Search Tree (BST).
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Args:
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root: The root of the binary search tree.
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key: The key for which to find the floor and ceiling.
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Returns:
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A tuple containing the floor and ceiling values, respectively.
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Examples:
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>>> root = Node(10)
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>>> root.left = Node(5)
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>>> root.right = Node(20)
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>>> root.left.left = Node(3)
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>>> root.left.right = Node(7)
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>>> root.right.left = Node(15)
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>>> root.right.right = Node(25)
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>>> tuple(root)
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(3, 5, 7, 10, 15, 20, 25)
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>>> floor_ceiling(root, 8)
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(7, 10)
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>>> floor_ceiling(root, 14)
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(10, 15)
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>>> floor_ceiling(root, -1)
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(None, 3)
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>>> floor_ceiling(root, 30)
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(25, None)
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"""
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floor_val = None
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ceiling_val = None
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while root:
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if root.key == key:
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floor_val = root.key
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ceiling_val = root.key
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break
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if key < root.key:
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ceiling_val = root.key
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root = root.left
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else:
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floor_val = root.key
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root = root.right
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return floor_val, ceiling_val
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if __name__ == "__main__":
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import doctest
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doctest.testmod()
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