74 lines
2.2 KiB
Markdown
74 lines
2.2 KiB
Markdown
---
|
|
title: "Treap, revisited"
|
|
date: 2024-07-27T14:12:27+01:00
|
|
draft: false # I don't care for draft mode, git has branches for that
|
|
description: "An even simpler BST"
|
|
tags:
|
|
- algorithms
|
|
- data structures
|
|
- python
|
|
categories:
|
|
- programming
|
|
series:
|
|
- Cool algorithms
|
|
favorite: false
|
|
disable_feed: false
|
|
---
|
|
|
|
My [last post]({{< relref "../2024-07-20-treap/index.md" >}}) about the _Treap_
|
|
showed an implementation using tree rotations, as is commonly done with [AVL
|
|
Trees][avl] and [Red Black Trees][rb].
|
|
|
|
But the _Treap_ lends itself well to a simple and elegant implementation with no
|
|
tree rotations. This makes it especially easy to implement the removal of a key,
|
|
rather than the fiddly process of deletion using tree rotations.
|
|
|
|
[avl]: https://en.wikipedia.org/wiki/AVL_tree
|
|
[rb]: https://en.wikipedia.org/wiki/Red%E2%80%93black_tree
|
|
|
|
<!--more-->
|
|
|
|
## Implementation
|
|
|
|
All operations on the tree will be implemented in terms of two fundamental
|
|
operations: `split` and `merge`.
|
|
|
|
We'll be reusing the same structures as in the last post, so let's skip straight
|
|
to implementing those fundaments, and building on them for `insert` and
|
|
`delete`.
|
|
|
|
### Split
|
|
|
|
Splitting a tree means taking a key, and getting the following output:
|
|
|
|
* a `left` node, root of the tree of all keys lower than the input.
|
|
* an extracted `node` which corresponds to the input `key`.
|
|
* a `right` node, root of the tree of all keys higher than the input.
|
|
|
|
```python
|
|
type OptionalNode[K, V] = Node[K, V] | None
|
|
|
|
def split(
|
|
root: OptionalNode[K, V],
|
|
key: K,
|
|
) -> tuple[OptionalNode[K, V], OptionalNode[K, V], OptionalNode[K, V]]:
|
|
# Base case, empty tree
|
|
if root is None:
|
|
return None, None, None
|
|
# If we found the key, simply extract left and right
|
|
if root.key == key:
|
|
left, right = root.left, root.right
|
|
root.left, root.right = None, None
|
|
return left, root, right
|
|
# Otherwise, recurse on the corresponding side of the tree
|
|
if root.key < key:
|
|
left, node, right = split(root.right, key)
|
|
root.right = left
|
|
return root, node, right
|
|
if key < root.key:
|
|
left, node, right = split(root.left, key)
|
|
root.left = right
|
|
return left, node, root
|
|
raise RuntimeError("Unreachable")
|
|
```
|