100 lines
2.5 KiB
Markdown
100 lines
2.5 KiB
Markdown
---
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title: "Treap"
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date: 2024-07-20T14:12:27+01:00
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draft: false # I don't care for draft mode, git has branches for that
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description: "A simpler BST"
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tags:
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- algorithms
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- data structures
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- python
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categories:
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- programming
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series:
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- Cool algorithms
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favorite: false
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disable_feed: false
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graphviz: true
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---
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The [_Treap_][wiki] is a mix between a _Binary Search Tree_ and a _Heap_.
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Like a _Binary Search Tree_, it keeps an ordered set of keys in the shape of a
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tree, allowing for binary search traversal.
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Like a _Heap_, it associates each node with a priority, making sure that a
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parent's priority is always higher than any of its children.
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[wiki]: https://en.wikipedia.org/wiki/Treap
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<!--more-->
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## What does it do?
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By randomizing the priority value of each key at insertion time, we ensure a
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high likelihood that the tree stays _roughly_ balanced, avoiding degenerating to
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unbalanced O(N) height.
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Here's a sample tree created by inserting integers from 0 to 250 into the tree:
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{{< graphviz file="treap.gv" />}}
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## Implementation
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I'll be keeping the theme for this [series] by using Python to implement the
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_Treap_. This leads to somewhat annoying code to handle the rotation process,
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which is easier to do in C using pointers.
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[series]: {{< ref "/series/cool-algorithms/" >}}
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### Representation
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Creating a new `Treap` is easy: the tree starts off empty, waiting for new nodes
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to insert.
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Each `Node` must keep track of the `key`, the mapped `value`, and the node's
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`priority` (which is assigned randomly). Finally it must also allow for storing
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two children (`left` and `right`).
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```python
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class Node[K, V]:
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key: K
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value: V
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priority: float
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left: Node[K, V] | None
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righg: Node[K, V] | None
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def __init__(self, key: K, value: V):
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# Store key and value, like a normal BST node
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self.key = key
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self.value = value
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# Priority is derived randomly
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self.priority = random()
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self.left = None
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self.right = None
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class Treap[K, V]:
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_root: Node[K, V] | None
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def __init__(self):
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# The tree starts out empty
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self._root = None
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```
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### Search
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Searching the tree is the same as in any other _Binary Search Tree_.
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```python
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def get(self, key: K) -> T | None:
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node = self._root
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# The usual BST traversal
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while node is not None:
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if node.key == key:
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return node.value
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elif node.key < key:
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node = node.right
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else:
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node = node.left
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return None
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```
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