51 lines
1.7 KiB
Markdown
51 lines
1.7 KiB
Markdown
---
|
|
title: "Union Find"
|
|
date: 2024-06-24T21:07:49+01:00
|
|
draft: false # I don't care for draft mode, git has branches for that
|
|
description: "My favorite data structure"
|
|
tags:
|
|
- algorithms
|
|
- data structures
|
|
- python
|
|
categories:
|
|
- programming
|
|
series:
|
|
- Cool algorithms
|
|
favorite: false
|
|
disable_feed: false
|
|
---
|
|
|
|
To kickoff the [series]({{< ref "/series/cool-algorithms/">}}) of posts about
|
|
algorithms and data structures I find interesting, I will be talking about my
|
|
favorite one: the [_Disjoint Set_][wiki]. Also known as the _Union-Find_ data
|
|
structure, so named because of its two main operations: `ds.union(lhs, rhs)` and
|
|
`ds.find(elem)`.
|
|
|
|
[wiki]: https://en.wikipedia.org/wiki/Disjoint-set_data_structure
|
|
|
|
<!--more-->
|
|
|
|
## What does it do?
|
|
|
|
The _Union-Find_ data structure allows one to store a collection of sets of
|
|
elements, with operations for adding new sets, merging two sets into one, and
|
|
finding the representative member of a set. Not only does it do all that, but it
|
|
does it in almost constant (amortized) time!
|
|
|
|
Here is a small motivating example for using the _Disjoint Set_ data structure:
|
|
|
|
```python
|
|
def connected_components(graph: Graph) -> list[set[Node]]:
|
|
# Initialize the disjoint set so that each node is in its own set
|
|
ds: DisjointSet[Node] = DisjointSet(graph.nodes)
|
|
# Each edge is a connection, merge both sides into the same set
|
|
for (start, dest) in graph.edges:
|
|
ds.union(start, dest)
|
|
# Connected components share the same (arbitrary) root
|
|
components: dict[Node, set[Node]] = defaultdict(set)
|
|
for n in graph.nodes:
|
|
components[ds.find(n)].add(n)
|
|
# Return a list of disjoint sets corresponding to each connected component
|
|
return list(components.values())
|
|
```
|