---
id: dsu
title: "Disjoint Set Union"
author: Benjamin Qi, Michael Cao 
prerequisites:
 - Silver - Depth First Search
description: The Disjoint Set Union (DSU) data structure allows you to add edges to an initially empty graph and test whether two vertices of the graph are connected.
---

## Tutorial

 - CPH 15.2
 - [PAPS 11.1](https://www.csc.kth.se/~jsannemo/slask/main.pdf)
 - Chapter 10.6 of "An Introduction to the US Computing Olympiad"
 - [CSAcademy Disjoint-Set](https://csacademy.com/lesson/disjoint_data_sets)
 - [Topcoder Union Find](https://www.topcoder.com/community/data-science/data-science-tutorials/disjoint-set-data-structures/)
 - [CPC.3](https://github.com/SuprDewd/T-414-AFLV/tree/master/03_data_structures)
 - DSU Complexity Proofs (optional of course)
   - [log\*n](https://en.wikipedia.org/wiki/Proof_of_O(log*n)\_time_complexity\_of_union%E2%80%93find)
   - [a(m,n)](https://dl.acm.org/doi/pdf/10.1145/321879.321884)

with rollback: https://codeforces.com/contest/1140/problem/F

## Problems

- [Mootube](http://www.usaco.org/index.php?page=viewproblem2&cpid=789)
  - same as [CSES Road Construction](https://cses.fi/problemset/task/1676)
- [Closing the Farm](http://www.usaco.org/index.php?page=viewproblem2&cpid=646)
- [CSES Network Breakdown](https://cses.fi/problemset/task/1677)
- [Favorite Colors](http://www.usaco.org/index.php?page=viewproblem2&cpid=1042)
  - fairly tricky