---
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.
frequency: 3
---
import { Problem } from "../models";
export const metadata = {
problems: {
sample: [
new Problem("YS", "Union Find", "unionfind", "Easy", false, []),
],
general: [
new Problem("Gold", "Mootube", "789", "Easy", false, [], "same as [CSES Road Construction](https://cses.fi/problemset/task/1676)"),
new Problem("Gold", "Closing the Farm", "646", "Easy", false, [], "similar to [CSES Network Breakdown](https://cses.fi/problemset/task/1677)"),
new Problem("Gold", "Favorite Colors", "1042", "Hard", false, [], ""),
],
rollback: [
new Problem("YS", "Persistent Union Find", "persistent_unionfind", "Normal", false, [], ""),
new Problem("YS", "Vertex Add Component Sum", "dynamic_graph_vertex_add_component_sum", "Hard", false, [], ""),
new Problem("CF", "Edu F - Extending Set of Points", "contest/1140/problem/F", "Hard", false, [], ""),
],
}
};
## Tutorial
- [$\log^* n$](https://en.wikipedia.org/wiki/Proof_of_O(log*n)\_time_complexity\_of_union%E2%80%93find)
- [$\alpha (m,n)$](https://dl.acm.org/doi/pdf/10.1145/321879.321884)
## Problems
## Rollback
no path compression