Find the representative
Two nodes are connected when their roots are the same.
Union Find
5 chapters · 6 challenges · The Connected Expanse
Understand the idea, practise through play, then prove it in code. Choose your next quest below.
Visual introduction to this topic
Start here · 3 minute mental model
What is union find?
Union find maintains disjoint groups while connections are added. It answers whether two items share a representative and merges their groups efficiently.
Think of forming alliances. Each player follows a captain. When two alliances merge, only their captains need to be connected; everyone inherits the new group.
Find a representative; union representatives; compress the route for next time.
Union balanced roots
Attach the smaller or shallower tree to the larger one.
Compress paths
Make every visited node point closer to the root after a find.
What you will learn firstThe Province Roots
Begin the guided lesson Merge direct roads into connected regions
01
Components
0/2 completePractice components through 2 visual expeditions.
02
Path Compression
0/1 completePractice path compression through 1 visual expedition.
03
Union By Rank
0/1 completePractice union by rank through 1 visual expedition.
04
Redundant Edge
0/1 completePractice redundant edge through 1 visual expedition.
05
Offline Connectivity
0/1 completePractice offline connectivity through 1 visual expedition.
Source reviewed
Built from authoritative material
This track is checked against the sources below. Visual traces still carry their own complete or guided coverage label, so unfinished explanations are not presented as complete executions.