Disjoint Sets Simulator

Disjoint Sets Simulator

A disjoint sets structure, also called Union-Find, maintains a collection of non-overlapping sets. It answers which component an element belongs to and merges two components cheaply, thanks to path compression and union by rank.

How to use it

• Make Set adds a new element as a component of its own. Pick two elements and press Union or Connected?.
• Find Representative walks the find path step by step and then compresses it; Compress All Paths flattens every tree.
• Each arrow points from an element to its parent. The table lists every element's parent, representative (Root), rank, and component size (Size).

Union-Find ideas

• Disjoint components: every element belongs to exactly one component, which is represented by a rooted tree of parent links.
• Path compression: find rewrites the parent links along the search path to point straight at the representative, so later finds are shorter.
• Union by rank: the root of lower rank goes under the root of higher rank; when the ranks are equal, the new root's rank grows by one.
• Applications: Kruskal's minimum spanning tree algorithm, connectivity queries, image segmentation, and dynamic grouping.

Terms