Objective: Given a graph, check if the graph contains a cycle using disjoint set.
Note: Disjoint-set data structure, also called a union–find data structure or merge–find set.
It is strongly recommended to read “Disjoint-set data structure” before continue reading this article.
How to find cycle:
- The makeset operation makes a new set by creating a new element with a parent pointer to itself.
- Then process each edge of the graph and perform find and Union operations to make subsets using both vertices of the edge.
- If find operation on both the vertices returns the same parent (means both vertices belongs to the same subset) then cycle is detected.
Lets walk through one example for more understanding, see the animation below:
Graph contains cycle: true