UNION - FIND

ALGORITHM

Union Find problem and a set of algorithms for solving it

Dynamic connectivityQuick find algorithmQuick union algorithmImprovementsApplications

There are basically two major parts in each algorithm:

-> Union Command: Connect the two objects-> Find / Connected query: Is there a path

connecting the two objects !

QUICK FIND (Eager Approach)

Data StructureInteger array id[] of size NInterpretation : p and q are connected iff they

have the same id.FindCheck if p and q have the same id.UnionTo merge components containing p and q,

change all entries whose id equals id[p] to id[q].

QUICK UNION (Lazy Approach)

Data StructureInteger array id[] of size NInterpretation: id[i] is parent of IRoot of i is id[id[id[…id[i]…]]].FindCheck if p and q have the same root.UnionTo merge components between p and q, set the

id ofp’s root to the id of q’s root.

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