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Running times of disjoint-set Throughout this chapter,we shall analyze the running times of disjoint-set data structures in terms of two parameters n,the number of MAKE-SET operations, and m,the total number of MAKE-SET,UNION,and FIND-SET operations.Since the sets are disjoint,each UNION operation reduces the number of sets by one. After n-1 UNION operations,therefore,only one set remains.The number of UNION operations is thus at most n-1.Note also that since the MAKE-SET operations are included in the total number of operations m,we have m >n.We assume that the n MAKE-SET operations are the first n operations performed.Running times of disjoint-set
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