Question

2. Consider the following pseudocode for a disjoint-set implementation: Make-Set Cx) rank ) 0 Find-Set(x) return Find-Set (pLx) return LinkCx, y if rank]rank[y] else if rankx)rank y) rank[y]ran[y]1 Union (,y) Link (Find-Set (x), Find-Set(y)) Show the data structure that results and the answers returned by the Find-Set operations in the following program for i ? 1 to 16 Make-Set() for i ? 1 to 15 by 2 Union, ) for i1 to 13 by 4 UnionC, 2) UnionCi xs) Union(x11, x13) Union(x1, x10) Find-Set() Find-Set(g) 3. Repeat question 2, except that you use the following Find-Set routine instead. Find-Set(x) (p[r] ? Find-Set (p())) return return

Answer 1

The main thing to understand is that in the first part the FindSet method is implemented without Path Compression, whereas in the second part, the FindSet method is implemented with Path Compression.

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