R$-7\mathrm{.}7$ Suppose we have $20$ singleton sets, numbered $0$ through $19,$ and we

call the operation union$($find$($i$),$find$(i+5),$ for $i=0,1,2,$dots,$14.$ Draw a picture

of a tree$-$based representation of the sets that result, assuming we don't

implement the union$-$by$-$size and path compression heuristics.

R$-7\mathrm{.}8$ Answer the previous exercise assuming that we implement both the

union$-$by$-$ size and path compression heuristics.