Suppose we want to add an extra operation, deunion, which undoes the last union
operation that has not been already undone.
a. Show that if we do union-by-height and finds without path compression, then deunion is easy, and a sequence of M union, find, and deunion operations takes O(M logN) time.
b. Why does path compression make deunion hard?
c. Show how to implement all three operations so that the sequence of M operations takes O(M logN/ log logN) time.
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