Show that any sequence of m MAKE-SET, FIND-SET, and LINK operations, where all the LINK operations appear before any of the FIND-SET operations, takes only O.m/ time if we use both path compression and union by rank. What happens in the same situation if we use only the path-compression heuristic?

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Disjoint set forest

The concept of the disjoint set forest was introduced by Bernard A. Galler and Michael J. Fischer in 1964. The disjoint set forest is a method of implementing disjoint sets quickly. In the disjoint-set forest, each tree member points only to its parent. The root of every tree includes its representative and its parent. The disjoint set forest is a special kind of forest that performs Union and Find operations in near-constant amortized time.