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In this problem, we would like to show the amortized time of a union operation when...

In this problem, we would like to show the amortized time of a union operation when union by-weight on linked-lists is used is Ω(log n). For that, we need to come up with a sequence of Θ(n) operations for which the amortized cost per operation is Ω(log n). We start with make-set(xi) for i ∈ {1, 2, . . . n} where n is a power of 2. Provide a consequent sequence of Θ(n) union operations so that the total number of updated pointers for all operations is Ω(n log n).

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