Show that for any positive integer n, a sequence of Fibonacci-heap operations that creates a Fibonacci heap consisting of one tree is a linear chain of n nodes.

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Chapter 19.4, Problem 1E

Program Plan Intro

Show that for any positive integer n, a sequence of Fibonacci-heap operations that creates a Fibonacci heap consisting of one tree is a linear chain of n nodes.

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Consider the problem of determining the smallest element in a maxheap. The smallest elements of a max heap must be one of the n/2 leaves. (Otherwise,there must be a nonleaf that is smaller than one of its descendants, which means thetree is not a max heap.) Thus, it is sufficient to search all leaves. Prove a lower boundthat searching all the leaves is necessary

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