Establish that any compare-based sorting algorithm must use at least N lg N compares (assuming that all possible input orderings are equally probable). Hint: When the compare tree is balanced, the external route length—the total length of the paths from the root to all leaves—which is minimized—is at least what the expected number of compares is.

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Q: Prove that the expected number of compares used by any compare-based sorting algorithm must be at…

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