Which of the following inputs prove that Mergesort is not a stable sort (or choose the answer that indicates that Mergesort is a stable sort)?

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BlackTom AI · Accepted Answer

The question asks us to identify which inputs demonstrate that Mergesort is not a stable sort, or to choose the option that indicates Mergesort is stable.
Option a: 'a. (none of the other answers, since Mergesort is a stable sort).'
- This option asserts stability as a fact, rather than providing an input that proves stability. It effectively selects the stability claim, but it does not present an input scenario showing stability via equal keys and preserved order. Since the prompt wants inputs that prove instability (or an explicit statement of stability), this option is making a direct claim about stability rather than supplying a test case. It's reasonable to treat this as the option that indicates stability, though it does not demonstrate stability with an input example.
Option b: 'MERGEEXAMPLE'
- The term 'MERGEEXAMPLE' is ambiguous without context. If it were a concrete input sequence designed to test stability (e.g., two equal keys that appear in a different relative order after merging), it could potentially demonstrate stability. However, as written, it provides no concrete data or order information to judge stability. Therefore, this option does not definitively prove stability or instability.
Option c: 'UNSTABLE'
- This option asserts instability. Since Mergesort is widely taught and implemented as a stable sorting algorithm, claiming it is unstable contradicts standard algorithmic properties. If this were presented as a test input, it would be incorrect because it does not align with the known behavior of Mergesort. The logic flaw here is confusing algorithmic stability with an unsupported assertion that the algorithm misbehaves in general.
Option d: 'SHUFFLE'
- Like option b, 'SHUFFLE' is vague and not a concrete stability test. Without a concrete sequence or description showing how equal keys could reverse order during the merge step, this option fails to prove instability or stability.
To determine correctness conceptually: Mergesort is stable, so the option that aligns with selecting stability would be the one that claims stability rather than providing an actual instability test. The other options either make an unsupported claim of instability or provide insufficient or ambiguous input descriptions to judge stability.

Which of the following inputs prove that Mergesort is not a stable sort (or choose the answer that indicates that Mergesort is a stable sort)?

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