Is Mergesort a stable sorting algorithm?

Question

BlackTom AI · Accepted Answer

Question: Is Mergesort a stable sorting algorithm?

Option 1: True. Mergesort is widely taught as a stable sort in most algorithm courses and textbooks. The stability comes from the merge step: when two equal elements are encountered from the left and right subarrays, the algorithm typically places the left element before the right one, preserving the original relative order of equal items from the input. This behavior ensures that equal elements retain their relative positions, which is the essence of stability in sorting.

Option 2: False. This would claim that mergesort does not preserve the original order of equal elements. In contrast to certain sorting methods like some implementations of quicksort or heapsort, naive or poorly implemented mergesort variants could potentially disrupt order during merging if care is not taken. However, the standard, correctly implemented mergesort explicitly uses a stable merge process, so this statement is generally incorrect.

To deepen the distinction:
- Stability means: if two elements have equal keys, their relative order in the sorted output matches their relative order in the input.
- In the merge step of a typical stable mergesort, when left[i] and right[j] have the same key, the algorithm appends left[i] before right[j], which preserves their input order.
- If someone uses an unstable merge (or alters the merging criterion in a way that could switch the ordering of equal elements), then stability could be lost. But with a standard stable merge implementation, mergesort remains stable.

Therefore, considering standard definitions and implementations, the option asserting stability (True) aligns with the conventional understanding of mergesort.

Is Mergesort a stable sorting algorithm?判断题

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