What is the difference between a stable and unstable merge of two lists, and which operations preserve stability?

• A. Stable merge preserves the relative order of equal elements; unstable may reorder; merging two sorted lists can be stable.
• B. Stable merges preserve memory usage.
• C. Unstable merges preserve equal elements.
• D. Stable merges require extra memory; unstable merges do not.

Answer: (A)

Stability in merging means keeping the original relative order of equal elements from the input lists in the merged result. When you merge two sorted lists, you compare their heads and take the smaller key. If the keys are equal, a stable merge outputs the element from the left list first, then the one from the right. This rule preserves the order of equal items as they appeared across the inputs. Since the merge step can be implemented in this way, merging two sorted lists can be stable. The idea isn’t about memory usage; stability is about ordering. An unstable merge might pick from the right list first when keys are equal, which can swap the relative order of equal elements.