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.

FIT1008-FIT1054-FIT2085_S2_2025 Week 10 Workshop Quiz

Is Mergesort a stable sorting algorithm?

View Explanation

Log in for full answers

Similar Questions

Is Mergesort a stable sorting algorithm?

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)?

In a consumer society, many adults channel creativity into buying things

Economic stress and unpredictable times have resulted in a booming industry for self-help products

People born without creativity never can develop it

A product has a selling price of $20, a contribution margin ratio of 40% and fixed cost of $120,000. To make a profit of $30,000. The number of units that must be sold is: Type the number without $ and a comma. Eg: 20000

Which of the following statement regarding cost is correct:

Under the assumptions used in cost-volume-profit analysis, as the activity increases:

More Practical Tools for Students Powered by AI Study Helper

Homework AI Solver

Stylized AI Paper Writer

Plagiarism Checker Assistant

Citation AI Academic Writing Tool

In-Class Translation Assistant

AI Note Generator

AI Quiz Answers

Past Exam Questions from University Test Bank

Smart Practice Assistant

Adaptive Practice

Making Your Study Simpler