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Explain a Sorting Algorithm Such as Merge Sort: Mechanics, Correctness, Complexity

VoleonQuantitative Researcher · Technical Screen
MediumQuantitative ResearcherTechnical ScreenSoftware Engineering Fundamentals

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Explain a sorting algorithm of your choice, such as merge sort, in a technical screen for a quantitative role. Tests whether you can describe the split and merge steps, trace a small example, argue correctness, derive time and space complexity, and discuss stability and alternatives.

This is the first of three questions in a 60-minute technical screen for a quantitative role: explain a sorting algorithm of your choice. Merge sort is an acceptable choice. Describe how the algorithm works, trace it on a small array, explain why its output is sorted, and state its time and extra-space cost.

Constraints and Clarifications

  • Sort an array of n mutually comparable elements into ascending order, unless the interviewer specifies otherwise.
  • Pseudocode or code in any language is fine if it helps the explanation.

Clarifying Questions

  • Should the explanation include code, or is a description with a worked example enough?
  • Do stability or sorting in place matter for this discussion?
  • Can the data be assumed to fit in memory?

Hints

Hint 1

Pick one you can defend: Choose an algorithm whose worst case, memory use and stability you can state precisely, and prepare a short trace on an array of about five elements.

Hint 2

Where the work happens: For merge sort, most of the reasoning lives in combining two sorted halves. Ask what is true of the output after each element is copied into it.

Follow-up questions

  • How would you sort a data set too large to fit in memory?
  • Why do some standard libraries sort primitive arrays with a quicksort variant but objects with a merge-sort variant?
  • How would you write merge sort iteratively, bottom-up, and what does that change?
  • What is the lower bound on comparisons for any comparison sort, and why?