FAQ: Merge Sort: Conceptual - Merge Sort Performance


This community-built FAQ covers the “Merge Sort Performance” exercise from the lesson “Merge Sort: Conceptual”.

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This exercise can be found in the following Codecademy content:

Sorting Algorithms

FAQs on the exercise Merge Sort Performance

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Why is merge sort O(N * LOG N) and not instead O(N + LOG N). I ask because splitting the original list into singleton will take O(LOG N) steps, after which we’ll merge those O(N) singletons. Isn’t that O(N + LOG N)?

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Yes, the divide and conquer is O(log(n)), and merge is O(n), but there is not just one merge, there is one for every divide step.

Good analysis here.

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If you think of it like a geometric shape where the area is the amount of work required…

The first row is the single array
then two halves
four fourths
eight eights
… N ones

Each row is still N elements
Each row involves N work
How many rows are needed to split the array down into 1-size arrays?
You’ve now got a height and a width of the work that you can multiply for the total size.

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