Quicksort worst case runtime is quadratic, O(n^2)

[raypereda]

Doug McIlroy's 1999 paper “A Killer Adversary for Quicksort” describes how to find inputs to the sort that exhibit this quadratic behavior.

Here's a discussion on the topic by Russ Cox at http://research.swtch.com/qsort

[raypereda]

@ericdrowell If there is any doubt about the the correctness of the proposal I'm glad to discuss more. Thanks for creating the Big O Cheat Sheet on github!

[dasilvacontin]

Please merge! 👍
It's even on the Wikipedia linked article for Quicksort.

[jaredsburrows]

@ericdrowell Let's get this merged in please.

[ericdrowell]

Thanks guys! Yea that was just a clerical error. Thanks for fixing it up.

[dasilvacontin]

Nice!

[983]

The paper makes the assumption that "2. Pivot-choosing takes O(1) comparisons".

The approximate median-selection algorithm can also be used as a pivot strategy in quicksort, yielding an optimal algorithm, with worst-case complexity O(n log n).

If you don't believe wikipedia, here is some code comparing qsort from the C standard library to a quicksort implementation that chooses the median as the pivot element, both using the worst case sequence generator from the paper.

[raypereda]

@983 In standard quicksort, choosing the pivot is O(1). quicksort with perfect pivot selection, call it quicksort2, is a different algorithm than quicksort. The performance of quicksort2 is different than performance of quicksort. On average, quicksort is going to be faster than quicksort2.

In the benchmark code you provided, you initialize the array with a[i] = i. That is a special case that is going to do very well with quicksort2. Please try running the benchmark with a[i] = random number between 0 and 5000, or better yet randomly shuffle the array a[i] before running your benchmark. I'd would be interested in seeing the results of the plot after those changes are made.

[983]

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