I remember, at uni, in the second semester, we had an assignment to specifically craft a sequence of n numbers 1..n that would trigger the worst case (#permutations) in a quicksort algorithm that always takes the first number in the array as the pivot. It was a nightmare. I spent days on it, and I was barely able to scrape together a notation to specify such a series. Turns out the sample solutions were like "The appropriate sequence is not easy to write. The sequence must be designed such that every chosen pivot halves the area that will be stored." Well, yeah.
EDIT: I wrote worst case #permutations. That's the best case #comparisons. So, no, I don't mean a sorted sequence ;)
Doesn't a sorted array trigger the worst case in that case? Either ascending or decending. It's one of the reasons not to choose the first element as the pivot, iirc.
A much more interesting case is the median-of-three pivot. (Namely, median of first / middle / last elements). You can still do it, however.
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I remember, at uni, in the second semester, we had an assignment to specifically craft a sequence of n numbers 1..n that would trigger the worst case (#permutations) in a quicksort algorithm that always takes the first number in the array as the pivot. It was a nightmare. I spent days on it, and I was barely able to scrape together a notation to specify such a series. Turns out the sample solutions were like "The appropriate sequence is not easy to write. The sequence must be designed such that every chosen pivot halves the area that will be stored." Well, yeah.
EDIT: I wrote worst case #permutations. That's the best case #comparisons. So, no, I don't mean a sorted sequence ;)
If quicksort always takes the first element in the array as the pivot, then an array that is already sorted is the worst case.
Doesn't a sorted array trigger the worst case in that case? Either ascending or decending. It's one of the reasons not to choose the first element as the pivot, iirc.
A much more interesting case is the median-of-three pivot. (Namely, median of first / middle / last elements). You can still do it, however.
What do you mean by worst case #permutations?