Comment by kragen | Hacker News Reader

Comment by kragen | Hacker News Reader

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i think i wrote that page originally 22 years ago, before the switch from usemodwiki to mediawiki; while i've often been referred to wikipedia to correct my errors, i think this is the first time i've been referred to a wikipedia page that i wrote in the first place :)

it's true that, if your data is exactly sorted, or has a small number of items that are far too early (e.g., 43 3 4 5 6 7 8 9 10), you can modify bubble sort to notice this and exit early, at the expense of making it more complicated and even slower in the average case

however, this doesn't help if instead you have a small number of items that are far too late (e.g., 4 5 6 7 8 9 10 43 3), in which case bubble sort takes the same number of passes as it normally would, while insertion sort takes linear time. of course you can complicate bubble sort further into "shaker sort" to handle this, which makes it even more complicated but at least doesn't slow it down any further

but all of this is sort of futile because it's still half as fast as insertion sort in the case of unsorted input, and even without the tweaks, no simpler

You did: https://en.wikipedia.org/w/index.php?title=Bubble_sort&oldid...

well, that's just the first mediawiki revision of the page; i was working on it earlier than that, which is why i was editing the subpage link syntax in that version, but the usemodwiki history has been lost

someone else might have written the original version, i can't remember any more, but i think it was probably me

I do not have access to the historic definition of bubble sort, but all the modern implentation i've seen so far, all have a check if there were no swaps. I absolutely cannot wrap my mind how exactly it would make it slower in the average case, I almost certain it won't, how exactly this would make code sgnificantly more complex to any meaningful extent.

we're talking about six lines of code if we don't count the curly braces (which can be omitted)

bubble sort with early exit is

    for (size_t i = 0; i < n; i++) {
        bool sorted = 1;
        for (size_t j = 1; j < n - i; j++) {
            if (a[j-1] > a[j]) {
                item_t tmp = a[j];
                a[j] = a[j-1];
                a[j-1] = tmp;
                sorted = 0;
            }
        }
        if (sorted) break;
    }

which is three more lines of code, which is in some crude sense a complexity increase of 50% over both the simple bubble sort in my earlier comment and over insertion sort

if you compile it https://godbolt.org/z/jdzov8cPn you can see that the inner loop goes from 10 instructions to 11. that doesn't guarantee that it's 9% slower (that depends a lot on the platform, and in particular on a big superscalar cpu it probably just uses a little more power but the same number of clocks) but it does tend in that direction. of course occasionally it will save you a pass or two over the array, which will tend to compensate, but it won't usually save you 9% of the passes

if some item is in position n and needs to be in position m, where m < n, it will require n - m passes of bubble sort to get there. a little thought suffices to show that, for randomly shuffled input, where m = 0 the item has to move about half the size of the array, where m = 1 it has to move about half the size of the array minus one half, where m = 2 it has to move about half the size of the array minus one; but it's the maximum of these three numbers which determines the number of passes after which all three of those positions will have the correct item, and that maximum is heavily skewed to be almost the entire size of the array. the chance that none of those three items is in the last 25% of the array originally is only .75*3 = 42%. and as the value of three increases, it gets worse. so in general early exit doesn't buy you much

as for modern implementations of bubble sort, they're all either didactic classroom exercises like this one or careless mistakes like the original freebsd code; because insertion sort always beats it, there aren't like a community of bubble sort implementors who have annual bubble sort conferences. so you can expect some variation in precise terminology and shouldn't worry about it

(fwiw clrs 3ed. gives bubblesort without an early termination test, as i did; their definition is in exercise 2-2 on p. 40. but they're counting in the opposite direction, so everything i said above about items moving forward quickly and backward slowly is reversed for the clrs version of bubblesort)

Your original claim that is more complex or slower is unsubstantiated. Yes, it is trivially more complex to add a flag, but it does not actually make it any more difficult to understand or error prone. Your argument is way too pedantic. Claim about the performance is equally unsubstantiated. To make a proper proof you need to show that on average, we still have all N outer passes executed, before we face no swaps situation. Which almost certainly is never true, especially with non-random data.

Although I certainly agree that Bubble Sort is almost always a bad choice, it still is used in computer graphics, or other situations when you have only one or two misplaced pairs of elements. In this case it will outperform the other algorithms, in average case while maintainig functionally in the less than ideal situation.

Besides it is entirely irrelevant what are the purposes the algorithm is used today, didactic, deliberate or poor judgement, the de facto standard way of doing it today is to check for the early exit. Your argument about poor performance on the already sorted data is a straw man argument, your are stubbornly defending. Well ok, if you believe so...

if you aren't convinced that adding the early exit generally hurts performance, well, it's not surprising; measuring performance is difficult and tricky, and you're faced here with claims you don't really have the knowledge to evaluate properly, so it's entirely proper that you are dubious about them, even if you're confused about what a proper proof would consist of

it might help your intuition to think of it this way:

1. with random input, the first ten positions of output are pretty likely (65%) to have an item that was originally in the last 10% of the input, and almost certain (97%) to have an item that was originally in the last 30% of the input. so those ten items alone account for needing 95% of the passes you'd need without an early exit, minus about five, in 65% of cases.

2. the first 20 positions are pretty likely (64%) to have an item that was originally in the last 5% of the input, and almost certain (96%) to have an item that was originally in the last 15% of the input. so those 20 items account for needing 97% of the passes you'd need without an early exit, minus about ten, in 64% of cases.

3. the first 30 positions are pretty likely (64%) to have an item that was originally in the last 3.3% of the input, and almost certain (96%) to have an item that was originally in the last 10% of the input. so those 30 items account for needing 98.5% of the passes you'd need without an early exit, minus about 15, in 64% of cases.

of course, if you're only sorting 30 items, the first ten positions of output are actually a third of all the positions, so "minus five" is pretty significant. and probably if you're sorting more than about 30 items at a time you ought to use a linearithmic sort or a linear-time radix sort instead of a quadratic sort

similarly, it's reasonable to argue that complexity (in the sense of containing many parts, not in the sense of asymptotic computational work required) is subjective, and to disagree about it

but i think these are sort of moot points

insertion sort still beats bubble sort in the situations where you have only one or two misplaced pairs of elements, and generally replaces it as soon as somebody notices

as for 'the de facto standard way of doing it today', i suggest you argue with clrs, not with me

Count number of outer passes of insertion sort (it is N) vs bubble sort (with early exit; it is 2) if you have only a single pair misplaced.

insertion sort only ever makes one outer pass; it does almost exactly half as many comparisons as bubble sort (n rather than 2n-2) in that case, and the same number of swaps (1)

the wikipedia article has a cleverer early-exit version of bubble sort that keeps track of the last pair it had to swap; it will do 1.5n-1 comparisons in that case on average (because the swapped pair is on average in the middle of the array)

above i linked to working code on godbolt (modulo the extra unnecessary swaps on duplicate keys that you were kind enough to point out earlier); edit a comparison counter and a swap counter into it and you'll see

The early exit can be done without an extra flag, but increased code size.

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