When would you ever want bubblesort?(buttondown.email)
buttondown.email
When would you ever want bubblesort?
https://buttondown.email/hillelwayne/archive/when-would-you-ever-want-bubblesort/
69 comments
> choosing k elements from 1..n uniformly at random
Can you clarify the problem?
k elements uniformly at random, independently, with replacement, sounds like it’s trivially O(k), or perhaps O(k log n) if n is so big that you need O(k log n) bits to merely represent the answer. (Those logs are pesky and can appear and disappear in different models of computation!)
Maybe you mean k distinct elements? Off the top of my head, if n is not huge (n = O(k), or more concretely, n < ck for your choice or c > 1, and I would probably start with 2 if I were implementing this), I would make an array of all the elements and draw k of them using any of a number of straightforward algorithms. (Fischer-Yates, for example, but I admit I had to look up the name.)
For larger n, make a hash table to store the elements selected so far. Now repeat k times: choose an element at random and retry if it’s a duplicate. Then add it to the hash table and continue. Each iteration takes at most 1/c tries on average, so the overall expected time is O(k). (For n < ck, the last few draws may retry quite a lot.)
Thinking of this as sorting seems odd, but I admit I’m thinking about this in 2023, not the 1970s :)
Can you clarify the problem?
k elements uniformly at random, independently, with replacement, sounds like it’s trivially O(k), or perhaps O(k log n) if n is so big that you need O(k log n) bits to merely represent the answer. (Those logs are pesky and can appear and disappear in different models of computation!)
Maybe you mean k distinct elements? Off the top of my head, if n is not huge (n = O(k), or more concretely, n < ck for your choice or c > 1, and I would probably start with 2 if I were implementing this), I would make an array of all the elements and draw k of them using any of a number of straightforward algorithms. (Fischer-Yates, for example, but I admit I had to look up the name.)
For larger n, make a hash table to store the elements selected so far. Now repeat k times: choose an element at random and retry if it’s a duplicate. Then add it to the hash table and continue. Each iteration takes at most 1/c tries on average, so the overall expected time is O(k). (For n < ck, the last few draws may retry quite a lot.)
Thinking of this as sorting seems odd, but I admit I’m thinking about this in 2023, not the 1970s :)
Yes, distinct elements. Fixed. That's the only way what I said makes sense, like how one error-corrects listening to a talk.
They were concerned with the case where n could be absurdly large, and wanted no time or space dependence on n. They improved my idea to cut the multiple of k needed for space.
They were concerned with the case where n could be absurdly large, and wanted no time or space dependence on n. They improved my idea to cut the multiple of k needed for space.
> Bins would have an average occupancy of 1, so it didn't matter what sort you used.
That's not quite right, though - you only care about the average occupancy if your sorting algorithm is O(b) for b elements. If you're using a O(b^2) sort, you actually care about the root-mean-square occupancy (or in general just the average runtime, or just the total runtime since you'll multiply the average by the number of bins anyway).
The k-bin approach is definitely much faster than O(k log k), but I'm fairly sure it's slightly slower than truely linear, asymptotically, since the runtime will be something like 1+0+4+1 in typical cases, where linear would have to be 1+0+2+1.
Edit: on some cursory Monte Carlo testing, the sum of squares of occupancies actually seems to still converge on a constant factor (of two) times the sum of plain/linear occupancies, which I was not expecting but does make the above point rather moot. (Also, the sum of cubed occupancies seems to converge on a factor of five, which seems downright bizzare.)
(Tangential edit: The factors seem to be 1 2 5 15 52±2 200±20, which might be https://oeis.org/A000110, though none of the interpretations there seem obviously related.)
That's not quite right, though - you only care about the average occupancy if your sorting algorithm is O(b) for b elements. If you're using a O(b^2) sort, you actually care about the root-mean-square occupancy (or in general just the average runtime, or just the total runtime since you'll multiply the average by the number of bins anyway).
The k-bin approach is definitely much faster than O(k log k), but I'm fairly sure it's slightly slower than truely linear, asymptotically, since the runtime will be something like 1+0+4+1 in typical cases, where linear would have to be 1+0+2+1.
Edit: on some cursory Monte Carlo testing, the sum of squares of occupancies actually seems to still converge on a constant factor (of two) times the sum of plain/linear occupancies, which I was not expecting but does make the above point rather moot. (Also, the sum of cubed occupancies seems to converge on a factor of five, which seems downright bizzare.)
(Tangential edit: The factors seem to be 1 2 5 15 52±2 200±20, which might be https://oeis.org/A000110, though none of the interpretations there seem obviously related.)
There's a fixed, rapidly vanishing probability distribution on bin occupancies, which evaluates to a constant per bin when one applies a sorting algorithm. One gets linear algorithms with different constants, depending on the sorting algorithm. You're thinking "deep end of the pool" worrying about b log b versus b^2. I was in the "shallow end of the pool" where the constants in front of fancy sorts took them out of the running.
Like I said about Strassen and matrix multiplication. Great algorithm, but it takes a while to kick in for the lead.
Like I said about Strassen and matrix multiplication. Great algorithm, but it takes a while to kick in for the lead.
> There's a fixed, rapidly vanishing probability distribution on bin occupancies,
Pretty much; my mistake was underestimating just how rapidly it vanishes. In actuality any sorting algorithm that isn't pathologically horrible garbage like bogosort will work fine, because it runs on meaningful numbers of elements so rarely that it doesn't matter (and I'm not totally sure bogosort is garbage enough).
> where the constants in front of fancy sorts took them out of the running.
For beating O(k log k), the constants don't actually matter, since they just increase the constant factor inside your O(k) runtime. It's just that apparently, the asymptotics don't matter much either for that.
Pretty much; my mistake was underestimating just how rapidly it vanishes. In actuality any sorting algorithm that isn't pathologically horrible garbage like bogosort will work fine, because it runs on meaningful numbers of elements so rarely that it doesn't matter (and I'm not totally sure bogosort is garbage enough).
> where the constants in front of fancy sorts took them out of the running.
For beating O(k log k), the constants don't actually matter, since they just increase the constant factor inside your O(k) runtime. It's just that apparently, the asymptotics don't matter much either for that.
Do people really use Strassen in practice? I don’t seem to see them in the wild.
I've written a sort perhaps a handful of times in the last 40 years. Each of those was a bubble sort. I was nearly-always sorting <4 elements (and often just 1, or even 0).
These were rare cases where I didn't have a sort algorithm in a library -- perhaps because I needed to pass in a comparator that wasn't easily supported in the language. So I banged out whatever was easiest to get me moving on to the actual problem. If the sort became a noticeable part of the running time, I'd deal with that when I had performance numbers.
Bubble sort was easy to remember and quick to bang out. For all I know I really was writing an insertion sort; all O(n^2) sorts look pretty much the same.
I haven't written any sorts at all in well over a decade, since all languages have substantial support. If I'm writing a sort, something has gone very wrong.
These were rare cases where I didn't have a sort algorithm in a library -- perhaps because I needed to pass in a comparator that wasn't easily supported in the language. So I banged out whatever was easiest to get me moving on to the actual problem. If the sort became a noticeable part of the running time, I'd deal with that when I had performance numbers.
Bubble sort was easy to remember and quick to bang out. For all I know I really was writing an insertion sort; all O(n^2) sorts look pretty much the same.
I haven't written any sorts at all in well over a decade, since all languages have substantial support. If I'm writing a sort, something has gone very wrong.
> I was nearly-always sorting <4 elements (and often just 1, or even 0).
In my opinion, a bubble sort is a solid choice for that sort of use case.
In my opinion, a bubble sort is a solid choice for that sort of use case.
Are you being cheeky? Cause I would think insertion sort would be a more than reasonable alternative
Is everyone here feeling a bit... devilish?
I would pick a standard library sort function at that point.
I would pick a standard library sort function at that point.
No, I'm serious. With datasets that small, there's very little performance difference between the two methods, so a bubble sort isn't unreasonable at all. Depending on the circumstances, a bubble sort can be the better choice due to other considerations becoming relatively more important.
In what way?
Especially if there’s little or no performance difference, may as well minimize code size.
> On some very particular hardwares bubblesort stills ends up better, like in this NVIDIA study, but you probably don't have that hardware.
The author might have misunderstood the hardware in question and the reasons why bubble sort works well here. You probably do have applicable hardware; it’s any GPU. The bubble sort wasn’t running on ray tracing hardware, it was just CUDA code. The reason bubble sort works well is because it’s running on a SIMD machine, and it’s better when all threads in a work unit (a “warp” in CUDA parlance) all do the same thing at all times.
If you try to do insertion sort on a SIMD machine, you’re very likely to approach worst-case O(N^2) performance very quickly, even when each individual thread involved would have had average-case perf on it’s own. Bubble sort is good for the parallel SIMD machine because of it’s deterministic and regular evaluation order that is the same across all threads.
Of course, it’s still true that for anything larger than very small arrays of data, bubble sort complexity is unacceptable on SIMD or parallel processors. There are better parallel sorting algorithms for that.
The author might have misunderstood the hardware in question and the reasons why bubble sort works well here. You probably do have applicable hardware; it’s any GPU. The bubble sort wasn’t running on ray tracing hardware, it was just CUDA code. The reason bubble sort works well is because it’s running on a SIMD machine, and it’s better when all threads in a work unit (a “warp” in CUDA parlance) all do the same thing at all times.
If you try to do insertion sort on a SIMD machine, you’re very likely to approach worst-case O(N^2) performance very quickly, even when each individual thread involved would have had average-case perf on it’s own. Bubble sort is good for the parallel SIMD machine because of it’s deterministic and regular evaluation order that is the same across all threads.
Of course, it’s still true that for anything larger than very small arrays of data, bubble sort complexity is unacceptable on SIMD or parallel processors. There are better parallel sorting algorithms for that.
In the other words, you are sorting lots of equally-sized slabs at once, and you can do the same operation to each slab efficiently. Algorithms with no data-dependent control flow would be optimal in this situation, and bubblesort is one of them. But there are even better algorithms, I think shellsort with a fixed gap sequence (since the slab size is known in advance) could've been a good alternative. On the other hands, if you are sorting a single huge list, you need a parallel sorting algorithm like bitonic sort.
Can confirm, have used bubble sort in a production game engine to keep transparent objects mostly sorted.
You do the compare-and-swap when you're iterating over the objects to do some other render pass, so it adds almost nothing to the CPU time.
You do the compare-and-swap when you're iterating over the objects to do some other render pass, so it adds almost nothing to the CPU time.
>> bubble sort in a production game engine to keep transparent objects mostly sorted.
A single pass of bubble sort per frame is often enough to keep things in order. And if something glitches because it takes 2 passes it's just a single frame glitch!
A single pass of bubble sort per frame is often enough to keep things in order. And if something glitches because it takes 2 passes it's just a single frame glitch!
> so it adds almost nothing to the CPU time.
If two threads go to CAS-sort at the same time, the cache coherency overhead would be apocalyptically bad. I'm assuming that's not what you meant?
If two threads go to CAS-sort at the same time, the cache coherency overhead would be apocalyptically bad. I'm assuming that's not what you meant?
> > so it adds almost nothing to the CPU time.
> If two threads go to CAS-sort at the same time, the cache coherency overhead would be apocalyptically bad. I'm assuming that's not what you meant?
I think it's apparent they didn't mean the CAS atomic instruction, just the compare-and-swap operation in bubblesort. Nothing in their comment suggested this was a multi-threaded situation.
> If two threads go to CAS-sort at the same time, the cache coherency overhead would be apocalyptically bad. I'm assuming that's not what you meant?
I think it's apparent they didn't mean the CAS atomic instruction, just the compare-and-swap operation in bubblesort. Nothing in their comment suggested this was a multi-threaded situation.
>> You do the compare-and-swap when you're iterating over the objects to do some other render pass
OP is describing using CAS to bubblesort an array while it is concurrently read by another thread rendering something based on its contents? That seems kind of wild to me but I don't know why else you add the words "some other". Sometimes sorting is an optimization and isn't necessary for correctness.
The idea of two threads concurrently bubblesorting the same array with CAS is hilarious and intriguing. On x86 the double-wide CAS requires double wide alignment so I guess it couldn't actually work without extra trouble...
OP is describing using CAS to bubblesort an array while it is concurrently read by another thread rendering something based on its contents? That seems kind of wild to me but I don't know why else you add the words "some other". Sometimes sorting is an optimization and isn't necessary for correctness.
The idea of two threads concurrently bubblesorting the same array with CAS is hilarious and intriguing. On x86 the double-wide CAS requires double wide alignment so I guess it couldn't actually work without extra trouble...
No, there was no mention of concurrency. As I understsand it, OP was describing a "render pass" that looked like this:
for (int i = 0; i < length; i++) {
// do some rendering or something
}
for (int i = 0; i < length; i++) {
if (obj[i] > obj[i+1]) swap(&obj[i], &obj[i+1])
// do some rendering or something
}
This.
I explained another way to interpret what OP said. Your way is boring and uninteresting: this is a forum for discussion, so I picked the more interesting way :)
Picked a more belligerent interpretation, certainly. Your original comment made no allowances for the obvious interpretation and said that the consequences of the simple solution were "apocalyptically bad". While I found the ensuing discussion interesting you definitely did not approach it from a standpoint of engendering more interesting conversation. You could have gotten the same result much more easily by simply pointing out that this was not thread safe and only works in a single threaded application, and instead of nit picking we could have actually talked about better options for concurrency.
> OP is describing using CAS to bubblesort an array while it is concurrently read by another thread rendering something based on its contents?
No. I'm not OP, but 99% certain this is not the case.
No. I'm not OP, but 99% certain this is not the case.
You misunderstood. The CAS term isn't related to threads in aappleby's comment.
aappleby is saying the following: He wrote a game engine, it renders transparent items using the painter's algorithm, which requires the items to be sorted in Z. He has a routine that iterates over all items to render them, and bubble-sorts the items in-place while iterating over the items (all in the same thread). The "compare and swap" in this case is the innermost functionality of bubblesort.
I assume the author is https://github.com/aappleby but I don't see any obvious candidate for this code. Maybe this? https://github.com/aappleby/metroboy but I can't see why a gate-level emulator woudl need to render transparent items using painter's algorithm.
aappleby is saying the following: He wrote a game engine, it renders transparent items using the painter's algorithm, which requires the items to be sorted in Z. He has a routine that iterates over all items to render them, and bubble-sorts the items in-place while iterating over the items (all in the same thread). The "compare and swap" in this case is the innermost functionality of bubblesort.
I assume the author is https://github.com/aappleby but I don't see any obvious candidate for this code. Maybe this? https://github.com/aappleby/metroboy but I can't see why a gate-level emulator woudl need to render transparent items using painter's algorithm.
I was writing code for production game engines ~20 years ago.
Bubble sorts are useful in broad-phase collision detection. Each object has an axis-aligned bounding box, and you want to sort those by X, Y, and Z values, then check for overlap in all dimensions. Only if the bounding boxes overlap in all three dimensions do you have to check the object pair's detailed geometry.
Most objects aren't moving that much. The lists are thus almost in order. So running a bubble sort on each axis to check the ordering is not much worse than O(N).
Startup has a transient. The very first sort will be O(N^2). If the number of objects is large enough it may be worthwhile to do something different at startup.
Most objects aren't moving that much. The lists are thus almost in order. So running a bubble sort on each axis to check the ordering is not much worse than O(N).
Startup has a transient. The very first sort will be O(N^2). If the number of objects is large enough it may be worthwhile to do something different at startup.
> Most objects aren't moving that much.
There are certainly simulations where this approach is fine (if you can be absolutely confident that no object ever "skips" around, like when you're running a simulation that is configured with an explicit upper bound on velocity), but I think that this still requires this warning label.
Funny, if I were doing that I'd use a spatial index using oct-trees since I have a fairly optimized one. You find all potential overlaps in O(logN), But to check them all would be O(NlogN). So by your approach it looks like bubble sort wins!
Bubble-sort is great if you have many cores to spare but no extra memory. It parallelizes nicely and works in-place.
Insertion sort is great if you don't have any cores or memory to spare. It uses one core and works in-place.
Selection sort is much like insertion sort, runs in-place, single-threaded, but it will be faster if your CPU is much faster than your memory access as it uses more comparisons and fewer swaps.
Insertion sort is great if you don't have any cores or memory to spare. It uses one core and works in-place.
Selection sort is much like insertion sort, runs in-place, single-threaded, but it will be faster if your CPU is much faster than your memory access as it uses more comparisons and fewer swaps.
Why bubble sort when a slight modification can create a still simple but much more respectable algorithm called "comb sort".
https://www.delftstack.com/tutorial/algorithm/comb-sort/
https://www.delftstack.com/tutorial/algorithm/comb-sort/
Comb sort tip --- instead of dividing by 1.3 use 1.333 (repeating) instead.
In practical terms using integers, this makes almost no difference *except* it can be performed using faster shift and add operations:
gap = ((gap << 1) + gap) >> 2;
For even more speed, I'd also recommend in-lining this to eliminate the function call. Properly implemented, respectable speed can be achieved from a really trivial implementation.
In practical terms using integers, this makes almost no difference *except* it can be performed using faster shift and add operations:
gap = ((gap << 1) + gap) >> 2;
For even more speed, I'd also recommend in-lining this to eliminate the function call. Properly implemented, respectable speed can be achieved from a really trivial implementation.
For an N^2 sorting algorithm, I think insertion sort is superior to bubble sort when you want something simple:
http://warp.povusers.org/grrr/bubblesort_misconceptions.html
That link seems to insist on defining bubble sort without a termination condition, which is not how I think of bubble sort and I suspect is not how anyone is defining it in the cases it argues against. Also the use case in this article isn't listed.
It's O(n) if the array is already sorted, which is better than other n*log(n) CS101 algorithms (merge/heap/quicksort)
Unless the element that should be at the start is at the end, everything else being sorted (ex: 2 3 4 5 6 1). Insertion sort is the best simple algorithm for almost sorted lists. In fact, it is generally considered the best O(n2) sorting algorithm.
That's my memory from college: bubble sort is fine when the data is almost completely sorted.
The game dev example is really cool. I've never encountered a situation where "more sorted" is better for performance but completely sorted doesn't really matter (or maybe I have, but didn't know it).
When you read Knuth's The Art of Computer Programming he challenges you to come up with your own sorting algorithm. I feel really fortunate that I was able to do this without knowing any algorithms already. I came up with bubblesort. I think it was the intuition of thinking about it becoming "more sorted" on each pass that led me there.
When you read Knuth's The Art of Computer Programming he challenges you to come up with your own sorting algorithm. I feel really fortunate that I was able to do this without knowing any algorithms already. I came up with bubblesort. I think it was the intuition of thinking about it becoming "more sorted" on each pass that led me there.
Can I have Cheeky Retorts for $100 Alex.
1. If you have a very large (say 100 million elements ) array in descending order, you can use Bubblesort to sort it in the ascending order - the worst case complexity is kn^2, and this is literaly the worst case, so its the equivalent of a sleep(t) routine for a large t ( depending on how sow your system is).
2. If you have a very small array (say n < 10), you can create toy examples where kn^2 < m*nlogn, for carefully chosen values of k, m & n. Say n = 3, k = 1, m = 7.
1. If you have a very large (say 100 million elements ) array in descending order, you can use Bubblesort to sort it in the ascending order - the worst case complexity is kn^2, and this is literaly the worst case, so its the equivalent of a sleep(t) routine for a large t ( depending on how sow your system is).
2. If you have a very small array (say n < 10), you can create toy examples where kn^2 < m*nlogn, for carefully chosen values of k, m & n. Say n = 3, k = 1, m = 7.
Bubblesort is hard to beat if you're optimizing for object code size. I'm surprised that wasn't mentioned.
Unless you have a thousand of sorting routines it wouldn't matter much. And compilers generally produce a much larger code than actually possible, you can implement bubblesort in 16 bytes of x86-32 assembly [1] for example.
[1] https://gist.github.com/jibsen/8afc36995aadb896b649
[1] https://gist.github.com/jibsen/8afc36995aadb896b649
It matters a great deal if you have 1KB of flash to fit the whole firmware in :)
Oh, if you are already writing an assembly my comment doesn't apply ;-)
I was expecting that, too. The one person I’ve heard say they’d implemented bubble sort in the current century worked on automotive controllers where they had absurdly tight memory budgets and the data he had to sort was relatively small so they quite happily traded a few cycles for the smaller executable.
Yes. Ignorant question: if you use bubble sort but go through the array in alternating senses, could it not improve locality and speed?
Array v with N elements:
First pass: go from v[0] to v[N-1] comparing v[i] with v[i+i] Second pass: go from v[N-1] to v[0] comparing v[i] with v[i+i]
This is so obvious that it should have a name...
Array v with N elements:
First pass: go from v[0] to v[N-1] comparing v[i] with v[i+i] Second pass: go from v[N-1] to v[0] comparing v[i] with v[i+i]
This is so obvious that it should have a name...
Answering myself. Yes, it was an ignorant question as the name is Cocktail Shaker sort: https://en.wikipedia.org/wiki/Cocktail_shaker_sort
Because in a certain company i couldnt use anything except a limited old language and there was no straightforward way to sort a list of custom types and internet searching was limited . You cannot just download your favorite open source library or whatever in a lot of environments, you are stuck with the tools you got.
It would likely be handy during your exams in CS 101.
This blog post would make a fantastic addition to the sorting part of a CS101.
Bubble sort is just fantastic to wind up arrogant algo-nerd snobs because you can bust it out for anything that is likely to be already sorted or nearly so and it dominates. Algo-nerd snobs rarely seem to take into account that knowledge and understanding of the input is the most crucial part.
Do it in job interviews only if you've already decided you're unlikely to want to work there and be sure to be smiling and humble as you demonstrate this to their peers, noting that the pure forms of the algo, selection sort is arguably better (Knuth!) but this is unlikely to be an interesting practical concern and totally dwarfed compared to readability of the code.
Do it in job interviews only if you've already decided you're unlikely to want to work there and be sure to be smiling and humble as you demonstrate this to their peers, noting that the pure forms of the algo, selection sort is arguably better (Knuth!) but this is unlikely to be an interesting practical concern and totally dwarfed compared to readability of the code.
> it dominates
Not compared to insertion sort, which is the actual contender here.
Weirdly aggressive comment.
Not compared to insertion sort, which is the actual contender here.
Weirdly aggressive comment.
Before I knew anything about sorting algorithms, I invented my own algorithm to sort the high score list in my little BASIC game. It was very simple: Find the highest score, swap it to the top and continue, this time starting with the second item, until done. I imagine that if I ever find myself in need of writing a sorting algorithm from memory, I'll still go with this one.
Sounds like Selection sort[1]. It was probably the first sorting algorithm I ever implemented. I don't know why bubble sort is usually taught first. Selection sort seems more obvious. Perhaps the implementation is slightly harder due to the need to keep track of two indexes.
1. https://en.wikipedia.org/wiki/Selection_sort
1. https://en.wikipedia.org/wiki/Selection_sort
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I've done this. In a production application.
Why? It was the easiest sort I had memorized, I didn't have my college Data Structure 201 book handy. It did exactly what I wanted. And for my datasets, it was not impacting performance. Measurably? Probably. Noticeably from the user level? No. If it was slow, I would have changed it. I did it in BASIC.
But it was never my bottle neck. We're talking 10 or less items here most of the time, my bottleneck was sucking rows from the ISAM database on our 10 user, 16Mhz 68020.
I was doing best fit scheduling across a selection of resources.
It was a very cool system.
Why? It was the easiest sort I had memorized, I didn't have my college Data Structure 201 book handy. It did exactly what I wanted. And for my datasets, it was not impacting performance. Measurably? Probably. Noticeably from the user level? No. If it was slow, I would have changed it. I did it in BASIC.
But it was never my bottle neck. We're talking 10 or less items here most of the time, my bottleneck was sucking rows from the ISAM database on our 10 user, 16Mhz 68020.
I was doing best fit scheduling across a selection of resources.
It was a very cool system.
Bubblesort's big advantage is that it's the one sorting algorithm that I understand well enough to write from scratch in pinch.
When the bucket of things to sort drifts below count ~100, bubble sort will hammer it into order in an amount of time which is, for all intents and purposes, zero. Use the smallest hammer which drives the nail...
This is also known as "hardware caches and branch prediction beat smart humans almost every time"
Also a good time to shelve any binary search because linear search will beat it for short sequences. The threshold varies by platform.
I used bubble sort for sorting an HTML table, because, as others say, it is easy to write quickly. It stayed that way until I asked gpt to rewrite it for me.
Bubble sort's true complexity is O(n+d) where d is the number of inversions in the array. So if an array is almost sorted better to use bubble sort.
(Always check your assumptions. Sorting has an k log k lower bound if all you can do is compare elements. With integers 1..n, one can do much more.)
I showed up at 5pm at his office, as he was bracing himself for the drive from Swarthmore back to Philly, wondering why he ever took this gig. I proposed a linear algorithm: Break 1..n into k bins, and only sort to detect collisions within each bin. Bins would have an average occupancy of 1, so it didn't matter what sort you used.
(I found this idea later in Knuth, and was briefly disillusioned that adults didn't read everything.)
I looked like George Harrison post-Beatles, I probably smelled of pot smoke, and he dismissed my idea. Then my dorm hall phone rang at 10pm, a professor of mine relaying an apology. For that and other ideas, the second edition of his book opened with thanks to me.
I'm surprised now that I realized then that bubble sort actually had the least overhead, in such an application. People don't use Strassen to multiple matrices unless the matrices are really big. For sorting, "really big" is 2 or 3 elements.