Every good cs course has a section on cache aware algorithms. And i call bullshit that constant factor is not mentioned too
If your linked list nodes are all allocated sequentially in memory then it'd only be 2x as slow as an array of 64 bit integers.
But maybe it's not fair to call sequentially allocated linked list a "trivial linked list".
1) Do you think about cache at all or is it just something you heard mentioned as important that one time?
2) It's a good lead-in to discussing the effects of cache in algorithms. How that conversation goes helps me to understand how that person thinks and discusses complex problems.
A good answer would be "I'm not sure, but probably way, way slower because linked list can point all over memory but arrays cache really well."
An excellent, A+ answer would be "In the best case it might not be too much slower if you have an intrusive linked list is arranged sequentially in memory like an array like onekorg explained. But, in practice most will be 20-200x slower because they are usually implemented as pointers to nodes containing pointers to data and each piece is allocated piecemeal in a already fragmented heap. Uncached memory reads can take 100+ cycles and summing an int is not enough work to hide that even if the CPU speculatively prefetches."
I mainly expect a surprised reaction that they could be so slow and looked forward to the follow-up discussion.
It's not that Big O isn't useful - it's that it's taught as a set of "proofs" which somehow make it appear objective and "correct", when in reality performance is at least as dependent on cache architecture, median size-of-n, memory bandwidth, and other implementation details.
Anyone who graduates CS without having been taught this very forcefully - preferably during a practical project - should be refunded at least some of their course fees.
My A+ answer is "My guess is [x] but instead of speculating we can create a test to discover the performance. [Describes test]."
Koala_man above says:
> I wrote a benchmark and found the difference in this case to be 3x-3.5x.
The actual number depends on a lot of things, of course (language, architecture, test methodology...), but it is possible that your 20-200x A+ answer is incorrect.
200x can be a reasonable outcome. So can be 3x in other conditions.
As a rule of thumb I now consider that a completely random memory access is on the order of accessing 1000 sequential bytes.
I'm guessing it's not CRUD apps.
Imagine for the array it's 1 CPU instruction to load a value, 1 to load the next value, 1 to add them, and one to store the result, that would be 4 instructions per sum; ideally the array would stream into the CPU after a single main memory lookup delay up-front, and then be 4 instructions per pair, summed as fast as the CPU can loop.
The linked list at worst needs an imaginary 1 CPU instruction to load a value, 1 to load the pointer value, 1 to reference the pointer, a delay of 2 seconds to get that value from L1 cache - missed, it's not in cache - 240 seconds stalled waiting for main memory, 1 to add, 1 to store the result. Worst case, >240x slower.
The linked list is not guaranteed to be in contiguous memory, but it might be, so the cache might have the right data in it. The linked list is 50% data, 50% metadata, so the cache is half wasted / can hold half as much data, and if the linked list is coming in from a big memory read quickly, half the bandwidth is carrying pointer addresses not data, so the throughput is halved for that, too, and the processor cycles were already able to happen much faster than the main memory bus max speed. If it's not contiguous memory, you don't know in advance where it is to request all the right memory areas at once - not until you read sequentially to the last item pointer and find there are no more.
Maybe if they are both small, both in contiguous memory and go into Level 1 cache after a single main memory delay, it could be only ~2x time, but the more data there is overall, the more chance the linked list will bust the cache or be discontinuous in memory. And on the plain array side, it might be possible to speed up with SIMD/SSE instructions to spend fewer cycles adding and storing per element, which the linked list approach might not be amenable to at all[2], then best case might be ~4x slower, worst case ~500x slower.
[1] https://www.prowesscorp.com/computer-latency-at-a-human-scal...
[2] https://stackoverflow.com/questions/10930595/sse-instruction...
Take a look at Real-time Collision Detection[1]. I takes a great look at both algorithmic complexity and cache awareness. That's how it should be done.
Does anyone have a good textbook suggestion for cache/simd aware algorithm design? I've seen plenty of papers that cover single examples but never something the scope of a book.