Each time a discussion about sorting starts, I'm reminded of a "lively debate" I had with my boss/friend about the most optimal sorting approach. He claimed it's O(n) pointing to counting sort as an example. This didn't sit well with me. A sorting algorithm, I insisted, should be defined something like "a function taking an unsorted array of elements and returning a sorted one". But it seems there is no agreed upon definition and you can have something like counting sort where you get an array in O(n) but still need O(m) to get the index of a specific element. I argued that then the best sorting algorithm is the do-nothing algorithm. It returns the initial array in O(1), but needd O(m log m) to get you the index of an element (it uses merge sort to do it).
Usually when one talk about sorting, without specifying closer, one means comparison sort [1], which indeed has an average-case lower bound of O(n*log(n)). In more special cases all kinds of other runtimes are possible.
1: https://en.wikipedia.org/wiki/Comparison_sort
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counting sort is O(nW), where W is largest value
if you don't care about W or it is essentially constant - then it can be dropped
but it is an input parameter that will change execution time
It's O(n+W), not O(n*W).
> if you don't care about W or it is essentially constant - then it can be dropped
Also, every algorithm that ends in a real computer is bound to a constant time. That's still not a practical thing to do.
W is the span or range.
I can’t think of a single time I’ve needed a sorted list of only numbers. It’s always numbers and something else, like names or dates. Maybe for median calculations, but I don’t even use those that much either. Especially in telemetry, where mean is easy and median is not.
To be pedantic, median is cheaper than sorting. O(n) with a quicksort-like algorithm.
Also, if you're taking an average of floating point numbers, you might want to sort it first and add from smallest to largest, to better preserve precision
An aside, but I recently learned -- if one is willing to use a very modest amount of memory -- summing floating-point numbers with no loss of precision is effectively a solved problem with the XSUM algorithm.
https://glizen.com/radfordneal/ftp/xsum.pdf
That paper explains some useful optimisation details, but obviously since the floats are all (either infinity or) some multiple of a known tiny fraction (their smallest non-zero number), we can definitely sum them accurately.
Not if the ratio between the largest and smallest floats is very large (2^(2^n)) where n is the number of bits in the exponent.
I think you either haven't thought about this or you did your math wrong.
You need (2^e)+m+1 bits. That is more bits than would fit in the cheap machine integer type you just have lying around, but it's not that many in real terms.
Let's do a tiny one to see though first, the "half-precision" or f16 type, 5 bits of exponent, 10 bits of fraction, 1 sign bit. We need 43 bits. This will actually fit in the 64-bit signed integer type on a modern CPU.
Now lets try f64, the big daddy, 11 exponent, 52 fraction, 1 sign bit so total 2048 + 52 + 1 = 2101 bits. As I said it doesn't fit in our machine integer types but it's much smaller than a kilobyte of RAM.
Edited: I can't count, though it doesn't make a huge difference.
If the primary key is the number, it still works (and dates are just numbers by the way) because you can sort a heterogenous dataset by a single numeric key pretty trivially.
But sorting by arbitrary strings like names can’t avoid comparison sort.
"ordering" means arranging things in order by some metric.
"sorting" means assigning things into bins (which are usually ordered).
This is news to me. Source?
That's because it's not true.
https://www.merriam-webster.com/dictionary/ordering
Order - transitive verb - 1. to put in order : arrange - "The books are ordered alphabetically by author."
noun - 4. b(1) the arrangement, organization, or sequence of objects or of events - "alphabetical/chronological/historical order" "listed the items in order of importance"
https://www.merriam-webster.com/dictionary/sorting
Sort - transitive verb - 1. to put in a certain place or rank according to characteristics - "sort the mail" "sorted the winners from the losers" "sorting the data alphabetically"
noun - 5. an instance of sorting - "a numeric sort of a data file"
"The children were sorted in to two lines by gender then ordered by height"
You might substitute "sorted by height" but its certainly not a correction. While "ordered into lines" would be an error.
The sorting office for a postal service.
What do you do when you sort your washing?
You reminded me of "Sleep Sort" [0]
[0] https://news.ycombinator.com/item?id=2657277
Don't know about if Sleep Sort even is a valid sorting algorithm? Is this even real?