'[H]ow is the array sorted' is one question that computer science can be used to solve. However, assuming it has been solved (which, for many cases, it has), a much more interesting question is 'what can we do with a sorted array'; or, 'given that sorting has such-and-such time or memory complexity, how hard is this other algorithm?' The OP isn't showing off a particular sorting algorithm, he's showing off a sorting interface, because that's more novel in context.
Sorting according to a predicate could be done with outer product/table+reduction, but usually you don't need anything like that. Let's say you have an array of 3-vectors, and you want to sort the vectors according to the 2nd item in each vector. So your sort predicate is v1[1] < v2[1]. We can just sort the whole array according to the vector of the 2nd items of each vector; so:
] x =. ?@] 9 3$10
2 4 9
3 8 2
8 0 4
3 9 6
3 1 8
2 6 8
1 2 5
9 4 0
5 0 9
(<a:;1) { x NB. index: the first element of every row of x
4 8 0 9 1 6 2 4 0
1 { |: x NB. first element of the transpose of x; equivalent
4 8 0 9 1 6 2 4 0
x /: 1 { |: x NB. x sorted according to the above. Notice that the second column is now sorted
8 0 4
5 0 9
3 1 8
1 2 5
2 4 9
9 4 0
2 6 8
3 8 2
3 9 6The article showed how J solves some mathematical problems with built in functions or their built-in modifiers. But in general programming, you won't find a function that does exactly what you wanted, maybe with a little adverb. You'll usually have to write that function yourself, to describe how it works in terms of some of those pre-existing functions.
Note that your second example could be expressed as something like
x.OrderBy(y => y[1])
Ah - I see. Here[1] is quicksort in j. John scholes's videos are excellent and very illustrative, though they deal with apl rather than j; conway's game of life[2] and sudoku[3].
> The article showed how J solves some mathematical problems with built in functions or their built-in modifiers. But in general programming, you won't find a function that does exactly what you wanted, maybe with a little adverb. You'll usually have to write that function yourself, to describe how it works in terms of some of those pre-existing functions.
Right. This is true, but you generally stay much closer to the builtins in j than you do in other language.
> Note that your second example could be expressed as something like
> x.OrderBy(y => y[1])
> In C#, assuming x is int[N][M]. I understand that J's version can work with many other shapes of X, but that is hard to appreciate without seeing example of how that comes in handy when writing some other (hopefully well known) algorithm.
Right; you mentioned sort predicates, so I was giving an example of a way in which you could sort according to another relation. My point is: being able to change the layout of your data so easily can obviate sort predicates. (Though I do think a sort adverb taking a predicate would be cool.)
1. https://code.jsoftware.com/wiki/Essays/Quicksort
The example with sorting was the oddest from this point of view. The author praised the idea of the permutation vector as being a relatively direct mathematical specification of sorting (return the permutation of the original array in sorted order) while leaving out the 'sorted' part. Also, this focuses entirely on the result, but there is no word on the algorithm - 'how is the array sorted' is the question that computer science is designed to solve, as opposed to 'what are the fixed points of a sorted array'.
As such, as someone with no experience of J, I'm left wondering if this is another example of the infamous Haskell quicksort - well-picked examples of code which produces a desired result are extraordinarily terse and expressive, but actually implementing well-known algorithms is often just as verbose as C, give or take.