在J中找到可被x和y整除的整数

Question

Writing my first J program to solver Euler problem #1 (find the sum of all natural numbers below 1000 that are multiples of 3 or 5), I got the following solution:

+/(+./0=3 5|/n)#n=.i.1000

However, I pretty sure there is a clever way of doing it, without using a variable. I tried to rewrite it using a fork, but I don't see how I could replace the expression between () as a verb applied to 3 5 and i.1000 . Could anybody help me?

Answer 1

To parameterize both values, and thus generalize to a dyadic verb, we'll need to pass each of the parameters through to the places where they're needed. We can focus on the sole point where 3 5 is actually needed by starting with this fork:

   3 5 ([ |/ i.@]) 1000

In the overall program we need the integers list in two places. The name ( n ) gave us an easy way to use that list in both places. To quickly get the whole program in place, in writing this I initially calculated the list twice:

   3 5 ([: +/ i.@] # [:+./ 0= [ |/ i.@]) 1000

This succeeds at phrasing your whole program as a dyadic verb, but there are disadvantages to having i. appear twice. We can extract it to occur only once by making it the right tine of a fork. The center of that fork is a new, inner, verb.

   3 5 ([: +/ [ (] # [:+./ 0= [ |/ ]) i.@]) 1000
NB.              ___________________             new "inner" verb, parenthesized

This inner verb needs to receive the 3 5 as an argument so I pass through the left argument of the outermost verb as the left argument to this inner verb. This means Left ( [ ) in the inner verb has the same value it had in the previous version, when it referred to the outermost argument. Within this new verb Right ( ] ) refers to the list of integers, occurring in the two places that i.@] appeared before.

Postscript: As you showed in your comment, [ |/ ] simplifies to |/