Description

APL trains are a series of functions, that get applied to an argument in this way:

(f g) x = f g x
(f g h) x = (f x) g (h x)
(a b c d e f) x = (a (b c (d e f))) x = a (b x) c (d x) e (f x)

Trains evaluate from the right to the left, so in the last example, (f x) is evaluated, then (d x), then (d x) e (f x), then (b x), etc.

The final evaluation order there is FDEBCA, or using numbers instead, 6 4 5 2 3 1.

Challenge

Given a number n, output the evaluation order of a train with n functions. Your result can be 0 indexed or 1 indexed.

Examples

Here are the first 10 outputs starting from n=1 (1 indexed)

1 (0 if 0 indexed)
2 1 (1 0 if 0 indexed)
3 1 2
4 2 3 1
5 3 4 1 2
6 4 5 2 3 1
7 5 6 3 4 1 2 
8 6 7 4 5 2 3 1
9 7 8 5 6 3 4 1 2
10 8 9 6 7 4 5 2 3 1

posted over 3 years ago

CC BY-SA 4.0

3y ago by Adám‭

rak1507‭

691 reputation 7 4 69 13