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This suggested edit was approved and applied to the post over 3 years ago by rak1507‭.

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Evaluation order of an APL n-train
  • ## Description
  • APL [trains](https://aplwiki.com/wiki/Tacit_programming#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 3 2 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
  • ```
  • ## Description
  • APL [trains](https://aplwiki.com/wiki/Tacit_programming#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
  • ```

Suggested over 3 years ago by Adám‭