[racket] Racket style question

From: Rodolfo Carvalho (rhcarvalho at gmail.com)
Date: Mon Mar 19 03:44:36 EDT 2012

On Mon, Mar 19, 2012 at 04:35, Joe Gilray <jgilray at gmail.com> wrote:

> Thanks Rodolfo and Eli for the education, very elegant solutions.
> I really like the clever use of the "(and (right-triangle? a b c) (list a
> b c))))" idiom.
> I had to look up in-value... unfortunately the manual is a bit sparse
> there, but I got the gift by running some examples... thanks.
> After going "D'oh" about the infinite loop, here is the code I ended up
> with:
> (define (pythagorean-triple n)
>   (let loop-ab ([a 1] [b 2])
>      (define c (- n a b))
>     (cond [(>= a n) '()]
>           [(<= c b) (loop-ab (add1 a) (+ a 2))]
>           [(right-triangle? a b c) (list a b c)]
>           [else (loop-ab a (add1 b))])))
> I noticed that the sequence-based solutions are quite a bit slower than
> the code above probably because they don't short-cut on (<= c b), is there
> an elegant way to speed them up?
Before you asked I wrote this:

; by Rodolfo Carvalho
(define (pythagorean-triple/alt n)
  (for*/first ([a (in-range 1 (ceiling (/ n 3)))]
               [b (in-range (add1 a) (ceiling (/ (- n a) 2)))]
               [c (in-value (- n a b))]
               #:when (and (< b c)
                           (right-triangle? a b c)))
    (list a b c)))

; by Eli on the mailing list, modified by Rodolfo
(define (pythagorean-triple/alt2 n)
  (for*/or ([a (in-range 1 n)]
            [b (in-range (add1 a) n)]) ; start from `a+1' instead of `a'.
    (define c (- n a b))
    (and (< b c) (right-triangle? a b c) (list a b c)))) ; added `(< b c)'

And counted how many times they call right-triangle -- the same number of
Indeed your (first) solution with let loops seems slightly faster, but not
by a significant margin in my experiments.

I didn't take the time to analyze it much, but looking at the code
expansion using the Macro Stepper suggested that the for macros generate a
lot more code to be executed than the nested lets.


Rodolfo Carvalho
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