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  1. ; searching for hypotenuses
  2.  
  3. (define (range . args)
  4.   (case (length args)
  5.     ((1) (range 0 (car args) (if (negative? (car args)) -1 1)))
  6.     ((2) (range (car args) (cadr args) (if (< (car args) (cadr args)) 1 -1)))
  7.     ((3) (let ((le? (if (negative? (caddr args)) >= <=)))
  8.            (let loop ((x(car args)) (xs '()))
  9.              (if (le? (cadr args) x)
  10.                  (reverse xs)
  11.                  (loop (+ x (caddr args)) (cons x xs))))))
  12.     (else (error 'range "unrecognized arguments"))))
  13.  
  14. (define (mappend f . xss) (apply append (apply map f xss)))
  15.  
  16. (define sort #f)
  17. (define merge #f)
  18. (let ()
  19.   (define dosort
  20.     (lambda (pred? ls n)
  21.       (if (= n 1)
  22.           (list (car ls))
  23.           (let ((i (quotient n 2)))
  24.             (domerge pred?
  25.                      (dosort pred? ls i)
  26.                      (dosort pred? (list-tail ls i) (- n i)))))))
  27.   (define domerge
  28.     (lambda (pred? l1 l2)
  29.       (cond
  30.         ((null? l1) l2)
  31.         ((null? l2) l1)
  32.         ((pred? (car l2) (car l1))
  33.          (cons (car l2) (domerge pred? l1 (cdr l2))))
  34.         (else (cons (car l1) (domerge pred? (cdr l1) l2))))))
  35.   (set! sort
  36.     (lambda (pred? l)
  37.       (if (null? l) l (dosort pred? l (length l)))))
  38.   (set! merge
  39.     (lambda (pred? l1 l2)
  40.       (domerge pred? l1 l2))))
  41.  
  42. (define (unique eql? xs)
  43.   (cond ((null? xs) '())
  44.         ((null? (cdr xs)) xs)
  45.         ((eql? (car xs) (cadr xs))
  46.           (unique eql? (cdr xs)))
  47.         (else (cons (car xs) (unique eql? (cdr xs))))))
  48.  
  49. (define (hypotenuse? qs n2)
  50.   (let loop ((rs (reverse qs)) (qs qs))
  51.     (cond ((or (null? qs) (null? rs)) #f)
  52.           ((= (+ (car qs) (car rs)) n2) #t)
  53.           ((< (+ (car qs) (car rs)) n2)
  54.             (loop (cdr rs) qs))
  55.           (else (loop rs (cdr qs))))))
  56.  
  57. (define (hypotenuses n)
  58.   (let loop ((h 1) (qs (list)) (hs (list)))
  59.     (if (= h n) (reverse hs)
  60.       (let* ((h2 (* h h)) (qs (cons h2 qs)))
  61.         (if (hypotenuse? qs h2)
  62.             (loop (+ h 1) qs (cons h hs))
  63.             (loop (+ h 1) qs hs))))))
  64.  
  65. (display (hypotenuses 100)) (newline)
  66.  
  67. (define (pyth n)
  68.   (let loop ((a 3) (b 4) (c 5))
  69.     (if (< n c) (list)
  70.       (append
  71.         (list (if (< a b) (list a b c) (list b a c)))
  72.         (loop (+ a (- b) (- b) c c)
  73.               (+ a a (- b) c c)
  74.               (+ a a (- b) (- b) c c c))
  75.         (loop (+ a b b c c)
  76.               (+ a a b c c)
  77.               (+ a a b b c c c))
  78.         (loop (+ (- a) b b c c)
  79.               (+ (- a) (- a) b c c)
  80.               (+ (- a) (- a) b b c c c))))))
  81.  
  82. (define (hypotenuses n)
  83.   (unique = (sort <
  84.     (mappend (lambda (z) (range z n z))
  85.       (unique = (sort < (map caddr (pyth n))))))))
  86.  
  87. (display (hypotenuses 100)) (newline)
  88.  
  89. (time (display (length (hypotenuses 10000))))
Success #stdin #stdout #stderr 0.29s 7364KB
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stdin
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Standard input is empty
stdout
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(5 10 13 15 17 20 25 26 29 30 34 35 37 39 40 41 45 50 51 52 53 55 58 60 61 65 68 70 73 74 75 78 80 82 85 87 89 90 91 95 97)
(5 10 13 15 17 20 25 26 29 30 34 35 37 39 40 41 45 50 51 52 53 55 58 60 61 65 68 70 73 74 75 78 80 82 85 87 89 90 91 95 97)
6448
stderr
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0.268s CPU time, 0.048s GC time (major), 174277 mutations, 21/2384 GCs (major/minor)
https://ideone.com/B8zGvC
language:
Scheme (chicken 4.13)
created:
8 years ago
visibility:
secret

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