; project euler 12

(define (factors n)
  (if (even? n) (cons 2 (factors (/ n 2)))
    (let loop ((n n) (f 3) (fs '()))
      (cond ((< n (* f f)) (reverse (cons n fs)))
            ((zero? (modulo n f)) (loop (/ n f) f (cons f fs)))
            (else (loop n (+ f 2) fs))))))

(define (numdiv n)
  (let ((fs (factors n)))
    (let loop ((prev (car fs)) (fs (cdr fs)) (f 2) (d 1))
      (cond ((null? fs) (* d f))
            ((= (car fs) prev) (loop prev (cdr fs) (+ f 1) d))
            (else (loop (car fs) (cdr fs) 2 (* d f)))))))

(define (euler-12 n)
  (let loop ((i 1) (tri 1))
    (if (< n (numdiv tri)) tri
      (loop (+ i 1) (+ tri i 1)))))

(time (begin (display (euler-12 500)) (newline)))

76576500
cpu time: 210 real time: 998 gc time: 0