Question

I am just trying to learn some Lisp, so I am going through project euler problems. I found problem no. 14 interesting (so if you are planning to solve this problems stop reading now, because I pasted my solution at the bottom). With my algorithm it was so slow, but after using memoization (I copied the function from Paul Graham’s “on Lisp” book) it was much more faster (around 4 to 8 seconds).

My question is about this bunch of warnings that I got:
Am I doing something wrong? Can I improve my style?

> ;; Loading file
> /euler-lisp/euler-14.lisp
> ... WARNING in COLLATZ-SERIE :
> COLLATZ-SERIE-M is neither declared
> nor bound, it will be treated as if it
> were declared SPECIAL. WARNING in
> COLLATZ-SERIE : COLLATZ-SERIE-M is
> neither declared nor bound, it will be
> treated as if it were declared
> SPECIAL. WARNING in COMPILED-FORM-314
> : COLLATZ-SERIE-M is neither declared
> nor bound, it will be treated as if it
> were declared SPECIAL. (525 837799) 
> Real time: 18.821894 sec. Run time:
> 18.029127 sec. Space: 219883968 Bytes GC: 35, GC time: 4.080254 sec. Las
> siguientes variables especiales no han
> sido definidas:  COLLATZ-SERIE-M 0
> errores, 0 advertencias ;; Loaded file

This is the code:

 (defun collatz (n)
      (if (evenp n) (/ n 2) (+ (* 3 n) 1)))

    (defun memoize (fn)
      (let ((cache (make-hash-table :test #'equal)))
        #'(lambda (&rest args)
            (multiple-value-bind (val win) (gethash args cache)
              (if win
                  val
                (setf (gethash args cache)
                      (apply fn args)))))))

    (defun collatz-serie (n)
      (cond ((= n 1) (list 1))
        ((evenp n) (cons n (funcall collatz-serie-m (/ n 2))))
        (t (cons n (funcall collatz-serie-m (+ (* 3 n) 1))))))

    (defun collatz-serie-len (n)
      (length (collatz-serie n)))

    (setq collatz-serie-m (memoize #'collatz-serie))

    (defun gen-series-pairs (n)
      (loop for i from 1 to n collect 
           (list (collatz-serie-len i) i)))

    (defun euler-14 (&key (n 1000000))
      (car (sort (gen-series-pairs n) #'(lambda (x y) (> (car x) (car y))))))

    (time (print (euler-14)))

Thanks a lot, and forgive the probable errors, I am just beginning with Lisp.
Br

UPDATE:
i want to share the final code that i wrote. using custom external hash table for memoization and improving the final loop.

(defvar *cache* (make-hash-table :test #'equal))

(defun collatz (n)
       (if (evenp n) (/ n 2) (+ (* 3 n) 1)))

(defun collatz-serie (n)
  (cond ((= n 1) (list 1))
    ((evenp n) (cons n (collatz-serie (/ n 2))))
    (t (cons n (collatz-serie (+ (* 3 n) 1))))))

(defun collatz-serie-new (n)
  (labels ((helper (n len) 
             (multiple-value-bind (val stored?) (gethash n *cache*)
               (if stored? 
                   val
                 (setf (gethash n *cache*) (cond ((= n 1) len)
                                                 ((evenp n) (+ len (helper (/ n 2) len)))
                                                 (t (+ len (helper (+ (* 3 n) 1) len)))))))))
    (helper n 1)))

;; learning how to loop
(defun euler-14 (&key (n 1000000))
  (loop with max = 0 and pos = 0 
        for i from n downto 1 
        when (> (collatz-serie-new i) max) 
        do (setf max (collatz-serie-new i)) and do (setf pos i) 
        finally (return (list max pos))))

Answer 1

It is bad style to setq an unknown name. It is assumed that you mean to create a new global special variable, then set it, but this should be made explicit by introducing these bindings first. You do this at the top level by using defvar (or defparameter or defconstant) instead, and in lexical blocks by using let, do, multiple-value-bind or similar constructs.