[racket] a small programming exercise

Code is below.  There's something stupidly verbose about the way I extract
the first digit, so suggestions are welcome.

(define (count-firsts d)
  (let ((c (make-vector 9 0)))
    (let loop ((d d))
      (if (null? d)
      (let* ((cl (vector->list c))
         (sum (exact->inexact (apply + cl))))
        (map list
         (build-list 9 add1)
         (map (lambda (x) (/ x sum)) cl)))
      (let* ((first (string->number
             (list->string
              (list
               (car (string->list
                 (number->string (car d))))))))
         (ind (sub1 first)))
        (vector-set! c ind (add1 (vector-ref c ind)))
        (loop (cdr d)))))))


On Thu, Oct 14, 2010 at 12:10 AM, Shriram Krishnamurthi <sk at cs.brown.edu>wrote:

> Given: A list of numbers.  Assume integers (though it isn't necessary
> for the underlying issue).
>
> Task: To determine how often the first digit is 1, the first digit is
> 2, ..., the first digit is 9, and present as a table.  You may exploit
> DrRacket's pretty-printer, e.g., by using a list of lists:
>
> '((#\1 22.51539138082674)
>  (#\2 16.44678979771328)
>  (#\3 15.567282321899736)
>  (#\4 12.401055408970976)
>  (#\5 9.058927000879507)
>  (#\6 7.651715039577836)
>  (#\7 6.420404573438875)
>  (#\8 5.804749340369393)
>  (#\9 4.133685136323659))
>
> I leave the precise format of the output unstated so you're free to
> choose a clever representation; your answer should be at least as
> visually clear as the above.
>
> You should not mutate the original list, since it may be necessary for
> other computations.
>
> Smallest/tightest/cleanest/best?
>
> Shriram
>
> PS: Of course, this is to explore Benford's Law:
>
>    http://en.wikipedia.org/wiki/Benford's_law<http://en.wikipedia.org/wiki/Benford%27s_law>
>
>    which is the subject of my lecture tomorrow.  The above
>    distribution is from the size of the littoral zone (in acres) of
>    the lakes of Minnesota.
>
> PPS: If you really want to you can assume the data are actually in a
>     CSV file (as mine are -- thanks, Neil!), in case you can come up
>     with something even cleverer.
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