On Thu, Oct 14, 2010 at 1:10 AM, Shriram Krishnamurthi <s...@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 actually adapted a previous algorithm of mine...
(define (benford ns)
(let ((ns (if (number? (car ns))
(map first-digit ns)
ns))
(total (length ns)))
(let benford0 ((ns ns) (digits (map first-digit '(1 2 3 4 5 6 7 8 9))))
(if (null? digits) '()
(let* ((d (first digits))
(all-d (filter ns (lambda (n) (char=? n d))))
(all-but-d (filter ns (lambda (n) (not (char=? n d))))))
(pair
(pair d (* 100.0 (/ (length all-d) total)))
(benford0 all-but-d (rest digits))))))))
; given these aliases for lisp n00bs
(define pair cons)
(define first car)
(define rest cdr)
; this utility
(define (first-digit n) (string-ref (number->string n) 0))
; and these well-known functions
(define (fold f init ls)
(if (null? ls) init
(fold f (f (car ls) init) (cdr ls))))
(define (filter ls f)
(fold (lambda (i o) (if (f i) (pair i o) o)) '() ls))
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