[racket] shortest paths, resource allocation/scheduling

On 12/05/2011 08:40 AM, Sam Tobin-Hochstadt wrote:
> On Mon, Dec 5, 2011 at 10:00 AM, Geoffrey S. Knauth<geoff at knauth.org>  wrote:
>> I'm wondering if there is something in the now very rich set of Racket libraries that already does this.  Let's say I have 5 points {A,B,C,D,E}.  I want to interconnect all of them:
>>
>> {AB,AC,AD,AE,AF,BC,BD,BE,BF,CD,CE,CF,DE,DF,EF}
>>
>> That's 15 edges rather than the 5x5=25 that a dumb interconnect
>> would do.  To start, I just need to track and sort the edge
>> weights, and AB is the same as BA.
>
> Here's the start of an answer (sadly quadratic, but for N=121 I don't
> think that will matter much):
>
> #lang racket
> (require unstable/sequence)
> (define (subsets-of-size-2 l)
>    (for*/lists (r) ([i l] [j l]
>                     #:unless (eq? i j)
>                     #:unless (member (cons j i) r))
>      (cons i j)))
>
> (for ([(p q) (in-pairs (subsets-of-size-2 '(A B C D E F)))])
>    (printf "~a<->  ~a\n" p q))
>

That looks quartic in the length of l, because of the member check.

Here's a quadratic version:

(require srfi/1)
(define (subsets-of-size-2 l)
   (for*/list ([ne-sublist (pair-fold-right cons null l)]
               [b (in-list (cdr ne-sublist))])
     (cons (car ne-sublist) b)))

Note: (pair-fold-right cons null l) produces a list of the non-empty 
sublists of l.

Ryan