scheme sort list diffent criteria

Question

I have a finite list of quadruples, e.g.

(list (list 1 3 5 5) (list 2 3 4 9) (list 3 4 4 6)(list 4 7 10 3)).

I denote each of the elements by (a1 a2 a3 a4).

Please help me to write a sorting function which provides a "increasing" list created according to the following criteria:

1. the numbers a2,
2. later the difference (a3 - a4),
3. and later the numbers a3.

Please help if you can.

Answer 1

As far as I can tell, your ordered criteria are the order in which to sort. If this is the case, then the following program should perform that sorting.

(define (strange-sort quadruples)
  (define (a2 quad)
    (cadr quad))
  (define (a3 quad)
    (caddr quad))
  (define (a4 quad)
    (cadddr quad))
  (sort quadruples
        (lambda (x y)
          (cond ((< (a2 x) (a2 y))
                 #t)
                ((> (a2 x) (a2 y))
                 #f)
                (else
                 (cond ((< (- (a3 x) (a4 x))
                           (- (a3 y) (a4 y)))
                        #t)
                       ((> (- (a3 x) (a4 x))
                           (- (a3 y) (a4 y)))
                        #f)
                       (else
                        (cond ((< (a3 x) (a3 y))
                               #t)
                              (else #f)))))))))