stones.scm

gistfile1.scm

(usefd)

(define (powerset a)
  (if (null? a) (list '())
      (let ((p (powerset (cdr a))))
        (append (map (lambda (x) (cons (car a) x)) p) p))))

(define (remove-duplicates l)
  (do ((a '() (if (member (car l) a) a (cons (car l) a)))
       (l l (cdr l)))
      ((null? l) (reverse a))))

(define (solutions)
  (run #f (q)
    (fresh (a b c d s1 s2)
      (domfd a b c d s1 s2 (range 1 40))
      (all-differentfd `(,a ,b ,c ,d ,s1 ,s2)) 
      (== a 1)
      (<fd a b) (<=fd a 34)
      (<fd b c) (<=fd b 34)
      (<fd c d) (<=fd c 34)
      (plusfd a b s1) 
      (plusfd s1 c s2)
      (plusfd s2 d 40)
      (== q `(,a ,b ,c ,d)))))

(define (all-sums)
  (map (lambda (x)
         (let* ((ps (powerset x))
                (sums (cdr (remove-duplicates
                            (list-sort < (map (lambda (l) (apply + l)) ps))))))
           `(stones ,x length ,(length sums) sums ,sums)))
       (solutions)))

 (time (all-sums)) ;; 85ms

;; {stones {1 2 4 33} length 15 sums {1 2 3 4 5 6 7 33 34 35 36 37 38 39 40}}
;; {stones {1 2 5 32} length 15 sums {1 2 3 5 6 7 8 32 33 34 35 37 38 39 40}}
;; {stones {1 3 5 31} length 15 sums {1 3 4 5 6 8 9 31 32 34 35 36 37 39 40}}
;; {stones {1 2 6 31} length 15 sums {1 2 3 6 7 8 9 31 32 33 34 37 38 39 40}}
;; {stones {1 2 7 30} length 15 sums {1 2 3 7 8 9 10 30 31 32 33 37 38 39 40}}
;; {stones {1 3 6 30} length 15 sums {1 3 4 6 7 9 10 30 31 33 34 36 37 39 40}}
;; {stones {1 2 8 29} length 15 sums {1 2 3 8 9 10 11 29 30 31 32 37 38 39 40}}
;; {stones {1 2 9 28} length 15 sums {1 2 3 9 10 11 12 28 29 30 31 37 38 39 40}}
;; {stones {1 4 6 29} length 15 sums {1 4 5 6 7 10 11 29 30 33 34 35 36 39 40}}
;; {stones {1 3 7 29} length 15 sums {1 3 4 7 8 10 11 29 30 32 33 36 37 39 40}}
;; {stones {1 2 10 27} length 15 sums {1 2 3 10 11 12 13 27 28 29 30 37 38 39 40}}
;; {stones {1 2 11 26} length 15 sums {1 2 3 11 12 13 14 26 27 28 29 37 38 39 40}}
;; {stones {1 3 8 28} length 15 sums {1 3 4 8 9 11 12 28 29 31 32 36 37 39 40}}
;; {stones {1 2 12 25} length 15 sums {1 2 3 12 13 14 15 25 26 27 28 37 38 39 40}}
;; {stones {1 2 13 24} length 15 sums {1 2 3 13 14 15 16 24 25 26 27 37 38 39 40}}
;; {stones {1 4 7 28} length 15 sums {1 4 5 7 8 11 12 28 29 32 33 35 36 39 40}}
;; {stones {1 3 9 27} length 15 sums {1 3 4 9 10 12 13 27 28 30 31 36 37 39 40}}
;; {stones {1 2 14 23} length 15 sums {1 2 3 14 15 16 17 23 24 25 26 37 38 39 40}}
;; {stones {1 2 15 22} length 15 sums {1 2 3 15 16 17 18 22 23 24 25 37 38 39 40}}
;; {stones {1 3 10 26} length 15 sums {1 3 4 10 11 13 14 26 27 29 30 36 37 39 40}}
;; {stones {1 2 16 21} length 15 sums {1 2 3 16 17 18 19 21 22 23 24 37 38 39 40}}
;; {stones {1 5 7 27} length 15 sums {1 5 6 7 8 12 13 27 28 32 33 34 35 39 40}}
;; {stones {1 2 18 19} length 12 sums {1 2 3 18 19 20 21 22 37 38 39 40}}
;; {stones {1 4 8 27} length 15 sums {1 4 5 8 9 12 13 27 28 31 32 35 36 39 40}}
;; {stones {1 3 11 25} length 15 sums {1 3 4 11 12 14 15 25 26 28 29 36 37 39 40}}
;; {stones {1 3 12 24} length 15 sums {1 3 4 12 13 15 16 24 25 27 28 36 37 39 40}}
;; {stones {1 4 9 26} length 15 sums {1 4 5 9 10 13 14 26 27 30 31 35 36 39 40}}
;; {stones {1 3 13 23} length 15 sums {1 3 4 13 14 16 17 23 24 26 27 36 37 39 40}}
;; {stones {1 3 14 22} length 15 sums {1 3 4 14 15 17 18 22 23 25 26 36 37 39 40}}
;; {stones {1 5 8 26} length 15 sums {1 5 6 8 9 13 14 26 27 31 32 34 35 39 40}}
;; {stones {1 4 10 25} length 15 sums {1 4 5 10 11 14 15 25 26 29 30 35 36 39 40}}
;; {stones {1 3 15 21} length 15 sums {1 3 4 15 16 18 19 21 22 24 25 36 37 39 40}}
;; {stones {1 3 17 19} length 14 sums {1 3 4 17 18 19 20 21 22 23 36 37 39 40}}
;; {stones {1 4 11 24} length 15 sums {1 4 5 11 12 15 16 24 25 28 29 35 36 39 40}}
;; {stones {1 6 8 25} length 15 sums {1 6 7 8 9 14 15 25 26 31 32 33 34 39 40}}
;; {stones {1 5 9 25} length 15 sums {1 5 6 9 10 14 15 25 26 30 31 34 35 39 40}}
;; {stones {1 4 12 23} length 15 sums {1 4 5 12 13 16 17 23 24 27 28 35 36 39 40}}
;; {stones {1 4 13 22} length 15 sums {1 4 5 13 14 17 18 22 23 26 27 35 36 39 40}}
;; {stones {1 5 10 24} length 15 sums {1 5 6 10 11 15 16 24 25 29 30 34 35 39 40}}
;; {stones {1 4 14 21} length 15 sums {1 4 5 14 15 18 19 21 22 25 26 35 36 39 40}}
;; {stones {1 4 16 19} length 14 sums {1 4 5 16 17 19 20 21 23 24 35 36 39 40}}
;; {stones {1 6 9 24} length 15 sums {1 6 7 9 10 15 16 24 25 30 31 33 34 39 40}}
;; {stones {1 5 11 23} length 15 sums {1 5 6 11 12 16 17 23 24 28 29 34 35 39 40}}
;; {stones {1 4 17 18} length 13 sums {1 4 5 17 18 19 21 22 23 35 36 39 40}}
;; {stones {1 5 12 22} length 15 sums {1 5 6 12 13 17 18 22 23 27 28 34 35 39 40}}
;; {stones {1 7 9 23} length 15 sums {1 7 8 9 10 16 17 23 24 30 31 32 33 39 40}}
;; {stones {1 6 10 23} length 15 sums {1 6 7 10 11 16 17 23 24 29 30 33 34 39 40}}
;; {stones {1 5 13 21} length 15 sums {1 5 6 13 14 18 19 21 22 26 27 34 35 39 40}}
;; {stones {1 5 15 19} length 14 sums {1 5 6 15 16 19 20 21 24 25 34 35 39 40}}
;; {stones {1 6 11 22} length 15 sums {1 6 7 11 12 17 18 22 23 28 29 33 34 39 40}}
;; {stones {1 5 16 18} length 15 sums {1 5 6 16 17 18 19 21 22 23 24 34 35 39 40}}
;; {stones {1 7 10 22} length 15 sums {1 7 8 10 11 17 18 22 23 29 30 32 33 39 40}}
;; {stones {1 6 12 21} length 15 sums {1 6 7 12 13 18 19 21 22 27 28 33 34 39 40}}
;; {stones {1 6 14 19} length 14 sums {1 6 7 14 15 19 20 21 25 26 33 34 39 40}}
;; {stones {1 8 10 21} length 15 sums {1 8 9 10 11 18 19 21 22 29 30 31 32 39 40}}
;; {stones {1 7 11 21} length 15 sums {1 7 8 11 12 18 19 21 22 28 29 32 33 39 40}}
;; {stones {1 6 15 18} length 15 sums {1 6 7 15 16 18 19 21 22 24 25 33 34 39 40}}
;; {stones {1 6 16 17} length 13 sums {1 6 7 16 17 18 22 23 24 33 34 39 40}}
;; {stones {1 7 13 19} length 14 sums {1 7 8 13 14 19 20 21 26 27 32 33 39 40}}
;; {stones {1 7 14 18} length 15 sums {1 7 8 14 15 18 19 21 22 25 26 32 33 39 40}}
;; {stones {1 8 12 19} length 14 sums {1 8 9 12 13 19 20 21 27 28 31 32 39 40}}
;; {stones {1 7 15 17} length 15 sums {1 7 8 15 16 17 18 22 23 24 25 32 33 39 40}}
;; {stones {1 9 11 19} length 14 sums {1 9 10 11 12 19 20 21 28 29 30 31 39 40}}
;; {stones {1 8 13 18} length 15 sums {1 8 9 13 14 18 19 21 22 26 27 31 32 39 40}}
;; {stones {1 8 14 17} length 15 sums {1 8 9 14 15 17 18 22 23 25 26 31 32 39 40}}
;; {stones {1 9 12 18} length 15 sums {1 9 10 12 13 18 19 21 22 27 28 30 31 39 40}}
;; {stones {1 8 15 16} length 13 sums {1 8 9 15 16 17 23 24 25 31 32 39 40}}
;; {stones {1 10 12 17} length 15 sums {1 10 11 12 13 17 18 22 23 27 28 29 30 39 40}}
;; {stones {1 9 13 17} length 15 sums {1 9 10 13 14 17 18 22 23 26 27 30 31 39 40}}
;; {stones {1 9 14 16} length 15 sums {1 9 10 14 15 16 17 23 24 25 26 30 31 39 40}}
;; {stones {1 10 13 16} length 15 sums {1 10 11 13 14 16 17 23 24 26 27 29 30 39 40}}
;; {stones {1 11 13 15} length 15 sums {1 11 12 13 14 15 16 24 25 26 27 28 29 39 40}}
;; {stones {1 10 14 15} length 13 sums {1 10 11 14 15 16 24 25 26 29 30 39 40}}