chickens

chickens.lisp

;; utilities

(defun combinations (&rest lists)
	   (if (car lists)
	       (mapcan (lambda (inner-val)
			 (mapcar (lambda (outer-val)
				   (cons outer-val inner-val))
				 (car lists)))
		       (apply #'combinations (cdr lists)))
	       (list nil)))

(defmacro range (i j)
  `(loop for x from ,i to ,j collect x))

(defmacro intersection-3 (a b c)
  `(intersection ,a (intersection ,b ,c :test #'equal)
		 :test #'equal))


;; compute the candidates

(defun f (n)
  (labels ((test (i p1 p2)
	     (and (> p1 p2)
		  (equal 3500 (+ (* i p1) (* (- n i) p2))))))
    (loop with r = (range 1 400) 
	  for v in (combinations (range 0 n) r r)
	  when (apply #'test v)
	  collect (subseq v 1))))


#| 
The output:

cl-user> (time (intersection-3 (f 26) (f 10) (f 16))) 
; cpu time (non-gc) 0.638612 sec user, 0.007279 sec system
; cpu time (gc)     0.116465 sec user, 0.001272 sec system
; cpu time (total)  0.755077 sec user, 0.008551 sec system
; cpu time (thread) 0.637792 sec user, 0.006627 sec system
; real time  0.770082 sec (99.16%)
; space allocation:
;  18,568,715 cons cells, 7,680 other bytes, 0 static bytes
; Page Faults: major: 0 (gc: 0), minor: 0 (gc: 0)
((375 125))
|#

This is the solution for http://goo.gl/i433b9. First price is 375 and the second price is 125. If the second price can be zero, then change (range 1 400) to (range 0 400)