;;;; -*- Lisp -*-
;;;;
;;;; To execute, call (count-triangles (make-graph))

(defstruct link
  line
  destination)


(defun count-paths (links current-line destination length)
  "Count the paths starting from the position that has links LINKS and reaches DESTINATION
that are of length LEGNTH"
  (if (zerop length)
	  (if (eql links destination)
		  1
		0)
	(let ((num-paths-accum 0))
	  (dolist (link links)
		(when (not (eql (link-line link) current-line))
		  (incf num-paths-accum
				(count-paths (funcall (link-destination link))
							 (link-line link)
							 destination
							 (1- length)))))
	  num-paths-accum)))

(defun count-triangles (graph)
  "Count the number of triangles formed in the paths available by the graph.
This is the number of paths minus any redundant paths"
  (let ((num-triangles-accum 0))
	(dolist (point graph)
	  (incf num-triangles-accum (count-paths point nil point 3)))
	;; There are six ways to describe each triangle "A-B-C"
	;; A-B-C   A-C-B
	;; B-A-C   B-C-A
	;; C-A-B   C-B-A
	(/ num-triangles-accum 6)))


(defmacro ref (to-ref)
  `(lambda () ,to-ref))


(defmacro push-line (points line)
  (let (accum)
	(push 'progn accum)
	(dolist (start-point points)
	  (dolist (end-point points)
		(when (not (eq start-point end-point))
		  (push `(push (make-link :line ,line
								  :destination (ref ,end-point))
					   ,start-point)
				accum))))
	(reverse accum)))

(defun make-graph ()
  "Makes a graph as in the progblem"
  (let (p0 p1 p2 p3 p4 p5 p6 p7 p8 p9 p10)
	(push-line (p0 p5 p8 p10) 'p0-p10)
	(push-line (p0 p3 p7 p9) 'p0-p9)
	(push-line (p0 p2 p4 p6) 'p0-p6)
	(push-line (p0 p1) 'p0-p1)
	(push-line (p1 p2 p3 p5) 'p1-p5)
	(push-line (p1 p4 p7 p8) 'p1-p8)
	(push-line (p1 p6 p9 p10) 'p1-p10)
	
	(list p0 p1 p2 p3 p4 p5 p6 p7 p8 p9 p10)))