;; author: Tayssir John Gabbour
;; Permission is not granted for use in nuclear reactors or defense systems.
;; Contact for permission in these cases and I'll actually test whether this
;;   silly code works. If I like you.

;; lines: 37 lines without blank lines.
;; time:  30min +/- 5min for answer.
;;        10min to remove unused code, tediously eyeball whether it actually
;;             gave correct triangles, and write these comments.


(defconstant +lines+
  '((p0 p5 p8 p10)
    (p0 p1)
    (p0 p3 p7 p9)
    (p0 p2 p4 p6)
    (p1 p2 p3 p5)
    (p1 p4 p7 p8)
    (p1 p6 p9 p10)))

(defun colinear (blah1 blah2)
  (loop for i in +lines+
        thereis (and (member blah1 i)
                     (member blah2 i))))

(defun forms-triangle? (trip)
  (let ((n1 (first  trip))
        (n2 (second trip))
        (n3 (third  trip)))
    (and (colinear n1 n2)
         (colinear n1 n3)
         (colinear n2 n3)
         (loop for i in +lines+
               never (and (member n1 i)
                          (member n2 i)
                          (member n3 i))))))

(defun all-triples (points)
  (loop for sublist on points
        for i = (car sublist)
        nconc (loop for sublist2 on (cdr sublist)
                    for j = (car sublist2)
                    nconc (loop for sublist3 on (cdr sublist2)
                                for k = (car sublist3)
                                collect (list i j k)))))

(defconstant +points+ ;no, I didn't type these out by hand ;)
  '(p0 p1 p2 p3 p4 p5 p6 p7 p8 p9 p10))

(defparameter *answers*
  (loop for i in (all-triples +points+)
        when (forms-triangle? i) collect i))

(format t "~&Number of triangles: ~A. ~%Triangles: ~{~A ~}" (length *answers*) *answers*)
      



;;; Unused code.

;; (defun triple= (trip1 trip2)
;;   (equal (sort trip1 #'string<)
;;          (sort trip2 #'string<)))

;; (colinear 'p4 'p8)
;; (colinear 'p4 'p10)
;; (triple= '(p1 p3 p5) '(p5 p1 p3))
;; (all-triples +points+)
;; (loop for i from 0 to 10 do (format t "p~S " i))