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sudoku.lisp
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sudoku.lisp
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(defvar *puzzle*
'#(
#(4 0 0 0 0 0 8 0 5)
#(0 3 0 0 0 0 0 0 0)
#(0 0 0 7 0 0 0 0 0)
#(0 2 0 0 0 0 0 6 0)
#(0 0 0 0 8 0 4 0 0)
#(0 0 0 0 1 0 0 0 0)
#(0 0 0 6 0 3 0 7 0)
#(5 0 0 2 0 0 0 0 0)
#(1 0 4 0 0 0 0 0 0)
))
(defvar *easy-puzzle*
'#(
#(0 0 3 0 2 0 6 0 0)
#(9 0 0 3 0 5 0 0 1)
#(0 0 1 8 0 6 4 0 0)
#(0 0 8 1 0 2 9 0 0)
#(7 0 0 0 0 0 0 0 8)
#(0 0 6 7 0 8 2 0 0)
#(0 0 2 6 0 9 5 0 0)
#(8 0 0 2 0 3 0 0 9)
#(0 0 5 0 1 0 3 0 0)
))
(defun calc-unit (i j)
(let* ((x (- i 1))
(y (- j 1))
(m (floor x 3))
(n (floor y 3)))
(+ 1 n (* m 3))))
(defun calc-unit-check ()
(loop for i from 1 to 9 do
(loop for j from 1 to 9 do
(format t "~D " (calc-unit i j)))
(format t "~%")))
(defun name (v i j)
(list 'C v i j (calc-unit i j)))
(defun create-puzzle (puzzle)
(apply #'concatenate 'list
(loop for i from 1 to 9 collect
(loop for j from 1 to 9 collect
(let ((x (elt (elt puzzle (- i 1)) (- j 1))))
(if (= x 0)
(loop for v from 1 to 9 collect (name v i j))
(list (name x i j))))))))
(defun rows ()
(loop for i from 1 to 9 collect
(loop for j from 1 to 9 collect
(cons i j))))
(defun cols ()
(loop for i from 1 to 9 collect
(loop for j from 1 to 9 collect
(cons j i))))
(defun units ()
(apply #'concatenate 'list
(loop for m from 0 to 2 collect
(loop for n from 0 to 2 collect
(apply #'concatenate 'list
(loop for i from 0 to 2 collect
(loop for j from 0 to 2 collect
(cons (+ i (* m 3) 1) (+ j (* n 3) 1)))))))))
(defun namec (v ij)
(name v (car ij) (cdr ij)))
(defun add-constraints (reason css)
(loop for cs in css do
(loop for v from 1 to 9 do
(loop for b in cs do
(loop for a in cs
when (not (equal a b)) do
(assert! `(:NOT (:AND ,(namec v a) ,(namec v b))) `(:CONFLICT ,reason)))))))
(defun add-constraints-trigger (reason css)
(loop for cs in css do
(loop for a in cs do
(eval `(rule ((:TRUE ,(namec '?v a)))
(rassert! (:IMPLIES ,(namec '?v a)
(:AND ,@(loop for b in cs when (not (equal a b)) collect `(:NOT ,(namec '?v b)))))
(:CONFLICT ,reason)))))))
(defun sudoku-constraints ()
(add-constraints :ROW (rows))
(add-constraints :COL (cols))
(add-constraints :UNIT (units)))
(defun sudoku-constraints-trigger ()
(add-constraints-trigger :ROW (rows))
(add-constraints-trigger :COL (cols))
(add-constraints-trigger :UNIT (units)))
(defun sudoku-constraints-alt ()
(eval '(rule ((:TRUE (C ?v1 ?r1 ?c1 ?u1) :VAR ?a)
(:TRUE (C ?v2 ?r2 ?c2 ?u2) :VAR ?b
:TEST (and (= ?v1 ?v2)
(or (= ?r1 ?r2) (= ?c1 ?c2) (= ?u1 ?u2))
(not (and (= ?r1 ?r2) (= ?c1 ?c2) (= ?u1 ?u2))))))
(rassert! (:NOT (:AND ?a ?b)) :CONFLICT))))
(defun show-solution ()
(let ((r (remove-if-not #'true? (fetch-global '(C ?v ?i ?j ?u)))))
(format t "~%~A~%" r)
(loop for i from 1 to 9 do
(loop for j from 1 to 9 do
(loop for v from 1 to 9
when (member (name v i j) r :TEST #'equal) do
(format t "~D " v)))
(format t "~%"))
(break)
))
(defun solve-sudoku (puzzle &key (debugging t))
(setq *debug-dds* debugging)
(in-LTRE (create-ltre "Sudoku" :DEBUGGING debugging))
;;(sudoku-constraints)
(sudoku-constraints-trigger)
;;(sudoku-constraints-alt)
(dd-search (assert-choices! (create-puzzle puzzle)) '(show-solution)))
;;(solve-sudoku *easy-puzzle* :debugging t)
;;(solve-sudoku *puzzle* :debugging t)