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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 name (i j)
(format nil "c~A~A" i j))
(defun create-puzzle (puzzle)
(setq *atms* (create-atms "sudoku" :debugging t))
(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 (tms-create-node *atms* (list (name i j) v) :assumptionp t))
(list (tms-create-node *atms* (list (name i j) x)))))))))
(defun rows ()
(loop for i from 1 to 9 collect
(loop for j from 1 to 9 collect
(name i j))))
(defun cols ()
(loop for i from 1 to 9 collect
(loop for j from 1 to 9 collect
(name 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
(name (+ i (* m 3) 1) (+ j (* n 3) 1)))))))))
(defun add-cell-constraints (reason cs)
(let ((get #'(lambda (x v) (let ((d (list (elt cs (- x 1)) v)))
(find-if #'(lambda (n) (equal d (tms-node-datum n))) (atms-nodes *atms*))))))
(loop for i from 1 to 9 do
(loop for j from 1 to 9
when (not (= i j)) do
(loop for v from 1 to 9 do
(let ((a (funcall get i v)) (b (funcall get j v)))
(when (and a b)
(nogood-nodes reason (list a b)))))))))
(defun add-unit-constraints (name css)
(loop for cs in css do
(add-cell-constraints name cs)))
(defun add-all-constraints ()
(add-unit-constraints 'CONFLICT-ROW (rows))
(add-unit-constraints 'CONFLICT-COL (cols))
(add-unit-constraints 'CONFLICT-UNT (units)))
(defun prune (vss env)
(sort
(loop for vs in vss collect
(loop for v in vs
when (node-consistent-with? v env) collect v))
#'< :key #'length))
(defun interpretations (atms choice-sets)
(if (atms-debugging atms)
(format *trace-output*
"~% Constructing interpretations..."))
(setq *solutions* nil)
(get-depth-solutions1 (atms-empty-env atms) choice-sets)
(setq *solutions* (delete nil *solutions* :TEST #'eq))
(unless *solutions*
(if choice-sets (return-from interpretations nil)
(setq *solutions* (list (atms-empty-env atms))))))
(defun get-depth-solutions1 (solution choice-sets &aux new-solution)
(cond ((null choice-sets)
(push solution *solutions*))
((env-nogood? solution)) ;something died.
(t (dolist (choice (car choice-sets))
(setq new-solution (cons-env choice solution))
(unless (env-nogood? new-solution)
(get-depth-solutions1
new-solution
(prune (cdr choice-sets) new-solution)))))))
(defun show-solution (env vars &aux counter)
(setq counter 0)
(loop for ns in vars do
(setq counter (+ 1 counter))
(loop for n in ns
when (in-node? n env) do
(format t "~A " (cadr (tms-node-datum n))))
(when (= counter 9)
(format t "~%")
(setq counter 0))))
(defvar *vars*)
(defun solve-sudoku (puzzle)
(setq *vars* (create-puzzle puzzle))
(loop for vs in *vars*
when (= (length vs) 1) do
(justify-node ':PUZZLE (car vs) nil))
(add-all-constraints)
(interpretations *atms* (prune (remove-if #'(lambda (vs) (= (length vs) 1)) *vars*) (atms-empty-env *atms*)))
(assert (= (length *solutions*) 1))
(show-solution (car *solutions*) *vars*))
;;(solve-sudoku *easy-puzzle*)
;;(solve-sudoku *puzzle*)