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(use-modules
(srfi srfi-1)
(srfi srfi-26)
(ice-9 match)
(sat solver)
(sat helpers))
(define (get-value board vals col row)
(1+
(find
(lambda (possible-value)
(array-ref vals
(array-ref board col row possible-value)))
(iota (biggest-value board)))))
(define (set-initial-value board col row val)
(add-clause
(list
(array-ref board
col
row
(1- val)))))
(define (map-for-0-to n f)
(map f (iota n)))
(define (make-row row board-size)
(map-for-0-to
board-size
(cut cons <> row)))
(define (make-col col board-size)
(map-for-0-to
board-size
(cut cons col <>)))
(define (rows board-size)
(map-for-0-to
board-size
(cut make-row <> board-size)))
(define (cols board-size)
(map-for-0-to
board-size
(cut make-col <> board-size)))
(define (make-box bcol brow box-size)
(let ((l '()))
(do ((icol 0 (1+ icol))) ((= icol box-size))
(do ((irow 0 (1+ irow))) ((= irow box-size))
(set! l (cons
(cons (+ (* box-size bcol) icol)
(+ (* box-size brow) irow))
l))))
l))
(define (boxes board-size box-size)
(let ((l '()))
(do ((bcol 0 (1+ bcol))) ((= bcol 3))
(do ((brow 0 (1+ brow))) ((= brow 3))
(set! l (cons
(make-box bcol brow box-size)
l))
))
l))
(define (biggest-value board)
(1+ (match
(array-shape board)
(((_ _) (_ _) (_ max-value))
max-value))))
(define (unique-values board coords-list)
(for-each
(lambda (n)
(exactly-one-true
(map
(lambda (coord)
(array-ref board (car coord) (cdr coord) n))
coords-list)))
(iota (biggest-value board))))
(define (all-unique-values board coord-lists)
(for-each
(cut unique-values board <>)
coord-lists))
(define (make-board size)
(let ((board (make-array #f size size size)))
(array-map! board make-sat-variable)
board))
(define (all-one-number board col row)
(exactly-one-true
(map
(lambda (value)
(array-ref board col row value))
(iota (biggest-value board)))))
(let* ((board-size 9)
(board (make-board board-size)))
;; The standard Sudoku rules
(all-unique-values board (rows board-size))
(all-unique-values board (cols board-size))
(all-unique-values board (boxes board-size 3))
;; Each position contains exactly one number
(do ((col 0 (1+ col))) ((= col board-size))
(do ((row 0 (1+ row))) ((= row board-size))
(all-one-number board col row)))
;; Initially specified values
(set-initial-value board 0 0 4)
(set-initial-value board 0 7 5)
(set-initial-value board 0 8 1)
(set-initial-value board 1 1 3)
(set-initial-value board 1 3 2)
(set-initial-value board 2 8 4)
(set-initial-value board 3 2 7)
(set-initial-value board 3 6 6)
(set-initial-value board 3 7 2)
(set-initial-value board 4 4 8)
(set-initial-value board 4 5 1)
(set-initial-value board 5 6 3)
(set-initial-value board 6 0 8)
(set-initial-value board 6 4 4)
(set-initial-value board 7 3 6)
(set-initial-value board 7 6 7)
(set-initial-value board 8 0 5)
(let ((vals (solve-sat)))
(do ((row 0 (1+ row))) ((= row board-size))
(do ((col 0 (1+ col))) ((= col board-size))
(format #t "~a" (get-value board vals col row)))
(newline))))
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