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sudoku.scm
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sudoku.scm
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;; sudoku - Wikipedia - http://ja.wikipedia.org/wiki/%E6%95%B0%E7%8B%AC
(define-module liv.game.sudoku
(export fix-naked-singles-solver backtrack-solver))
(select-module liv.game.sudoku)
(use srfi-1) ; drop, split-at
(use srfi-9) ; define-record-type
(use util.list) ; slices
(use liv.matrix) ; matrix-*, *-matrix
(define-constant region-size 3)
(define-constant fullset-numbers (iota (* region-size region-size) 1))
(define (single? ls)
(and (pair? ls)
(null? (cdr ls))))
;; matrix x or y -> region position
(define (region-pos mn)
(quotient mn region-size))
;; mmatrix x and y -> region index
(define (region-index mx my)
(+ (region-pos mx)
(* region-size
(region-pos my))))
(define (region-ref region n)
(list-ref region n))
(define (slice-matrix-rows matrix size)
(map (lambda (row)
(slices row size)) matrix))
(define (matrix->regions matrix size)
(let1 sliced (slice-matrix-rows matrix size)
(let rec ((m sliced)(acc '()))
(if (null? m)
(apply append (reverse acc))
(receive (took dropped)(split-at m size)
(rec dropped (cons (apply map append took) acc)))))))
(define (candidates matrix x y . keywords)
(let-keywords* keywords ((eq? =)
(empty? zero?)
(ignore '()))
(let1 f (pa$ filter (complement empty?))
(let* ((row-candidates (f (matrix-row-ref matrix y)))
(col-candidates (f (matrix-col-ref matrix x)))
(region-candidates (f (region-ref (matrix->regions matrix region-size)
(region-index x y)))))
(lset-difference eq? fullset-numbers row-candidates
col-candidates region-candidates
ignore)))))
(define (has-empty? matrix :optional (empty? zero?))
(let/cc hop
(fold (lambda (row acc)
(if-let1 it (any empty? row)
(hop it)
acc)) #f matrix)))
;;
;; naked single solve
;;
(define (fix-naked-singles matrix . keywords)
(let-keywords* keywords ((empty? zero?)
(car car))
(let1 exist? #f
(values (map-matrix-with-index
(lambda (e x y)
(if (empty? e)
(let1 can (candidates matrix x y)
(if (single? can)
(begin
(unless exist?
(set! exist? (not exist?)))
(car can))
e))
e)) matrix)
exist?))))
(define (fix-naked-singles-solver matrix
:optional (more identity))
(let rec ((m matrix))
(receive (cand exist?)(fix-naked-singles m)
(cond (exist? (rec cand))
((has-empty? cand)(more cand))
(else cand)))))
;;
;; backtrack solver
;;
(define-record-type point
(make-point x y) point?
(x point-x)
(y point-y))
(define (backtrack-solver matrix)
(let/cc hop
(let ((mstack '())(cstack '())(pstack '())(count 0))
(let backtrack ((m (matrix-copy matrix))(bt-cand '())
(bt-point (make-point -1 -1)))
(for-each-matrix-with-index
(lambda (e x y)
(when (zero? e)
(let1 cand (if (and (= x (point-x bt-point))
(= y (point-y bt-point)))
bt-cand
(candidates m x y))
(cond ((null? cand)
(inc! count)
(backtrack (pop! mstack)
(pop! cstack)
(pop! pstack)))
((single? cand)
(matrix-set! m x y (car cand)))
(else
(push! mstack (matrix-copy m))
(push! cstack (cdr cand))
(push! pstack (make-point x y))
(matrix-set! m x y (car cand))))))) m)
(hop m count)))))
;; (equal? test-data-1-ans (backtrack-solver test-data-1))
;; ;; #t
;; (equal? test-data-2-ans (backtrack-solver test-data-2))
;; ;; #t
;; (equal? test-data-3-ans (backtrack-solver test-data-3))
;; ;; #t
;; (equal? test-data-4-ans (backtrack-solver test-data-4))
;; ;; #t
;; (equal? most-difficult-data-ans (backtrack-solver most-difficult-data))
;; ;; #t
(provide "liv/game/sudoku")