sudoku.scm

(define (unit-valid unit) 
  (equal? (sort unit <) (list '1 '2 '3 '4 '5 '6 '7 '8 '9)))

(define (units-valid func lst n)
  (if (eqv? n 8)
    (unit-valid (func lst n 0))
    (and (units-valid func lst (+ n 1)) (unit-valid (func lst n 0)))))

(define (nth-row lst n i) 
  (let ((cell (list (list-ref lst (+ (* n 9) i)))))
    (if (eqv? i '8) cell (append cell (nth-row lst n (+ i 1))))))

(define (nth-col lst n i) 
  (let ((cell (list (list-ref lst (+ (* i 9) n)))))
    (if (eqv? i '8) cell (append cell (nth-col lst n (+ i 1))))))

(define (nth-box lst n i) 
  (let ((cell (list (list-ref lst (+ (* (quotient n 3) 27) (* (modulo n 3) 3) (* (quotient i 3) 9) (modulo i 3))))))
    (if (eqv? i '8) cell (append cell (nth-box lst n (+ i 1))))))

(define (valid str) 
  (let ((grid (map char->digit (string->list str)))) 
    (and (eqv? (length grid) '81) 
         (units-valid nth-row grid 0) 
         (units-valid nth-box grid 0) 
         (units-valid nth-col grid 0))))

(and (valid "751843926893625174642179583425316798176982345938754612364297851289531467517468239")
     (not (valid "751843927893625174642179583425316798176982345938754612364297851289531467517468239"))
     (not (valid "571843926893625174642179583425316798176982345938754612364297851289531467517468239"))
     (not (valid "851743926693825174142679583425316798976182345738954612364297851289531467517468239")))