(define (getRow list num)
  (cond ((eq? num 0) (car list))
        (else (getRow (cdr list) (- num 1)))))

(define (charAt row col board)
  (string-ref (getRow board row) col))

(define (mod a b)
  (modulo a b))

(define (read-board) ; This will _actually_ read a board at some point
  '("800000010"
    "031008264"
    "090060000"
    "006000037"
    "000936000"
    "140000800"
    "000040070"
    "659300140"
    "010000008"))

(define (string-set string n char)
  (string-append (substring string 0 n) (symbol->string char) (substring string (+ n 1) (string-length string))))
  

(define (board-insert row col char board)
  (let ((new-board '()))
  (do ((my-board board (cdr my-board)))
      ((null? my-board) new-board)
    (cond ((eq? (length new-board) row)
           (set! new-board (append new-board (list (string-set (car my-board) col char)))))
           (else (set! new-board (append new-board (list (car my-board)))))))))

(define (valid? num row col board)
  (let ((valid #t)
        (num (integer->char (+ (char->integer #\0) num)))
        (br (mod row 3))
        (bc (mod col 3)))
  (do ((count 0 (+ count 1)))
      ((or (not valid) (= count 9)) valid)
    (if (and (eq? (charAt row count board) num) (not (eq? row count)))
        (set! valid #f))
    (if (and (eq? (charAt (+ br (mod count 3)) (+ bc (truncate (/ count 3))) board) num)
             (not (eq? (+ br (mod count 3)) row)))
             (not (eq? (+ bc (truncate (/ count 3))) col))
        (set! valid #f))
    (if (and (eq? (charAt count col board) num) (not (eq? col count)))
        (set! valid #f)))))

(define (solve-board board)
  (let ((valid #t))
  (do ((rowCount 0 (+ rowCount 1)))
      ((= rowCount 9))
    (do ((colCount 0 (+ colCount 1)))
        ((= colCount 9))
      (if (eq? (string-ref (getRow board rowCount) colCount) #\0)
        (do ((testCount 0 (+ testCount 1))) ; Ok, its a zero -- we need to solve for this digit
            ((= testCount 9))
          (if (valid? testCount rowCount colCount board)
              (solve-board (board-insert rowCount colCount (string-ref (getRow board rowCount) colCount ) board))
              (set! valid #f))))))
    board))