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#lang racket
(define (pos board r c)
(list-ref (list-ref board r) c))
(define (scan-for-duplicates array)
(andmap (λ (row) (not (check-duplicates row)))
(map (curry filter-not (curry equal? ".")) array)))
(define (check-rows board)
(scan-for-duplicates board))
(define (check-cols board)
(scan-for-duplicates (apply map list board)))
(define (check-boxes board)
(define boxes-to-lists
(for*/list ([r (in-list '(0 3 6))]
[c (in-list '(0 3 6))])
(for*/list ([box-r (in-range r (+ r 3))]
[box-c (in-range c (+ c 3))]
#:unless (equal? "." (pos board box-r box-c)))
(pos board box-r box-c))))
(scan-for-duplicates boxes-to-lists))
(define/contract (is-valid-sudoku board)
(-> (listof (listof string?)) boolean?)
(and (check-rows board)
(check-cols board)
(check-boxes board)))
(define valid-sudoku '[["5" "3" "." "." "7" "." "." "." "."] ["6" "." "." "1" "9" "5" "." "." "."] ["." "9" "8" "." "." "." "." "6" "."] ["8" "." "." "." "6" "." "." "." "3"] ["4" "." "." "8" "." "3" "." "." "1"] ["7" "." "." "." "2" "." "." "." "6"] ["." "6" "." "." "." "." "2" "8" "."] ["." "." "." "4" "1" "9" "." "." "5"] ["." "." "." "." "8" "." "." "7" "9"]])
(define invalid-sudoku '[["8" "3" "." "." "7" "." "." "." "."] ["6" "." "." "1" "9" "5" "." "." "."] ["." "9" "8" "." "." "." "." "6" "."] ["8" "." "." "." "6" "." "." "." "3"] ["4" "." "." "8" "." "3" "." "." "1"] ["7" "." "." "." "2" "." "." "." "6"] ["." "6" "." "." "." "." "2" "8" "."] ["." "." "." "4" "1" "9" "." "." "5"] ["." "." "." "." "8" "." "." "7" "9"]])
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