;;;Programmed by Ron Danielson, 1/31/00

;;;

;;;This set of functions finds one solution for the N queens problem.

;;;Rows are tested sequentially, with a recursive function to trial

;;;place a queen in various columns on that row.

(DEFINE (SAFE board row col)

;;There is no diagonal attack if none of the queens already on the board

;;are in the same column, or have a slope of 1 or -1 from the tested

;;position (checked by subtracting corresponding row and column

;;coordinates, comparing absolute values of result).

(DO ((test board (CDR test))

(result #t)

)

((null? test) result)

(COND ((OR (EQUAL? (ABS (- row (CAAR test)))

(ABS (- col (CADAR test)))

)

(EQUAL? col (CADAR test))

)

(SET! result #f))

)

)

)

(DEFINE (PRINTSOLN board)

;;Recursively traverse board, printing out each queen as it's encountered.

(COND ((NULL? board) #t)

(ELSE (DISPLAY (CAAR board))

(DISPLAY ", ")

(DISPLAY (CADAR board))

(DISPLAY "; ")

(PRINTSOLN (CDR board))

)

)

)

(DEFINE (TRYROW currow n board)

(DO ((col 1 (+ col 1)) ;for col := 1 to n

(soln #f) ;set T when solution found

)

((OR (> col n) soln) soln) ;stop loop if > n or solution found

(COND ((safe board currow col) ;check current position

(SET! board (CONS (LIST currow col) board)) ;add if OK

(COND ((< currow n) (SET! soln (tryrow (+ currow 1) n board)))

;;if row < n, try next row

(ELSE (SET! soln (printsoln board))) ;solution found

)

(SET! board (CDR board)) ;backtrack - remove previous queen

)

)

)

)

(DEFINE (QUEENS n)

(tryrow 1 n ())

)