64 lines
2.5 KiB
Groff
64 lines
2.5 KiB
Groff
00050 .PR POINT .PR
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00110 # QUEEN #
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00120 .COMMENT THIS PROGRAM PLACES 8 QUEENS ON A CHESSBOARD
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00130 SUCH THAT NO TWO QUEENS ATTACK ONE ANOTHER. THE METHOD USED
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00140 IS OF RECURSIVE DESCENT : ALL VALID POSSIBILITIES
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00150 ON A GIVEN ROW ARE TRIED - EACH PRODUCES ANOTHER BRANCH OF
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00160 POSSIBILITIES ON FURTHER ROWS. IF A QUEEN MAY BE PLACED ON THE
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00170 LAST ROW THEN THIS IS A SOLUTION AND IS OUTPUT.
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00180 NOTE: TO SAVE MACHINE TIME SIMPLE REFLECTIONS ARE PRODUCED
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00190 MECHANICALLY IF EXHAUSTIVE SOLUTIONS ARE ONLY FOUND FOR
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00200 THE QUEEN ON THE FIRST ROW POSITIONS 1,2,3,4. THE
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00210 SYMMETRY OF THE CHESSBOARD MEANS THAT SOLUTIONS WITH
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00220 THE QUEEN IN ROW 1 IN POSITIONS 5,6,7,8 CORRESPOND 1-1
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00230 WITH THESE.
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00240 .COMMENT
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00250 ##
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00260 .BEGIN
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00270 .LOC .INT ROW := 0, COUNTSOLN := 0;
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00280 .LOC[1:8].INT RESULT;
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00282 .LOC[1:8, -6:15].BOOL ALLOWS;
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00290 ##
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00300 .PROC SOLUTIONHEAD = .VOID:
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00310 .BEGIN PRINT((NEWLINE, "SOLUTION", WHOLE(COUNTSOLN, -5), ":- ")); COUNTSOLN +:=1 .END;
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00320 ##
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00330 .PROC PLACE = (.INT POSITION).VOID:
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00340 .COMMENT THIS IS A RECURSIVE PROCEDURE.
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00350 IT ALLOCATES ALL POSSIBLE VALUES IN THE CURRENT ROW AS DEFINED
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00360 BY EACH ROW. AFTER CONSIDERING WHICH SQUARES ARE NOT PERMISSIBLE
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00370 (BECAUSE ALREADY ATTACKED), IT OUTPUTS ANY SOLUTIONS IT FINDS
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00380 (I.E. WHEN WE REACH THE LAST ROW).
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00390 .COMMENT
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00400 .BEGIN
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00420 ROW +:= 1; RESULT[ROW] := POSITION;
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00422 .REF [] .BOOL ALLOW = ALLOWS[ROW, ];
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00430 .IF ROW=8
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00440 .THEN #WE HAVE FOUND SOLUTION NUMBER COUNTSOLN
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00450 SO OUTPUT IT#
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00460 SOLUTIONHEAD;
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00470 .FOR K .TO 8 .DO PRINT(.REPR(RESULT[K]+.ABS"0")) .OD;
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00480 SOLUTIONHEAD;
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00490 .FOR K .TO 8 .DO PRINT(.REPR(9-RESULT[K]+.ABS"0")) .OD
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00500 .ELSE
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00510 .FOR I .TO 8 .DO ALLOW[I] := .TRUE .OD;
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00520 #DISALLOW ATTACKED SQUARES#
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00530 .FOR I .TO ROW
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00540 .DO .INT RES = RESULT[I];
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00550 ALLOW[RES] := .FALSE;
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00560 ALLOW[RES+ROW+1-I] := .FALSE;
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00570 ALLOW[RES-ROW-1+I] := .FALSE
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00580 .OD;
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00590 #CONSTRUCT ANOTHER LEVEL WHERE POSSIBLE#
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00600 .FOR I .TO 8 .DO .IF ALLOW[I] .THEN PLACE(I) .FI .OD
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00610 .FI;
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00620 #NOW UP A LEVEL#
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00630 ROW -:= 1
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00640 .END; #OF PLACE#
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00650 ##
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00660 #INITIALISE OUTPUT#
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00670 PRINT(("PLACEMENT OF QUEENS SUCH THAT NO TWO"
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00680 " ATTACK EACH OTHER", NEWLINE));
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00690 .FOR J .TO 4 .DO PLACE(J) .OD;
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00700 #TIDY UP OUTPUT#
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00710 PRINT(("LIST COMPLETE", NEWLINE))
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00720 .END
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