64 lines
1.8 KiB
Text
64 lines
1.8 KiB
Text
/*Knights.mathprog
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Find a Knights Tour
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Nigel_Galloway
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January 11th., 2012
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*/
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param ZBLS;
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param ROWS;
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param COLS;
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param D := 2;
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set ROWSR := 1..ROWS;
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set COLSR := 1..COLS;
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set ROWSV := (1-D)..(ROWS+D);
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set COLSV := (1-D)..(COLS+D);
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param Iz{ROWSR,COLSR}, integer, default 0;
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set ZBLSV := 1..(ZBLS+1);
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set ZBLSR := 1..ZBLS;
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var BR{ROWSV,COLSV,ZBLSV}, binary;
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void0{r in ROWSV, z in ZBLSR,c in (1-D)..0}: BR[r,c,z] = 0;
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void1{r in ROWSV, z in ZBLSR,c in (COLS+1)..(COLS+D)}: BR[r,c,z] = 0;
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void2{c in COLSV, z in ZBLSR,r in (1-D)..0}: BR[r,c,z] = 0;
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void3{c in COLSV, z in ZBLSR,r in (ROWS+1)..(ROWS+D)}: BR[r,c,z] = 0;
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void4{r in ROWSV,c in (1-D)..0}: BR[r,c,ZBLS+1] = 1;
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void5{r in ROWSV,c in (COLS+1)..(COLS+D)}: BR[r,c,ZBLS+1] = 1;
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void6{c in COLSV,r in (1-D)..0}: BR[r,c,ZBLS+1] = 1;
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void7{c in COLSV,r in (ROWS+1)..(ROWS+D)}: BR[r,c,ZBLS+1] = 1;
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Izfree{r in ROWSR, c in COLSR, z in ZBLSR : Iz[r,c] = -1}: BR[r,c,z] = 0;
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Iz1{Izr in ROWSR, Izc in COLSR, r in ROWSR, c in COLSR, z in ZBLSR : Izr=r and Izc=c and Iz[Izr,Izc]=z}: BR[r,c,z] = 1;
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rule1{z in ZBLSR}: sum{r in ROWSR, c in COLSR} BR[r,c,z] = 1;
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rule2{r in ROWSR, c in COLSR}: sum{z in ZBLSV} BR[r,c,z] = 1;
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rule3{r in ROWSR, c in COLSR, z in ZBLSR}: BR[0,0,z+1] + BR[r-1,c-2,z+1] + BR[r-1,c+2,z+1] + BR[r-2,c-1,z+1] + BR[r-2,c+1,z+1] + BR[r+1,c+2,z+1] + BR[r+1,c-2,z+1] + BR[r+2,c-1,z+1] + BR[r+2,c+1,z+1] - BR[r,c,z] >= 0;
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solve;
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for {r in ROWSR} {
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for {c in COLSR} {
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printf " %2d", sum{z in ZBLSR} BR[r,c,z]*z;
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}
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printf "\n";
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}
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data;
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param ROWS := 8;
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param COLS := 8;
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param ZBLS := 64;
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param
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Iz: 1 2 3 4 5 6 7 8 :=
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1 . . . . . . . .
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2 . . . . . . 48 .
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3 . . . . . . . .
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4 . . . . . . . .
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5 . . . . . . . .
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6 . . . . . . . .
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7 . 58 . . . . . .
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8 . . . . . . . .
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;
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end;
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