My code for solving n queens problem Compile Failed

Question

I want to make my code for solving n-queens problem faster, but it seems that MapIndexed can't be compiled. Mathematica return

CompiledFunction::cfse: Compiled expression If[Abs[1-Compile`GetElement[{2},1]]==1,Throw[False]] should be a machine-size real number. >>

Clear["`*"];
safe[col_, queens_] := 
  FreeQ[queens, col] && 
   Catch[MapIndexed[
     If[Abs[col - #] == Length@queens - First@#2 + 1, Throw@False] &, 
     queens];
    True];

safeCompiled = 
  Compile[{{col, _Integer}, {queens, _Integer, 1}}, 
   FreeQ[queens, col] && 
    Catch[MapIndexed[
      If[Abs[col - #] == Length@queens - First@#2 + 1, Throw@False] &,
       queens];
     True]
   ];

8 /. size_ :>
    Nest[Table[sol~Append~i, 
      {i, size}, {sol, Select[#, safeCompiled[i, #] &]}]~Flatten~1 &,
     {{}}, size] // Length // AbsoluteTiming

Updated

A bit faster version:

safe = Compile[{{col, _Integer}, {queens, _Integer, 1}}, 
   If[MemberQ[queens, col], Return@0];
   Catch[Do[If[Abs[col - queens[[i]] ] == Length@queens - i + 1, Throw@0],
      {i, Length@queens}]; 1],
   RuntimeAttributes -> Listable];

size = 11;
iter = Table[Append[sol, i], {i, size}, {sol, Pick[#, safe[i, #], 1]}]~ Flatten~1 &;
Nest[iter, List /@ Range@size, size - 1] // Length // AbsoluteTiming

{1.083062, 2680}

Just in case http://www.lauschkeconsulting.net/nqueens.html – Dr. belisarius Nov 08 '13 at 15:59 — Dr. belisarius, Nov 08 '13 at 15:59

score 3 · Accepted Answer · answered Nov 09 '13 at 03:51

The problem is with the return value of

If[Abs[col - #] == Length@queens - First@#2 + 1, Throw@False] &

which needs to be of a type handled by Compile. The If statement returns Null when the test is not True, and Compile does not support Null.

One fix is to make the value of the function be 0 (or whatever, since this value is not used).

safeCompiled = 
 Compile[{{col, _Integer}, {queens, _Integer, 1}}, 
  FreeQ[queens, col] && 
   Catch[MapIndexed[(If[Abs[col - #] == Length@queens - First@#2 + 1, 
        Throw@False]; 0) &, queens];
    True]]

A slightly more efficient approach is to use Do, since the list created by MapThread is immaterial.

safeCompiled = 
 Compile[{{col, _Integer}, {queens, _Integer, 1}}, 
  FreeQ[queens, col] && 
   Catch[Do[
     If[Abs[col - queens[[i]]] == Length@queens - i + 1, Throw@False],
     {i, Length @ queens}];
    True]]

8 /. size_ :> 
    Nest[Table[sol ~Append~ i,
      {i, size}, {sol, Select[#, safeCompiled[i, #] &]}] ~Flatten~ 1 &,
      {{}}, size] // Length // AbsoluteTiming
(* {0.023975, 92} *)

score 0 · Answer 2 · edited Apr 13 '17 at 12:56

0

MapIndexed is not a compilable function until Mathematica 9. See more information in this question.

edited Apr 13 '17 at 12:56

Community

1

answered Nov 08 '13 at 15:25

Murta

26,275
6
76
166

Try Compile`CompilerFunctions[]~MemberQ~MapIndexed. – expression Nov 08 '13 at 15:45

My code for solving n queens problem Compile Failed

2 Answers2