Top- Based Adaptive Enumeration in Constraint Programming

Algorithm 4

:-lib(ic).

magic(N):-

 NN is N*N,

 Sum is N*(NN+1)//2,

 dim(Square, N,N),

 Square:: 1..NN,

 alldifferent(Square),

 (for(I,1,N),

  foreach(U,UpDiag),

  foreach(D,DownDiag),

  param(N,Square,Sum)

 do

  Sum #= sum(SquareI,1..N),

  Sum #= sum(Square1..N,I),

  U is SquareI,I,

  D is SquareI,N+1-I

 ),

 Sum #= sum(UpDiag),

 Sum #= sum(DownDiag),

 Square1,1  #< Square1,N,

 Square1,1  #< SquareN,N,

 Square1,1  #< SquareN,1,

 Square1,N  #< SquareN,1,

 % call to search predicate

 write(Square).