LPL - A Mathematical Modeling Language

model intersec "Find No-intersecting Paths";
  set i,j     := [1..7]  "A set of columns and rows";
      k,k1,k2 := [1..3]  "Three colors (paths)";
  parameter a{i,j} "Initial assignment of colors"
     := [(1,4)=1, (7,4)=1, (4,1)=2, (4,5)=2, 
         (4,3)=3, (4,7)=3];
  binary variable x{k,i,j}; 
  constraint
    I{k,i,j|a=k}: x[k,i,j]=1;
    N{k,i,j|a=k}: x[k,i,j+1]+x[k,i-1,j+1]+x[k,i-1,j]
       +x[k,i-1,j-1]+x[k,i,j-1]+x[k,i+1,j-1]
       +x[k,i+1,j]+x[k,i+1,j+1] = 1;
    NN{k,i,j|a[i,j]<>k}: x[k,i,j] ->( x[k,i,j+1]
      +x[k,i-1,j+1]+x[k,i-1,j]+x[k,i-1,j-1]+x[k,i,j-1]
      +x[k,i+1,j-1]+x[k,i+1,j]+x[k,i+1,j+1] = 2);
    E{i,j}: atmost(1){k} x[k,i,j];
    K{i,j,k1,k2|k1<>k2 and i<#i and j<#j}:
      x[k1,i,j] and x[k1,i+1,j+1] and x[k2,i+1,j] 
        -> ~x[k2,i,j+1]; 
  minimize pathL: sum{k,i,j} x[k,i,j];
 
  Write('path length = %2d\n %3s  \n', pathL, {i}i); 
  Write{i}(' %s %s  \n', i, {j} if (x[1,i,j],'x  ',
             x[2,i,j],'*  ',x[3,i,j],'+  ','   ')); 
  Draw.Scale(30,30);
	{i,j,k} Draw.Rect(if(x,k&''),j,i,1,1,if(x,k+6,-1));  
end

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