1. CSPlib
  2. Problems
  3. prob019
  4. Models
  5. MagicSquare_oscar.scala

019: Magic Squares and Sequences

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/*******************************************************************************
 * OscaR is free software: you can redistribute it and/or modify
 * it under the terms of the GNU Lesser General Public License as published by
 * the Free Software Foundation, either version 2.1 of the License, or
 * (at your option) any later version.
 *  
 * OscaR is distributed in the hope that it will be useful,
 * but WITHOUT ANY WARRANTY; without even the implied warranty of
 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 * GNU Lesser General Public License  for more details.
 *  
 * You should have received a copy of the GNU Lesser General Public License along with OscaR.
 * If not, see http://www.gnu.org/licenses/lgpl-3.0.en.html
 ******************************************************************************/
package oscar.examples.cp.hakank
 
import oscar.cp.modeling._
 
import oscar.cp.core._
import scala.math._
 
/**
 
  Magic square in Oscar.
 
 
  @author Hakan Kjellerstrand hakank@gmail.com
  http://www.hakank.org/oscar/
 
 */
object MagicSquare {
 
  
  def main(args: Array[String]) {
 
    val cp = CPSolver()
 
    val n = if (args.length > 0) args(0).toInt else 4;
    val num_to_show = if (args.length > 1) args(1).toInt else 0;
 
    val n2 = n*n
 
    println("n:" + n + " num_to_show: " + num_to_show)
 
    //
    // variables
    //
    val x = Array.fill(n,n)(CPIntVar(1 to n2)(cp))
    val x_t = x.transpose
 
    // val total = CPIntVar(cp, 1 to n*n*n)
    val total = (n * (n*n + 1) / 2)
 
    //
    // constraints
    //
 
    cp.solve subjectTo {
 
       cp.add(allDifferent(x.flatten), Strong)
 
       // rows and columns
       for(i <- 0 until n) {
         cp.add(sum(x(i)) == total)
         cp.add(sum(x_t(i)) == total)
       }
   
       // diagonals
       cp.add(sum( for(i <- 0 until n) yield x(i)(i)) == total)
       cp.add(sum( for(i <- 0 until n) yield x(i)(n-i-1) ) == total)
 
       // symmetry breaking
       cp.add(x(0)(0)   < x(0)(n-1))
       cp.add(x(0)(n-1) < x(n-1)(0))
       cp.add(x(0)(0)   < x(n-1)(n-1))
 
 
     } search {
        
       binary(x.flatten.toSeq, _.size, _.min)
      
     } onSolution {
        
       println("\nSolution:\ntotal " + total)
       for(i <- 0 until n) {
         println(x(i).map(j=>"%3d".format(j.value)).mkString(""))
       }
       println()
        
     }
      
     println(cp.start(num_to_show))
   }
 
}