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package samples.integer;
import org.kohsuke.args4j.Option;
import org.slf4j.LoggerFactory;
import samples.AbstractProblem;
import solver.Solver;
import solver.constraints.Constraint;
import solver.constraints.IntConstraintFactory;
import solver.search.strategy.IntStrategyFactory;
import solver.variables.IntVar;
import solver.variables.VariableFactory;
import util.ESat;
/**
* CSPLib prob024:<br/>
* "Consider two sets of the numbers from 1 to 4.
* The problem is to arrange the eight numbers in the two sets into a single sequence in which
* the two 1's appear one number apart,
* the two 2's appear two numbers apart,
* the two 3's appear three numbers apart,
* and the two 4's appear four numbers apart.
* <p/>
* The problem generalizes to the L(k,n) problem,
* which is to arrange k sets of numbers 1 to n,
* so that each appearance of the number m is m numbers on from the last.
* <br/>
* For example, the L(3,9) problem is to arrange 3 sets of the numbers 1 to 9 so that
* the first two 1's and the second two 1's appear one number apart,
* the first two 2's and the second two 2's appear two numbers apart, etc."
* <p/>
* <br/>
*
* @author Charles Prud'homme
* @revision 04/03/12 revise model
* @since 19/08/11
*/
public class Langford extends AbstractProblem {
@Option(name = "-k", usage = "Number of sets.", required = false)
private int k = 3;
@Option(name = "-n", usage = "Upper bound.", required = false)
private int n = 9;
IntVar[] position;
Constraint[] lights;
Constraint alldiff;
@Override
public void createSolver() {
solver = new Solver("Langford number");
}
@Override
public void buildModel() {
// position of the colors
// position[i], position[i+k], position[i+2*k]... occurrence of the same color
position = VariableFactory.enumeratedArray("p", n * k, 0, k * n - 1, solver);
lights = new Constraint[(k - 1) * n + 1];
for (int i = 0; i < n; i++) {
for (int j = 0; j < this.k - 1; j++) {
lights[i + j * n] = IntConstraintFactory.arithm(VariableFactory.offset(position[i + j * n], i + 2), "=", position[i + (j + 1) * n]);
}
}
lights[(k - 1) * n] = IntConstraintFactory.arithm(position[0], "<", position[n * k - 1]);
solver.post(lights);
alldiff = IntConstraintFactory.alldifferent(position, "AC");
solver.post(alldiff);
}
@Override
public void configureSearch() {
solver.set(IntStrategyFactory.minDom_UB(position));
}
@Override
public void solve() {
solver.findSolution();
}
@Override
public void prettyOut() {
LoggerFactory.getLogger("bench").info("Langford's number ({},{})", k, n);
StringBuilder st = new StringBuilder();
if (solver.isFeasible() == ESat.TRUE) {
int[] values = new int[k * n];
for (int i = 0; i < k; i++) {
for (int j = 0; j < n; j++) {
values[position[i * n + j].getValue()] = j + 1;
}
}
st.append("\t");
for (int i = 0; i < values.length; i++) {
st.append(values[i]).append(" ");
}
st.append("\n");
} else {
st.append("\tINFEASIBLE");
}
LoggerFactory.getLogger("bench").info(st.toString());
}
public static void main(String[] args) {
new Langford().execute(args);
}
}