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package samples.integer;
import org.kohsuke.args4j.Option;
import samples.AbstractProblem;
import solver.ResolutionPolicy;
import solver.Solver;
import solver.constraints.Constraint;
import solver.constraints.IntConstraintFactory;
import solver.search.strategy.IntStrategyFactory;
import solver.variables.IntVar;
import solver.variables.VariableFactory;
/**
* CSPLib prob006:<br/>
* A Golomb ruler may be defined as a set of m integers 0 = a_1 < a_2 < ... < a_m such that
* the m(m-1)/2 differences a_j - a_i, 1 <= i < j <= m are distinct.
* Such a ruler is said to contain m marks and is of length a_m.
* <br/>
* The objective is to find optimal (minimum length) or near optimal rulers.
* <br/>
*
* @author Charles Prud'homme
* @revision 04/03/12 revise model : remove views
* @since 31/03/11
*/
public class GolombRuler extends AbstractProblem {
@Option(name = "-m", usage = "Golomb ruler order.", required = false)
private int m = 10;
IntVar[] ticks;
IntVar[] diffs;
IntVar[][] m_diffs;
Constraint[] lex;
Constraint alldiff;
Constraint[] distances;
@Override
public void createSolver() {
solver = new Solver("Golomb Ruler");
}
@Override
public void buildModel() {
ticks = VariableFactory.enumeratedArray("a", m, 0, ((m < 31) ? (1 << (m + 1)) - 1 : 9999), solver);
solver.post(IntConstraintFactory.arithm(ticks[0], "=", 0));
lex = new Constraint[m - 1];
for (int i = 0; i < m - 1; i++) {
lex[i] = IntConstraintFactory.arithm(ticks[i + 1], ">", ticks[i]);
}
solver.post(lex);
diffs = VariableFactory.enumeratedArray("d", (m * m - m) / 2, 0, ((m < 31) ? (1 << (m + 1)) - 1 : 9999), solver);
m_diffs = new IntVar[m][m];
distances = new Constraint[(m * m - m) / 2];
for (int k = 0, i = 0; i < m - 1; i++) {
for (int j = i + 1; j < m; j++, k++) {
// d[k] is m[j]-m[i] and must be at least sum of first j-i integers
// <cpru 04/03/12> it is worth adding a constraint instead of a view
distances[k] = IntConstraintFactory.scalar(new IntVar[]{ticks[j], ticks[i]}, new int[]{1, -1}, diffs[k]);
solver.post(distances[k]);
solver.post(IntConstraintFactory.arithm(diffs[k], ">=", (j - i) * (j - i + 1) / 2));
solver.post(IntConstraintFactory.arithm(diffs[k], "-", ticks[m - 1], "<=", -((m - 1 - j + i) * (m - j + i)) / 2));
solver.post(IntConstraintFactory.arithm(diffs[k], "<=", ticks[m - 1], "-", ((m - 1 - j + i) * (m - j + i)) / 2));
m_diffs[i][j] = diffs[k];
}
}
alldiff = IntConstraintFactory.alldifferent(diffs, "BC");
solver.post(alldiff);
// break symetries
if (m > 2) {
solver.post(IntConstraintFactory.arithm(diffs[0], "<", diffs[diffs.length - 1]));
}
}
@Override
public void configureSearch() {
solver.set(IntStrategyFactory.lexico_LB(ticks));
}
@Override
public void solve() {
solver.findOptimalSolution(ResolutionPolicy.MINIMIZE, (IntVar) solver.getVars()[m - 1]);
}
@Override
public void prettyOut() {
}
public static void main(String[] args) {
new GolombRuler().execute(args);
}
}