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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.VF;
import solver.variables.VariableFactory;
import util.ESat;
import java.util.Arrays;
/**
* CSPLib prob049:<br/>
* "This problem consists in finding a partition of numbers 1..N into two sets A and B such that:
* <ul>
* <li>A and B have the same cardinality</li>
* <li>sum of numbers in A = sum of numbers in B</li>
* <li>sum of squares of numbers in A = sum of squares of numbers in B</li>
* </ul>
* <p/>
* More constraints can thus be added, e.g also impose the equality on the sum of cubes.
* There is no solution for N < 8."
* <p/>
* <br/>
*
* @author Charles Prud'homme
* @since 31/03/11
*/
public class Partition extends AbstractProblem {
@Option(name = "-n", usage = "Partition size.", required = false)
int N = 2 * 32;
IntVar[] vars;
IntVar[] Ovars;
Constraint[] heavy = new Constraint[3];
@Override
public void createSolver() {
solver = new Solver("Partition " + N);
}
@Override
public void buildModel() {
int size = this.N / 2;
IntVar[] x, y;
x = VariableFactory.enumeratedArray("x", size, 1, 2 * size, solver);
y = VariableFactory.enumeratedArray("y", size, 1, 2 * size, solver);
// break symmetries
for (int i = 0; i < size - 1; i++) {
solver.post(IntConstraintFactory.arithm(x[i], "<", x[i + 1]));
solver.post(IntConstraintFactory.arithm(y[i], "<", y[i + 1]));
}
solver.post(IntConstraintFactory.arithm(x[0], "<", y[0]));
solver.post(IntConstraintFactory.arithm(x[0], "=", 1));
IntVar[] xy = new IntVar[2 * size];
for (int i = size - 1; i >= 0; i--) {
xy[i] = x[i];
xy[size + i] = y[i];
}
Ovars = new IntVar[2 * size];
for (int i = 0; i < size; i++) {
Ovars[i * 2] = x[i];
Ovars[i * 2 + 1] = y[i];
}
int[] coeffs = new int[2 * size];
for (int i = size - 1; i >= 0; i--) {
coeffs[i] = 1;
coeffs[size + i] = -1;
}
heavy[0] = IntConstraintFactory.scalar(xy, coeffs, VariableFactory.fixed(0, solver));
solver.post(heavy[0]);
IntVar[] sxy, sx, sy;
sxy = new IntVar[2 * size];
sx = new IntVar[size];
sy = new IntVar[size];
for (int i = size - 1; i >= 0; i--) {
sx[i] = VF.bounded("x^", 0, x[i].getUB() * x[i].getUB(), solver);
sxy[i] = sx[i];
sy[i] = VF.bounded("y^", 0, y[i].getUB() * y[i].getUB(), solver);
sxy[size + i] = sy[i];
solver.post(IntConstraintFactory.times(x[i], x[i], sx[i]));
solver.post(IntConstraintFactory.times(y[i], y[i], sy[i]));
solver.post(IntConstraintFactory.member(sx[i], 1, 4 * size * size));
solver.post(IntConstraintFactory.member(sy[i], 1, 4 * size * size));
}
heavy[1] = IntConstraintFactory.scalar(sxy, coeffs, VariableFactory.fixed(0, solver));
solver.post(heavy[1]);
coeffs = new int[size];
Arrays.fill(coeffs, 1);
solver.post(IntConstraintFactory.scalar(x, coeffs, VariableFactory.fixed(2 * size * (2 * size + 1) / 4, solver)));
solver.post(IntConstraintFactory.scalar(y, coeffs, VariableFactory.fixed(2 * size * (2 * size + 1) / 4, solver)));
solver.post(IntConstraintFactory.scalar(sx, coeffs, VariableFactory.fixed(2 * size * (2 * size + 1) * (4 * size + 1) / 12, solver)));
solver.post(IntConstraintFactory.scalar(sy, coeffs, VariableFactory.fixed(2 * size * (2 * size + 1) * (4 * size + 1) / 12, solver)));
heavy[2] = IntConstraintFactory.alldifferent(xy, "BC");
solver.post(heavy[2]);
vars = xy;
}
@Override
public void configureSearch() {
solver.set(IntStrategyFactory.minDom_LB(Ovars));
}
@Override
public void solve() {
solver.findSolution();
}
@Override
public void prettyOut() {
StringBuilder st = new StringBuilder();
if (ESat.TRUE == solver.isFeasible()) {
int sum1 = 0, sum2 = 0;
int i = 0;
st.append(vars[i].getValue());
sum1 += vars[i].getValue();
sum2 += vars[i].getValue() * vars[i++].getValue();
for (; i < N / 2; i++) {
st.append(", ").append(vars[i].getValue());
sum1 += vars[i].getValue();
sum2 += vars[i].getValue() * vars[i].getValue();
}
st.append(": (").append(sum1).append(")~(").append(sum2).append(")\n");
sum1 = sum2 = 0;
st.append(vars[i].getValue());
sum1 += vars[i].getValue();
sum2 += vars[i].getValue() * vars[i++].getValue();
for (; i < N; i++) {
st.append(", ").append(vars[i].getValue());
sum1 += vars[i].getValue();
sum2 += vars[i].getValue() * vars[i].getValue();
}
st.append(": (").append(sum1).append(")~(").append(sum2).append(")\n");
} else {
st.append("INFEASIBLE");
}
LoggerFactory.getLogger("bench").info(st.toString());
}
public static void main(String[] args) {
new Partition().execute(args);
}
}