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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.IntConstraintFactory;
import solver.search.strategy.selectors.variables.ImpactBased;
import solver.variables.IntVar;
import solver.variables.VariableFactory;
import util.tools.StringUtils;
import java.text.MessageFormat;
import java.util.Arrays;
/**
* CSPLib prob019:<br/>
* "An order n magic square is a n by n matrix containing the numbers 1 to n^2, with each row,
* column and main diagonal equal the same sum.
* As well as finding magic squares, we are interested in the number of a given size that exist."
* <br/>
*
* @author Charles Prud'homme
* @since 31/03/11
*/
public class MagicSquare extends AbstractProblem {
@Option(name = "-n", usage = "Magic square size.", required = false)
int n = 5;
IntVar[] vars;
@Override
public void createSolver() {
solver = new Solver("Magic square");
}
@Override
public void buildModel() {
int ms = n * (n * n + 1) / 2;
IntVar[][] matrix = new IntVar[n][n];
IntVar[][] invMatrix = new IntVar[n][n];
vars = new IntVar[n * n];
int k = 0;
for (int i = 0; i < n; i++) {
for (int j = 0; j < n; j++, k++) {
matrix[i][j] = VariableFactory.enumerated("square" + i + "," + j, 1, n * n, solver);
vars[k] = matrix[i][j];
invMatrix[j][i] = matrix[i][j];
}
}
IntVar[] diag1 = new IntVar[n];
IntVar[] diag2 = new IntVar[n];
for (int i = 0; i < n; i++) {
diag1[i] = matrix[i][i];
diag2[i] = matrix[(n - 1) - i][i];
}
solver.post(IntConstraintFactory.alldifferent(vars, "BC"));
int[] coeffs = new int[n];
Arrays.fill(coeffs, 1);
IntVar msv = VariableFactory.fixed(ms, solver);
for (int i = 0; i < n; i++) {
solver.post(IntConstraintFactory.scalar(matrix[i], coeffs, msv));
solver.post(IntConstraintFactory.scalar(invMatrix[i], coeffs, msv));
}
solver.post(IntConstraintFactory.scalar(diag1, coeffs, msv));
solver.post(IntConstraintFactory.scalar(diag2, coeffs, msv));
// Symetries breaking
solver.post(IntConstraintFactory.arithm(matrix[0][n - 1], "<", matrix[n - 1][0]));
solver.post(IntConstraintFactory.arithm(matrix[0][0], "<", matrix[n - 1][n - 1]));
solver.post(IntConstraintFactory.arithm(matrix[0][0], "<", matrix[n - 1][0]));
}
@Override
public void configureSearch() {
solver.set(new ImpactBased(vars, 2, 3, 10, 29091981L, false));
}
@Override
public void solve() {
solver.findSolution();
}
@Override
public void prettyOut() {
StringBuilder st = new StringBuilder();
String line = "+";
for (int i = 0; i < n; i++) {
line += "----+";
}
line += "\n";
st.append(line);
for (int i = 0; i < n; i++) {
st.append("|");
for (int j = 0; j < n; j++) {
st.append(StringUtils.pad(vars[i * n + j].getValue() + "", -3, " ")).append(" |");
}
st.append(MessageFormat.format("\n{0}", line));
}
st.append("\n\n\n");
LoggerFactory.getLogger("bench").info(st.toString());
}
public static void main(String[] args) {
new MagicSquare().execute(args);
}
}