N queens
Problem Description
Put n queens on a chessboard of n size, and no two queens can attack each other. The most common n-queens puzzle is the eight-queen puzzle, n = 8:
Constraints:
- Use a board with n columns and n rows.
- Place n queens on the chessboard.
- No two queens can fight each other. A queen can attack any other queen on the same horizontal, vertical, or diagonal line.
Solution results (time limit 5s)
Problem size
| n | search space |
|---|---|
| 4 | 256 |
| 8 | 10^7 |
| 16 | 10^19 |
| 32 | 10^48 |
| 64 | 10^115 |
| 256 | 10^616 |
domain model
@Data
@AllArgsConstructor
public class Column {
private int index;
}
@Data
@AllArgsConstructor
public class Row {
private int index;
}
@Data
@AllArgsConstructor
@NoArgsConstructor
@PlanningEntity
public class Queen {
@PlanningId
private Integer id;
@PlanningVariable
private Column column;
@PlanningVariable
private Row row;
// 升序对角线索引（左上到右下）
public int getAscendingDiagonalIndex() {
return column.getIndex() + row.getIndex();
}
// 降序对角线索引（左下到右上）
public int getDescendingDiagonalIndex() {
return column.getIndex() - row.getIndex();
}
}
@Data
@AllArgsConstructor
@NoArgsConstructor
@PlanningSolution
public class NQueen {
@ValueRangeProvider
@ProblemFactCollectionProperty
private List<Column> columnList;
@ValueRangeProvider
@ProblemFactCollectionProperty
private List<Row> rowList;
@PlanningEntityCollectionProperty
private List<Queen> queenList;
@PlanningScore
private HardSoftScore score;
}
For example:
| Queen | Column | Row | AscendingDiagonalIndex | DescendingDiagonalIndex |
|---|---|---|---|---|
| A1 | 0 | 1 | 1 (**) | -1 |
| B0 | 1 | 0 (*) | 1 (**) | 1 |
| C2 | 2 | 2 | 4 | 0 |
| D0 | 3 | 0 (*) | 3 | 3 |
(*)(**) queens can attack each other
Solver (constraint provider)
public class NQueenConstraintProvider implements ConstraintProvider {
@Override
public Constraint[] defineConstraints(ConstraintFactory constraintFactory) {
return new Constraint[]{
// 列冲突
columnConflict(constraintFactory),
// 行冲突
rowConflict(constraintFactory),
// 升序对角线冲突
ascendingDiagonalIndexConflict(constraintFactory),
// 降序对角线冲突
descendingDiagonalIndexConflict(constraintFactory),
};
}
public Constraint columnConflict(ConstraintFactory constraintFactory) {
return constraintFactory
.forEach(Queen.class)
.join(Queen.class,
Joiners.equal(Queen::getColumn),
Joiners.lessThan(Queen::getId))
.penalize(HardSoftScore.ONE_HARD)
.asConstraint("Column conflict");
}
public Constraint rowConflict(ConstraintFactory constraintFactory) {
return constraintFactory
.forEach(Queen.class)
.join(Queen.class,
Joiners.equal(Queen::getRow),
Joiners.lessThan(Queen::getId))
.penalize(HardSoftScore.ONE_HARD)
.asConstraint("Row conflict");
}
public Constraint ascendingDiagonalIndexConflict(ConstraintFactory constraintFactory) {
return constraintFactory
.forEach(Queen.class)
.join(Queen.class,
Joiners.equal(Queen::getAscendingDiagonalIndex),
Joiners.lessThan(Queen::getId))
.penalize(HardSoftScore.ONE_HARD)
.asConstraint("AscendingDiagonalIndex conflict");
}
public Constraint descendingDiagonalIndexConflict(ConstraintFactory constraintFactory) {
return constraintFactory
.forEach(Queen.class)
.join(Queen.class,
Joiners.equal(Queen::getDescendingDiagonalIndex),
Joiners.lessThan(Queen::getId))
.penalize(HardSoftScore.ONE_HARD)
.asConstraint("DescendingDiagonalIndex conflict");
}
}
application
public class NQueenApp {
public static void main(String[] args) {
SolverFactory<NQueen> solverFactory = SolverFactory.create(new SolverConfig()
.withSolutionClass(NQueen.class)
.withEntityClasses(Queen.class)
.withConstraintProviderClass(NQueenConstraintProvider.class)
.withTerminationSpentLimit(Duration.ofSeconds(5)));
NQueen problem = generateDemoData();
Solver<NQueen> solver = solverFactory.buildSolver();
NQueen solution = solver.solve(problem);
printTimetable(solution);
}
public static NQueen generateDemoData() {
List<Column> columnList = new ArrayList<>();
List<Row> rowList = new ArrayList<>();
List<Queen> queenList = new ArrayList<>();
for (int i = 0; i < 8; i++) {
columnList.add(new Column(i));
rowList.add(new Row(i));
queenList.add(new Queen(i, null, null));
}
return new NQueen(columnList, rowList, queenList, null);
}
private static void printTimetable(NQueen nQueen) {
System.out.println("");
List<Column> columnList = nQueen.getColumnList();
List<Row> rowList = nQueen.getRowList();
List<Queen> queenList = nQueen.getQueenList();
Map<Column, Map<Row, List<Queen>>> queenMap = queenList.stream()
.filter(queen -> queen.getColumn() != null && queen.getRow() != null)
.collect(Collectors.groupingBy(Queen::getColumn, Collectors.groupingBy(Queen::getRow)));
System.out.println("| | " + columnList.stream()
.map(room -> String.format("%-3s", room.getIndex())).collect(Collectors.joining(" | ")) + " |");
System.out.println("|" + "-----|".repeat(columnList.size() + 1));
for (Column column : columnList) {
List<List<Queen>> cellList = rowList.stream()
.map(row -> {
Map<Row, List<Queen>> byRowMap = queenMap.get(column);
if (byRowMap == null) {
return Collections.<Queen>emptyList();
}
List<Queen> cellQueenList = byRowMap.get(row);
if (cellQueenList == null) {
return Collections.<Queen>emptyList();
}
return cellQueenList;
})
.collect(Collectors.toList());
System.out.println("| " + String.format("%-3s", column.getIndex()) + " | "
+ cellList.stream().map(cellQueenList -> String.format("%-3s",
cellQueenList.stream().map(queen -> queen.getId().toString()).collect(Collectors.joining(", "))))
.collect(Collectors.joining(" | "))
+ " |");
System.out.println("|" + "-----|".repeat(columnList.size() + 1));
}
List<Queen> unassignedQueens = queenList.stream()
.filter(Queen -> Queen.getColumn() == null || Queen.getRow() == null)
.collect(Collectors.toList());
if (!unassignedQueens.isEmpty()) {
System.out.println("");
System.out.println("Unassigned Queens");
for (Queen Queen : unassignedQueens) {
System.out.println(" " + Queen.getColumn() + " - " + Queen.getRow());
}
}
}
}