N 个皇后

问题描述

将n个皇后放在n大小的棋盘上，没有两个皇后可以互相攻击。 最常见的 n 个皇后谜题是八个皇后谜题，n = 8：

约束：

• 使用 n 列和 n 行的棋盘。
• 在棋盘上放置n个皇后。
• 没有两个女王可以互相攻击。女王可以攻击同一水平线、垂直线或对角线上的任何其他女王。

求解结果（time limit 5s）

问题大小

n	搜索空间
4	256
8	10^7
16	10^19
32	10^48
64	10^115
256	10^616

域模型

@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;
}

例如：

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

(*)(**)的皇后可以互相攻击

求解器（约束提供者）

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");
    }
}

应用

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());
            }
        }
    }
}