A*算法之八数码问题（java代码）

以下是使用A*算法解决八数码问题的Java代码：

import java.util.*;

public class EightPuzzleSolver {

    private static final int[] GOAL = {1, 2, 3, 4, 5, 6, 7, 8, 0};

    public static void main(String[] args) {
        Scanner scanner = new Scanner(System.in);
        System.out.println("Enter initial state of the puzzle (0 represents blank tile):");
        int[] initialState = new int[9];
        for (int i = 0; i < 9; i++) {
            initialState[i] = scanner.nextInt();
        }
        EightPuzzleSolver solver = new EightPuzzleSolver();
        List<State> solution = solver.solve(initialState);
        if (solution == null) {
            System.out.println("No solution found!");
        } else {
            System.out.println("Solution steps:");
            for (State state : solution) {
                System.out.println(state);
            }
        }
    }

    private PriorityQueue<State> open;
    private Set<State> closed;

    public EightPuzzleSolver() {
        open = new PriorityQueue<>();
        closed = new HashSet<>();
    }

    public List<State> solve(int[] initialState) {
        State initial = new State(initialState, null, 0, getHeuristic(initialState));
        open.add(initial);
        while (!open.isEmpty()) {
            State current = open.poll();
            if (Arrays.equals(current.tiles, GOAL)) {
                List<State> solution = new ArrayList<>();
                while (current != null) {
                    solution.add(current);
                    current = current.parent;
                }
                Collections.reverse(solution);
                return solution;
            }
            closed.add(current);
            int blankIndex = getBlankIndex(current.tiles);
            if (blankIndex - 3 >= 0) {
                int[] newTiles = swap(current.tiles, blankIndex, blankIndex - 3);
                State newState = new State(newTiles, current, current.moves + 1, getHeuristic(newTiles));
                if (!closed.contains(newState)) {
                    open.add(newState);
                }
            }
            if (blankIndex + 3 < 9) {
                int[] newTiles = swap(current.tiles, blankIndex, blankIndex + 3);
                State newState = new State(newTiles, current, current.moves + 1, getHeuristic(newTiles));
                if (!closed.contains(newState)) {
                    open.add(newState);
                }
            }
            if (blankIndex % 3 != 0) {
                int[] newTiles = swap(current.tiles, blankIndex, blankIndex - 1);
                State newState = new State(newTiles, current, current.moves + 1, getHeuristic(newTiles));
                if (!closed.contains(newState)) {
                    open.add(newState);
                }
            }
            if (blankIndex % 3 != 2) {
                int[] newTiles = swap(current.tiles, blankIndex, blankIndex + 1);
                State newState = new State(newTiles, current, current.moves + 1, getHeuristic(newTiles));
                if (!closed.contains(newState)) {
                    open.add(newState);
                }
            }
        }
        return null;
    }

    private int getHeuristic(int[] tiles) {
        int heuristic = 0;
        for (int i = 0; i < 9; i++) {
            if (tiles[i] != 0) {
                int rowDist = Math.abs(i / 3 - (tiles[i] - 1) / 3);
                int colDist = Math.abs(i % 3 - (tiles[i] - 1) % 3);
                heuristic += rowDist + colDist;
            }
        }
        return heuristic;
    }

    private int getBlankIndex(int[] tiles) {
        for (int i = 0; i < 9; i++) {
            if (tiles[i] == 0) {
                return i;
            }
        }
        return -1;
    }

    private int[] swap(int[] tiles, int i, int j) {
        int[] newTiles = Arrays.copyOf(tiles, tiles.length);
        int temp = newTiles[i];
        newTiles[i] = newTiles[j];
        newTiles[j] = temp;
        return newTiles;
    }

    private static class State implements Comparable<State> {

        private int[] tiles;
        private State parent;
        private int moves;
        private int heuristic;

        public State(int[] tiles, State parent, int moves, int heuristic) {
            this.tiles = tiles;
            this.parent = parent;
            this.moves = moves;
            this.heuristic = heuristic;
        }

        @Override
        public int compareTo(State other) {
            return Integer.compare(moves + heuristic, other.moves + other.heuristic);
        }

        @Override
        public boolean equals(Object other) {
            if (other instanceof State) {
                return Arrays.equals(tiles, ((State) other).tiles);
            }
            return false;
        }

        @Override
        public int hashCode() {
            return Arrays.hashCode(tiles);
        }

        @Override
        public String toString() {
            StringBuilder builder = new StringBuilder();
            for (int i = 0; i < 9; i++) {
                builder.append(tiles[i]);
                if (i % 3 == 2) {
                    builder.append("\n");
                } else {
                    builder.append(" ");
                }
            }
            return builder.toString();
        }

    }

}

这个程序使用A*算法来找到八数码问题的解决方案。它使用一个优先队列来存储open状态，每次从队列中取出f值最小的状态进行扩展，并将其添加到closed集合中。我们还定义了一个State类来表示每个状态，包括当前状态的tiles数组，父状态，移动次数和启发式估计值。在getHeuristic方法中，我们使用曼哈顿距离作为启发式函数。最后，我们使用swap方法来交换空白图块和其他图块之间的位置。