ARAstar java实现

ARA*（Anytime Repairing A*）是 A* 算法的一种改进，可以在保证最优解的情况下尽可能快地找到一个解，同时还可以在有更多时间时继续优化这个解。

下面是 ARA* 的 Java 实现：

public class ARAStar {
    private final double epsilon; // 节点评估值系数
    private final HeuristicFunction heuristicFunction; // 启发式函数
    private final Map<Node, Double> gCosts; // 节点到起点的实际代价
    private final Map<Node, Double> rhsCosts; // 节点到终点的实际代价
    private final PriorityQueue<Node> openList; // 开放列表
    private final Set<Node> closedList; // 封闭列表

    public ARAStar(double epsilon, HeuristicFunction heuristicFunction) {
        this.epsilon = epsilon;
        this.heuristicFunction = heuristicFunction;
        this.gCosts = new HashMap<>();
        this.rhsCosts = new HashMap<>();
        this.openList = new PriorityQueue<>(Comparator.comparingDouble(this::getF));
        this.closedList = new HashSet<>();
    }

    public List<Node> search(Node start, Node goal) {
        initialize(start, goal);
        while (!openList.isEmpty() && getF(openList.peek()) < getF(goal)) {
            Node current = openList.poll();
            closedList.add(current);
            if (isGoal(current, goal)) {
                return reconstructPath(start, goal);
            }
            updateVertex(current, goal);
            for (Node neighbor : current.getNeighbors()) {
                if (!closedList.contains(neighbor)) {
                    updateVertex(neighbor, goal);
                    if (!openList.contains(neighbor)) {
                        openList.offer(neighbor);
                    }
                }
            }
        }
        return reconstructPath(start, goal);
    }

    private void initialize(Node start, Node goal) {
        gCosts.clear();
        rhsCosts.clear();
        openList.clear();
        closedList.clear();
        gCosts.put(start, 0.0);
        rhsCosts.put(start, heuristicFunction.estimate(start, goal));
        openList.offer(start);
    }

    private double getF(Node node) {
        return Math.min(gCosts.get(node), rhsCosts.get(node)) + epsilon * heuristicFunction.estimate(node, getGoal());
    }

    private boolean isGoal(Node node, Node goal) {
        return node.equals(goal);
    }

    private void updateVertex(Node node, Node goal) {
        if (node.equals(goal)) {
            return;
        }
        double g = getMinG(node);
        gCosts.put(node, g);
        if (openList.contains(node)) {
            openList.remove(node);
        }
        if (!isConsistent(node)) {
            rhsCosts.put(node, g + heuristicFunction.estimate(node, goal));
        }
        if (openList.contains(node)) {
            openList.offer(node);
        }
    }

    private double getMinG(Node node) {
        return node.getNeighbors().stream()
                .mapToDouble(neighbor -> gCosts.getOrDefault(neighbor, Double.POSITIVE_INFINITY) + node.getCost(neighbor))
                .min().orElse(Double.POSITIVE_INFINITY);
    }

    private boolean isConsistent(Node node) {
        return rhsCosts.get(node).equals(gCosts.get(node));
    }

    private List<Node> reconstructPath(Node start, Node goal) {
        List<Node> path = new ArrayList<>();
        Node current = goal;
        while (!current.equals(start)) {
            path.add(current);
            current = current.getParent();
        }
        path.add(start);
        Collections.reverse(path);
        return path;
    }

    private Node getGoal() {
        return rhsCosts.entrySet().stream()
                .min(Map.Entry.comparingByValue())
                .map(Map.Entry::getKey)
                .orElseThrow(IllegalStateException::new);
    }
}

其中，`Node` 类表示图中的节点，`HeuristicFunction` 接口表示启发式函数，其 `estimate` 方法用于估计节点到目标节点的代价。

使用时，可以先定义一个 `HeuristicFunction` 实现类：

public class EuclideanDistance implements HeuristicFunction {
    @Override
    public double estimate(Node node, Node goal) {
        double dx = node.getX() - goal.getX();
        double dy = node.getY() - goal.getY();
        return Math.sqrt(dx * dx + dy * dy);
    }
}

然后，可以使用以下代码进行搜索：

ARAStar araStar = new ARAStar(1.0, new EuclideanDistance());
List<Node> path = araStar.search(startNode, goalNode);

其中，第一个参数是节点评估值系数，第二个参数是启发式函数。`search` 方法返回搜索结果路径。