用Java实现带有ImprovePath函数的重用搜索结果的ARAstar算法

ARA*算法（Anytime Repairing A*）是一种基于A*算法的启发式搜索算法，用于解决最短路径问题。它通过逐步减小阈值来进行搜索，每次搜索都会返回一条路径，并且可以在任何时候停止搜索并返回当前找到的最佳路径。在搜索过程中，如果发现更好的路径，ARA*算法会重新展开节点以更新路径。

在实现带有ImprovePath函数的重用搜索结果的ARA*算法时，我们需要考虑以下几个步骤：

1. 创建一个节点类（Node），包含节点的状态、父节点、g值、h值和f值等信息。

2. 创建一个OpenList类，用于存储待扩展的节点，并使用二叉堆（BinaryHeap）来实现最小堆。

3. 创建一个CloseList类，用于存储已经扩展过的节点，并使用HashMap来实现快速查找。

4. 实现A*算法的核心函数，包括计算启发式函数h()、计算代价函数g()、计算估价函数f()、扩展节点、更新OpenList以及更新CloseList等操作。

5. 实现ImprovePath函数，用于在搜索过程中重用已经搜索过的节点，并对新的路径进行优化。

下面给出Java代码实现：

import java.util.*;

public class Node {
    public int[][] state;
    public int cost;
    public Node parent;
    public int f;

    public Node(int[][] s, int c) {
        state = s;
        cost = c;
        parent = null;
        f = 0;
    }
}

class OpenList {
    private BinaryHeap<Node> heap;

    public OpenList() {
        heap = new BinaryHeap<>();
    }

    public boolean isEmpty() {
        return heap.isEmpty();
    }

    public void add(Node node) {
        heap.add(node);
    }

    public Node remove() {
        return heap.remove();
    }

    public void update(Node node) {
        heap.update(node);
    }
}

class CloseList {
    private HashMap<String, Node> map;

    public CloseList() {
        map = new HashMap<>();
    }

    public boolean contains(String key) {
        return map.containsKey(key);
    }

    public void add(Node node) {
        map.put(Arrays.deepToString(node.state), node);
    }

    public Node get(String key) {
        return map.get(key);
    }
}

public class ARAstar {
    private int[][] goal;
    private int[][] start;
    private int n;
    private int m;
    private OpenList openList;
    private CloseList closeList;
    private int threshold;
    private int minCost;

    public ARAstar(int[][] s, int[][] g) {
        start = s;
        goal = g;
        n = start.length;
        m = start[0].length;
        openList = new OpenList();
        closeList = new CloseList();
        threshold = 0;
        minCost = Integer.MAX_VALUE;
    }

    public int[][] search() {
        Node node = new Node(start, 0);
        node.f = h(node);
        openList.add(node);
        while (!openList.isEmpty()) {
            node = openList.remove();
            if (Arrays.deepEquals(node.state, goal)) {
                return node.state;
            }
            closeList.add(node);
            expand(node);
        }
        return null;
    }

    private void expand(Node node) {
        int[][] state = node.state;
        int cost = node.cost;
        int g = cost;
        for (int i = 0; i < n; i++) {
            for (int j = 0; j < m; j++) {
                if (state[i][j] == 0) {
                    continue;
                }
                int[][] newState = move(state, i, j);
                if (newState == null) {
                    continue;
                }
                Node newNode = closeList.get(Arrays.deepToString(newState));
                if (newNode != null) {
                    if (newNode.cost > g + 1) {
                        newNode.parent = node;
                        newNode.cost = g + 1;
                        newNode.f = newNode.cost + h(newNode);
                        if (openList.contains(newNode)) {
                            openList.update(newNode);
                        } else {
                            openList.add(newNode);
                        }
                    }
                } else {
                    newNode = new Node(newState, g + 1);
                    newNode.parent = node;
                    newNode.f = newNode.cost + h(newNode);
                    openList.add(newNode);
                }
            }
        }
    }

    private int[][] move(int[][] state, int i, int j) {
        int[][] newState = new int[n][m];
        for (int k = 0; k < n; k++) {
            System.arraycopy(state[k], 0, newState[k], 0, m);
        }
        if (i > 0 && newState[i - 1][j] == 0) {
            newState[i - 1][j] = newState[i][j];
            newState[i][j] = 0;
            return newState;
        }
        if (i < n - 1 && newState[i + 1][j] == 0) {
            newState[i + 1][j] = newState[i][j];
            newState[i][j] = 0;
            return newState;
        }
        if (j > 0 && newState[i][j - 1] == 0) {
            newState[i][j - 1] = newState[i][j];
            newState[i][j] = 0;
            return newState;
        }
        if (j < m - 1 && newState[i][j + 1] == 0) {
            newState[i][j + 1] = newState[i][j];
            newState[i][j] = 0;
            return newState;
        }
        return null;
    }

    private int h(Node node) {
        int[][] state = node.state;
        int cost = node.cost;
        int h = 0;
        for (int i = 0; i < n; i++) {
            for (int j = 0; j < m; j++) {
                if (state[i][j] == 0) {
                    continue;
                }
                int di = Math.abs(i - (state[i][j] - 1) / m);
                int dj = Math.abs(j - (state[i][j] - 1) % m);
                h += di + dj;
            }
        }
        return h;
    }

    private void ImprovePath(Node node, int threshold) {
        int f = node.cost + h(node);
        if (f > threshold) {
            minCost = Math.min(minCost, f);
            return;
        }
        if (Arrays.deepEquals(node.state, goal)) {
            minCost = node.cost;
            return;
        }
        int[][] state = node.state;
        int cost = node.cost;
        for (int i = 0; i < n; i++) {
            for (int j = 0; j < m; j++) {
                if (state[i][j] == 0) {
                    continue;
                }
                int[][] newState = move(state, i, j);
                if (newState == null) {
                    continue;
                }
                Node newNode = closeList.get(Arrays.deepToString(newState));
                if (newNode != null) {
                    if (newNode.cost > cost + 1) {
                        newNode.parent = node;
                        newNode.cost = cost + 1;
                        ImprovePath(newNode, threshold);
                    }
                } else {
                    newNode = new Node(newState, cost + 1);
                    newNode.parent = node;
                    ImprovePath(newNode, threshold);
                }
            }
        }
    }

    public int[][] ARAstarSearch() {
        int[][] result = null;
        while (true) {
            result = search();
            if (result != null) {
                return result;
            }
            if (minCost == Integer.MAX_VALUE) {
                return null;
            }
            threshold = minCost;
            minCost = Integer.MAX_VALUE;
            closeList = new CloseList();
            Node node = new Node(start, 0);
            node.f = h(node);
            openList.add(node);
            while (!openList.isEmpty()) {
                node = openList.remove();
                if (node.cost + h(node) > threshold) {
                    minCost = Math.min(minCost, node.cost + h(node));
                    break;
                }
                if (Arrays.deepEquals(node.state, goal)) {
                    return node.state;
                }
                closeList.add(node);
                expand(node);
            }
            while (!openList.isEmpty()) {
                Node node1 = openList.remove();
                ImprovePath(node1, threshold);
                if (minCost == threshold) {
                    break;
                }
            }
        }
    }
}

以上就是用Java实现带有ImprovePath函数的重用搜索结果的ARAstar算法的方法。