java - 用Dijkstra算法求距离为坐标的最短路径

Question

我在 SO 上查看了与此相关的其他帖子。

我试图找到图中节点之间的最短路径。节点之间的每条边都有一个 (X, Y) 坐标。

我想计算从 Node I 到 Node J 的最短距离。一旦有了，我想从最短路径的坐标中将所有 X 值和 Y 值相加。

我已经坚持了几个小时，希望能有一些见解。

代码如下:

class Vertex implements Comparable<Vertex> {
    private int id;
    private List<Edge> adjacencyList;
    private Vertex previousVertex;
    private double minDistance;
    private Coordinate point;
    
    public Vertex(int id, Coordinate point) {
        this.id = id;
        this.point = point;
        this.adjacencyList = new ArrayList<>();
    }
    
    public int getID() {
        return this.id;
    }
    
    public Coordinate getPoint() {
        return this.point;
    }
    
    public List<Edge> getAdjacencyList() {
        return this.adjacencyList;
    }
    
    public void addNeighbour(Edge edge) {
        this.adjacencyList.add(edge);
    }
    
    public Vertex getPreviousVertex() {
        return this.previousVertex;
    }
    
    public void setPreviousVertex(Vertex previousVertex) {
        this.previousVertex = previousVertex;
    }
    
    public double getMinDistance() {
        return this.minDistance;
    }
    
    public void setMinDistance(double minDistance) {
        this.minDistance = minDistance;
    }
    
    public int compareTo(Vertex other) {
        return Double.compare(this.minDistance, other.minDistance);
    }
}


class Edge {
    private double weight;
    private Vertex targetVertex;
    
    public Edge(double weight, Vertex targetVertex) {
        this.weight = weight;
        this.targetVertex = targetVertex;
    }
    
    public double getWeight() {
        return this.weight;
    }
    
    public void setWeight(double weight) {
        this.weight = weight;
    }
    
    public Vertex getTargetVertex() {
        return this.targetVertex;
    }
        
    public void setTargetVertex(Vertex targetVertex) {
        this.targetVertex = targetVertex;
    }
}

class Algorithm {
    public void shortestPath(Vertex startVertex) {
        startVertex.setMinDistance(0);
        PriorityQueue<Vertex> queue = new PriorityQueue<>();
        queue.add(startVertex);
        
        while (!queue.isEmpty()) {
            Vertex actualVertex = queue.poll();
            
            for (Edge edge : actualVertex.getAdjacencyList()) {
                Vertex v = edge.getTargetVertex();
                double weight = edge.getWeight();               
                double currentDistance = actualVertex.getMinDistance() + weight;
                
                if (currentDistance < v.getMinDistance()) {
                    queue.remove(v);
                    v.setMinDistance(currentDistance);
                    v.setPreviousVertex(actualVertex);
                    queue.add(v);
                }
            }
        }
    }
    
    public List<Vertex> getShortestPathTo(Vertex targetVertex){
        List<Vertex> path = new ArrayList<Vertex>();
        for (Vertex vertex = targetVertex; vertex != null; vertex = vertex.getPreviousVertex()){
            path.add(vertex);
        }
        Collections.reverse(path);
        return path;    
    }
}

class Coordinate {
    private int x;
    private int y;
    
    Coordinate(int x, int y) {
        this.x = x;
        this.y = y;
    }
    
    public int getX() {
        return this.x;
    } 
    
    public int getY() {
        return this.y;
    }

    public static Coordinate readInput(Scanner in) {
       String[] temp = in.nextLine().split(" ");
       return new Coordinate(Integer.parseInt(temp[0]), Integer.parseInt(temp[1]));
    }
}

如果我从这个文本文件中读取

3 //# of coordinates

0 0 // (x, y)

1 1 // (x, y)

2 0 // (x, y)

1 2 //edge between coordinate 1 to 2

2 3 //edge between coordinate 2 to 3

我的测试用例看起来像这样:

class Test {
    public static void main(String[] args) {
        
        Scanner s = new Scanner(System.in);
        String[] constants = s.nextLine().split(" ");
        
        final int N = Integer.parseInt(constants[0]);
        
        List<Coordinate> junctions = new ArrayList<>();
        List<Coordinate> paths = new ArrayList<>();
        List<Vertex> vertices = new ArrayList<>();
        
        for(int i = 0; i < N; i++) {
            junctions.add(Coordinate.readInput(s));
        }
        
        for(int i = 0; i < N-1; i++) {
            paths.add(Coordinate.readInput(s));
        }
        
        for(int i = 0; i < N-1; i++) {
            int x = junctions.get(paths.get(i).getX() - 1).getX();
            int x1 = junctions.get(paths.get(i).getY() - 1).getX();
            int y = junctions.get(paths.get(i).getX() - 1).getY();
            int y1 = junctions.get(paths.get(i).getY() - 1).getY();
                
            Vertex vertex1 = new Vertex(paths.get(i).getX(), new Coordinate(x, y));
            Vertex vertex2 = new Vertex(paths.get(i).getY(), new Coordinate(x1, y1));
                
            double distance = Math.sqrt(Math.pow(x - x1, 2) + Math.pow(y - y1, 2));
            
            vertex1.addNeighbour(new Edge(distance, vertex2));
            
            vertices.add(vertex1);
            vertices.add(vertex2);
        }
        
        Algorithm a = new Algorithm();
        int x = 0;
        int y = 0;
        
        for(int i = 0; i < vertices.size(); i++) {
            a.shortestPath(vertices.get(i));
            
            for(Vertex vertex : a.getShortestPathTo(vertices.get(i+1))) {
                x += vertices.get(vertex.getID()).getPoint().getX();
                y += vertices.get(vertex.getID()).getPoint().getY();
            }
            
        }
        //This prints out "Total X: 5 Total Y: 3" (should be 3 and 1)
        System.out.println("Total X: " + x + " Total Y: " + y);
    }
}

Answer 1

您的问题出在这部分:

public void shortestPath(Vertex startVertex) {
    startVertex.setMinDistance(0);
    PriorityQueue<Vertex> queue = new PriorityQueue<>();
    queue.add(startVertex);
    //The rest is omitted
}

每次运行 shortestPath 方法时，您应该将所有顶点中的所有 minDistance 重置为无穷大，而不仅仅是 startVertex。

对于除startVertex之外的所有顶点，开头的minDistance应该设置为无穷大(或Double.MAX_VALUE)，或者它将始终为 0。

代码:

for(Vertex v : vertices){
    v.setMinDistance(Double.MAX_VALUE);
    v.setPreviousVertex(null);  
}
a.shortestPath(vertices.get(i));

此外，在 Test 类的第三个循环中，您多次初始化相同的顶点。所以，你应该做的是，预初始化所有顶点并将它们保存在一个数组中，如下所示:

for(int i = 0; i < N; i++){
    vertices.add(new Vertex(i + 1, junctions.get(i)); 
}

for(int i = 0; i < N - 1; i++){
    //Initialize x, y, x1, y1 here, I just skipped it
    Vertex vertex1 = vertices.get(paths.getX() - 1);
    Vertex vertex2 = vertices.get(paths.getY() - 1);

    double distance = Math.sqrt(Math.pow(x - x1, 2) + Math.pow(y - y1, 2));

    vertex1.addNeighbour(new Edge(distance, vertex2));


}