Java - 在距离加权 map 中找到两点之间的最短路径

Question

我需要一种算法来找到 map 中两点之间的最短路径其中道路距离由数字表示。

给出的是什么:起点城市A目的地城市Z

城市间距离列表:

A - B : 10
F - K : 23
右 - 中:8
K - O : 40
Z - P : 18
J - K : 25
D - B : 11
M - A : 8
P - R : 15

我以为我可以使用 Dijkstra 算法，但它找到了到所有目的地的最短距离。不只是一个。

如有任何建议，我们将不胜感激。

Answer 1

就像 SplinterReality 所说:没有理由不在这里使用 Dijkstra 算法。

下面的代码是我从 here 中截取的并对其进行修改以解决问题中的示例。

import java.util.PriorityQueue;
import java.util.List;
import java.util.ArrayList;
import java.util.Collections;

class Vertex implements Comparable<Vertex>
{
    public final String name;
    public Edge[] adjacencies;
    public double minDistance = Double.POSITIVE_INFINITY;
    public Vertex previous;
    public Vertex(String argName) { name = argName; }
    public String toString() { return name; }
    public int compareTo(Vertex other)
    {
        return Double.compare(minDistance, other.minDistance);
    }

}


class Edge
{
    public final Vertex target;
    public final double weight;
    public Edge(Vertex argTarget, double argWeight)
    { target = argTarget; weight = argWeight; }
}

public class Dijkstra
{
    public static void computePaths(Vertex source)
    {
        source.minDistance = 0.;
        PriorityQueue<Vertex> vertexQueue = new PriorityQueue<Vertex>();
        vertexQueue.add(source);

        while (!vertexQueue.isEmpty()) {
            Vertex u = vertexQueue.poll();

            // Visit each edge exiting u
            for (Edge e : u.adjacencies)
            {
                Vertex v = e.target;
                double weight = e.weight;
                double distanceThroughU = u.minDistance + weight;
                if (distanceThroughU < v.minDistance) {
                    vertexQueue.remove(v);

                    v.minDistance = distanceThroughU ;
                    v.previous = u;
                    vertexQueue.add(v);
                }
            }
        }
    }

    public static List<Vertex> getShortestPathTo(Vertex target)
    {
        List<Vertex> path = new ArrayList<Vertex>();
        for (Vertex vertex = target; vertex != null; vertex = vertex.previous)
            path.add(vertex);

        Collections.reverse(path);
        return path;
    }

    public static void main(String[] args)
    {
        // mark all the vertices 
        Vertex A = new Vertex("A");
        Vertex B = new Vertex("B");
        Vertex D = new Vertex("D");
        Vertex F = new Vertex("F");
        Vertex K = new Vertex("K");
        Vertex J = new Vertex("J");
        Vertex M = new Vertex("M");
        Vertex O = new Vertex("O");
        Vertex P = new Vertex("P");
        Vertex R = new Vertex("R");
        Vertex Z = new Vertex("Z");

        // set the edges and weight
        A.adjacencies = new Edge[]{ new Edge(M, 8) };
        B.adjacencies = new Edge[]{ new Edge(D, 11) };
        D.adjacencies = new Edge[]{ new Edge(B, 11) };
        F.adjacencies = new Edge[]{ new Edge(K, 23) };
        K.adjacencies = new Edge[]{ new Edge(O, 40) };
        J.adjacencies = new Edge[]{ new Edge(K, 25) };
        M.adjacencies = new Edge[]{ new Edge(R, 8) };
        O.adjacencies = new Edge[]{ new Edge(K, 40) };
        P.adjacencies = new Edge[]{ new Edge(Z, 18) };
        R.adjacencies = new Edge[]{ new Edge(P, 15) };
        Z.adjacencies = new Edge[]{ new Edge(P, 18) };


        computePaths(A); // run Dijkstra
        System.out.println("Distance to " + Z + ": " + Z.minDistance);
        List<Vertex> path = getShortestPathTo(Z);
        System.out.println("Path: " + path);
    }
}

上面的代码产生:

Distance to Z: 49.0
Path: [A, M, R, P, Z]