Dijkstra 算法中的多条路径

Question

我在我的一个项目中使用了 Dijksta 的方法。

我的问题是如何显示从 A 到 B 的所有最短路径（如果存在）。我的意思是，例如，如果有不止一条路径具有相同的最小长度。

完整代码如下：

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;
    }

    @Override
    public String toString() {
        return name;
    }

    @Override
    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 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 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;
    }
}

Answer 1

您需要一组先前的顶点而不是单个顶点。更新并找到等长路径时，将顶点附加到先前的顶点列表，清除并在找到更短路径时替换它。

然后处理它来显示取决于你用它做什么。对于您现在拥有的不同路径，您需要递归遍历前任以生成一组路径。

Dijkstra 算法中的多条路径

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