dijkstra算法不正确的条件

Question

我正在研究使用优先级队列的dijkstra算法。 我一直在做很多研究，我以为我的代码遵循算法，但是在比较最短路径时我无法进入条件式

    void dijkstra( int startingID ) {

        priority_queue<Vertex*, vector<Vertex*>, PathWeightComparer> dijkstra_queue{};
        vector<Vertex*> vert;
        vert = _vertices;
        int n = vert.size();
        vector< double > dis(n);

        for (int i = 0; i < n; i++)
        {
            dis[i] = std::numeric_limits< double >::infinity();
        }
        vert[startingID]->setPathWeight(startingID);
        dis[startingID] = 0;
        Vertex* temp = vert[startingID];
        dijkstra_queue.push(temp);


        while (!dijkstra_queue.empty())
        {
            double dist = dijkstra_queue.top()->getPathWeight();
            double u = dijkstra_queue.top()->getId();
            dijkstra_queue.pop();

            for (auto i : vert)
            {
                double v = i->getId();
                double weight = i->getPathWeight();
                double distance_total = dist + weight;
                cout << "distance_total " << distance_total << " dis[v] " << dis[v] << endl;
                if (distance_total < dis[v]) //PROBLEM
                {
                    dis[v] = distance_total;
                    Vertex* temp2 = i;
                    temp2->setPathWeight(dis[v]);
                    dijkstra_queue.push(temp2);
                }
            }
        }
    }
};

这是图类

class Graph
{
    vector<Vertex*> _vertices;      // All vertices in the graph (vertex id == index)
    int _last_startingID = -1;

这是顶点类

class Vertex
{
private:
    int _id;                    // ID (key) of given vertice
    bool _known = false;        // Dijkstra's algorithm "known" flag
    Vertex* _path = nullptr;    // Dijkstra's algorithm parent vertex pointer
        // Weight of path through graph - starts at a true infinity (inf)
    double _path_weight = std::numeric_limits<double>::infinity();

我试图只包含与dijkstra函数相关的代码，但是如果不清楚，我可以添加更多代码。

Answer 1

您对算法的实现不正确。

从队列中pop()顶点u后（因为它到源的距离是最小的），您应该只检查可直接从u到达的顶点（即，从u到该顶点存在一条边）。

无论当前顶点是否可以直接从u到达，您当前的实现似乎都在所有顶点之间循环，并且可能因此，您对距离计算进行了一些奇怪的操作，而没有意义。 更具体地说，您的实现中的distance_total似乎是荒谬的。

Dijkstra算法背后的关键思想是：

dis[u] = must be shortest path from source to u since u was popped.
dis[v] = current_known_distance_to_v

Then, for all v where edge exists from u to v:
IF dis[u] + weight(u, v) < dis[v]:
    // going via u is better than the current best known distance to v
    dis[v] = dis[u] + weight(u, v)