试图理解 Dijkstra 的算法

Trying to understand Dijkstra's Algorithm

我正在努力更好地理解 Dijkstra 算法。我附上了教科书中算法的图像。伪代码显示输入是无向图,但是有向图的算法有什么不同吗?我用有向图的输入查找了算法,但没有发现任何差异。

Algorithm ShortestPath(G, v)

Input: A simple undirected weighted graph G with nonnegative edge weights and a distinguished vertex v of G

Output: A label D[u], for each vertex u of G, such that D[u] is the length of a shortest path from v to u in G

Initialize D[v]<--0 and D[u]<--+infinity for each vertex u != v.

Let priority queue Q contain all the vertices of G using the D labels as keys.

while Q is not empty do

    {pull a new vertex u into the cloud}

u<-- Q.removeMin()

for each vertex z adjacent to u such that z is in Q do

    {preform the relaxation procedure on edge (u,z)}

    if D[u]+w((u,z))<D[z] then

         D[z]<-- D[u]+w((u,z))

         change to D[z] the of vertex z in Q

return the label D[u] of each vertex u

您可以在有向图和无向图中使用 Dijkstra 算法,因为当您有一条边可以从您的邻接列表前往时,您只需将边添加到 PriorityQueue 中。例如,如果我的一个节点有一条从 A 到 B 的边,权重为 3,那么如果它是从 B 定向的,我将无法将边添加回 A,而从 A 可以将它添加到 B。

与其他答案一样,请确保不要将它与权重混淆。 Dijkstra算法运行在正加权图上,否则优先级队列就没用了。