问题
Here's my interpretation of how Dijkstra's algorithm as described by wikipedia would deal with the below graph.
First it marks the shortest distance to all neighbouring nodes, so A gets 1 and C gets 7. Then it picks the neighbour with the current shortest path. This is A. The origin is marked as visited and will not be considered again. The shortest (and only) path from the origin to B through A is now 12. A is marked as visited. The shortest path from the origin to the Destination through B is 13. B is marked as visited. The shortest path from the Origin to C through the destination is 14, but this is double the previous shortest path to C, which is 7, so the 14 is discarded. The destination is now marked as visited.
Destination has been marked visited, therefore the alogorithm is complete. Here's the result:
So am I misinterpretting the description? Is the description on wikipedia wrong? Or have I somehow stumbled upon a case that shows Dijkstra's algorithm is incorrect (which I highly doubt)? I've noticed that the path chosen seems to be picked in a greedy manner, but apparently this is one of the defining characteristics of the algorithm, however in this case it seems to give the wrong result.
回答1:
Assign to every node a tentative distance value: set it to zero for our initial node and to infinity for all other nodes. Mark all nodes unvisited. Set the initial node as current. Create a set of the unvisited nodes called the unvisited set consisting of all the nodes except the initial node. (Wiki)
Using your example:
Unvisited
A = inf;
B = inf;
C = inf;
Dest = inf;
Visited
Origin = 0;
For the current node, consider all of its unvisited neighbors and calculate their tentative distances.
O => A = 1;
O => C = 7;
We are now at A.
From A, the only path is B, this gives us
O => AB = 12;
O => C = 7
C is now lowest distance, and is the new current node
O => CD = 8
Since D is destination and 8 < 12, the route CD is chosen.
回答2:
After visiting B, the total distance travelled so far is 12. 7 is smaller than 12, and hence the search will resume at C.
A node is only marked visited after all its neighbours have been considered. In the beginning, the origin is marked as visited and is assigned a distance of zero. All the other nodes are marked unvisited.
回答3:
Then it picks the neighbour with the current shortest path.
No, it picks the unvisited node with the current shortest path.
Wikipedia writes:
Set the unvisited node marked with the smallest tentative distance as the next "current node" and go back to step 3.
It doesn't say it is a neighbor.
And the pseudocode from Wikipedia says:
8 while Q is not empty: // The main loop
9 u := vertex in Q with smallest distance in dist[] ;
where Q contains all nodes that have not yet been visited.
来源：https://stackoverflow.com/questions/8597727/dijkstras-algorithm-doesnt-appear-to-work-my-understanding-must-be-flawed