So first let's define Dijkstra algorithm:
Dijkstra's algorithm finds single-source shortest paths in a directed graph with non-negative edge weights.
I want to know how can I save the shortest path form s to t with Dijkstra algorithm.
I searched on google, but I couldn't find anything particular; I also changed Dijkstra algorithm, but I could't get any answer. How can I save the shortest path from s to t with Dijkstra?
I know my question is basic and unprofessional, but any help would be appreciated. Thanks for considering my question.
Dijkstra's algorithm solves the shortest-path problem for any weighted, directed graph with non-negative weights. It can handle graphs consisting of cycles, but negative weights will cause this algorithm to produce incorrect results. Consequently, we assume that w(e) ≥ 0 for all e ∈ E here.
Dijkstra's algorithm solves the Single-Source Shortest Path problem if all edge weights are greater than or equal to zero. Without worsening the runtime complexity, this algorithm can in fact compute the shortest paths from a given start point s to all other nodes.
If you look at the pseudocode from the Wikipedia link you gave, you'll see an array in there called prev[]
. This array contains, for each node v in the graph, the previous node u in the shortest path between the source node s and v. (This array is also called the predecessor or parent array.)
In other words, the shortest path between s and v is:
s -> u -> v
where u = prev[v]
The path from s to u might have several nodes in between, so to reconstruct the path from s to v, you just walk back along the path defined by the prev[]
array using the code snippet below the main pseudocode (target is v):
1 S ← empty sequence
2 u ← target
3 while prev[u] is defined: // Construct the shortest path with a stack S
4 insert u at the beginning of S // Push the vertex onto the stack
5 u ← prev[u] // Traverse from target to source
6 end while
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