What is the pseudocode for Dijkstra's algorithm?

The pseudocode initializes distances to infinity and predecessors to nil, sets the source distance to 0, and uses a priority queue H. It repeatedly extracts the vertex u with the minimum distance, relaxes all outgoing edges (u,v), updating dist(v) and prev(v) if a shorter path is found, and decreases the key of v in H.

Conditions

Input: Graph $G = (V, E)$ , directed or undirected.
Positive edge lengths { $l_e$ : $e \in E$ }.
Source vertex $s \in V$ .
Output: dist(u) is the shortest distance from s to u for all reachable u.

Reasoning, step by step

Initialize dist(u) = infinity and prev(u) = nil for all u in V.
Set dist(s) = 0.
Create priority queue H with all vertices, keyed by dist values.
While H is not empty: extract min u from H.
For each edge (u,v) in E: if dist(v) > dist(u) + $l(u,v)$ , then dist(v) = dist(u) + $l(u,v)$ , prev(v) = u, and decreasekey(H, v).

Example

The video displays the full pseudocode: 'procedure dijkstra(G,l,s)... H = makequeue(V)... while H is not empty: u = deletemin(H)... if dist(v) > dist(u) + $l(u,v)$ : dist(v) = dist(u) + $l(u,v)$ ...'

Common misconceptions

Forgetting to initialize the source distance to 0.
Assuming the algorithm works with negative edge weights (the pseudocode specifies positive edge lengths).
Not updating the priority queue key when a shorter path is found.

Watch the explanation

YouTubeDijkstra's algorithm in 3 minutes

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Answers are generated from source material and independently checked. Consult the original video or creator if something is unclear.