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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.

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.