Question

function Dijkstra(Graph, source):
    for each vertex v in Graph:            // Initializations
        dist[v] := infinity ;              // Unknown distance function from source to v
        previous[v] := undefined ;         // Previous node in optimal path from source
    end for ;
    dist[source] := 0 ;                    // Distance from source to source
    Q := the set of all nodes in Graph ;
    // All nodes in the graph are unoptimized - thus are in Q
    while Q is not empty:                  // The main loop
        u := vertex in Q with smallest dist[] ;
        if dist[u] = infinity:
            break ;                        // all remaining vertices are inaccessible from source
        fi ;
        remove u from Q ;
        for each neighbor v of u:          // where v has not yet been removed from Q.
            alt := dist[u] + dist_between(u, v) ;
            if alt < dist[v]:              // Relax (u,v,a)
                dist[v] := alt ;
                previous[v] := u ;
            fi ;
        end for ;
    end while ;
    return dist[] ;
end Dijkstra.

the above algorithm has been mentioned in Wikipedia for Dijkstra shortest path. What I am not able to understand here is that, while we have set the distances to all the vertices as infinity [line number 3], at line 9 we are assigning u := vertex in Q with smallest dist[] but since all the distances are infinite (as set in line number 3) how can there be a smallest distance?

Answer 1

In line 6 it says dist[source] := 0 which makes one of the distances non-infinite. Once that is removed, successive iterations of the loop set dist[v] := alt, creating more non-infinite distances.