# 9.21. Analysis of Dijkstra’s Algorithm¶

Finally, let us look at the running time of Dijkstra’s algorithm. We
first note that building the priority queue takes \(O(V)\) time
since we initially add every vertex in the graph to the priority queue.
Once the queue is constructed the `while`

loop
is executed once for every vertex since vertices are all added at the
beginning and only removed after that. Within that loop each call to
`delMin`

, takes \(O(\log V)\) time. Taken together that part of
the loop and the calls to delMin take \(O(V \log(V))\). The
`for`

loop is executed once for each edge in the
graph, and within the `for`

loop the call to `decreaseKey`

takes
time \(O(E\log(V)).\) So the combined running time is \(O((V+E) \log(V)).\)

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