Overall Running Time

Accounting:

• Time before loop: O(|V|+|E|).
• Each iteration: O(2|P|+(|V|+|E|)) = O(|V|+|E|).

Total time is time for initialization plus time for each iteration times maximum number of iterations. How many iterations?

O((|V|+|E|)+|V|(|V|+|E|)) = O(|V||E|) (best algorithm known is $O(\sqrt{\vert V\vert}\vert E\vert)$.