dijkstra algorithm in C++

You have more than enough information on this well-known algorithm to implement it in C++. See http://en.wikipedia.org/wiki/Dijkstra's_algorithm[^].

Now, this article does not mention arc weights. You can easily modify the algorithm if you need to take it into account. Look at the distance calculation in the pseudocode (see dist, dist_between). When you calculate them, multiply each arc's distance with its weight, that's all you need.

—SA