Starting a map iterator not at city.begin() - c++

Question

In short, when trying to iterate through a map, is it possible to start the iterator at an index/key that isn't *.begin()?
I have a map of cities with a class "City". (City has coordinates for the city, and in the following code, calc_dist(c1, c2) will calculate the distance between the coordinates). What I am trying to do is create a "2D Map" (i.e. map<string, map<string, double>> dist) that can access the distance between the city by using dist[city1][city2].
to compute the distances I basically create a nested iterator over the cities, and it works, but it's slow when using many cities. since the distance between cities are symmetric, i can cut the loops in half by storing the distance in the reverse of the map.
what i was hoping to do was start the second iterator at the current city from the first iterator. http://www.cplusplus.com/reference/map/map/ tells me that the order is preserved so I feel like I should be able to do this.
Sample code:
// Function create_distance_chart(...)
map<string, map<string, double>> create_distance_chart(map<string, City> c){
map<string, map<string, double>> dist;
for (map<string, City>::iterator it = c.begin(); it != c.end(); ++it){
for (map<string, City>::iterator it2 = c.begin(); it2 != c.end(); ++it2) { // here i can make improvements, i hope
//calculate distance
dist[c[it->first]][c[it2->first]] = calc_dist(c[it->first],c[it2->first])// store in map
dist[c[it2->first]][c[it->first]] = calc_dist(c[it->first],c[it2->first])// store in map in the other direction.
}
}
}
in the line
for (map<string, City>::iterator it2 = c.begin(); it2 != c.end(); ++it2) {
i tried to change c.begin to c[it->first], c.at(it->first), just it->first, and a dummy variable that pulls the index for it->first.
the only other method i'm considering is doing a reverse iterator for the second iterator and having a termination condition that might cause the second loop to end before it2 != c.end() (i.e. at the first iterator's city), but i'm not making headway in that domain right now.
Thanks in advance!

Answer 1

First of all this statment:
c[it->first]
is a slow and convoluted way to simply say:
it->second
and as you use that 8 times in your loop there is no surprise it is slow indeed.
And for your loop, looks like you want to change second loop to:
for (map<string, City>::iterator it2 = std::next(it); it2 != c.end(); ++it2)
Note: if you do not have intention to change values in the map it is cleaner to use std::map::const_iterator instead.
Note2: I assumed that calculating distance btw a city and itself is meaningless. If it is not the case in your geometry then remove std::next() in above code and just assign it to it2 in the second loop initialization.