How can I sort an STL map by value?

Dump out all the key-value pairs into a set<pair<K, V> > first, where the set is constructed with a less-than functor that compares the pair's second value only. That way, your code still works even if your values aren't all distinct.

Or dump the key-value pairs into a vector<pair<K, V> >, then sort that vector with the same less-than functor afterwards.

You can build a second map, with the first map's values as keys and the first map's keys as values.

This works only if all values are distinct. If you cannot assume this, then you need to build a multimap instead of a map.

I wonder how can I implement the STL map sorting by value.

You can’t, by definition. A map is a data structure that sorts its element by key.