std::map will sort its elements by keys. It doesn't care about the values when sorting.
You can use std::vector<std::pair<K,V>> then sort it using std::sort followed by std::stable_sort:
std::vector<std::pair<K,V>> items;
//fill items
//sort by value using std::sort
std::sort(items.begin(), items.end(), value_comparer);
//sort by key using std::stable_sort
std::stable_sort(items.begin(), items.end(), key_comparer);
The first sort should use std::sort since it is nlog(n), and then use std::stable_sort which is n(log(n))^2 in the worst case.
Note that while std::sort is chosen for performance reason, std::stable_sort is needed for correct ordering, as you want the order-by-value to be preserved.
@gsf noted in the comment, you could use only std::sort if you choose a comparer which compares values first, and IF they're equal, sort the keys.
auto cmp = [](std::pair<K,V> const & a, std::pair<K,V> const & b)
{
return a.second != b.second? a.second < b.second : a.first < b.first;
};
std::sort(items.begin(), items.end(), cmp);
That should be efficient.
But wait, there is a better approach: store std::pair<V,K> instead of std::pair<K,V> and then you don't need any comparer at all — the standard comparer for std::pair would be enough, as it compares first (which is V) first then second which is K:
std::vector<std::pair<V,K>> items;
//...
std::sort(items.begin(), items.end());
That should work great.