Is the order of iterating through std::map known (and guaranteed by the standard)?

Question

Yes, that's guaranteed. Moreover, *begin() gives you the smallest and *rbegin() the largest element, as determined by the comparison operator, and two key values a and b for which the expression !compare(a,b) && !compare(b,a) is true are considered equal. The default comparison function is std::less<K>.

The ordering is not a lucky bonus feature, but rather, it is a fundamental aspect of the data structure, as the ordering is used to determine when two keys are the same (by the above rule) and to perform efficient lookup (essentially a binary search, which has logarithmic complexity in the number of elements).

This is guaranteed by Associative container requirements in the C++ standard. E.g. see 23.2.4/10 in C++11:

The fundamental property of iterators of associative containers is that they
iterate through the containers in the non-descending order of keys where
non-descending is defined by the comparison that was used to construct them.
For any two dereferenceable iterators i and j such that distance from i to j is
positive,
  value_comp(*j, *i) == false

and 23.2.4/11

For associative containers with unique keys the stronger condition holds,
  value_comp(*i, *j) != false.

I think there is a confusion in data structures.

In most languages, a map is simply an AssociativeContainer: it maps a key to a value. In the "newer" languages, this is generally achieved using a hash map, thus no order is guaranted.

In C++, however, this is not so:

• std::map is a sorted associative container
• std::unordered_map is a hash-table based associative container introduced in C++11

So, in order to clarify the guarantees on ordering.

In C++03:

• std::set, std::multiset, std::map and std::multimap are guaranteed to be ordered according to the keys (and the criterion supplied)
• in std::multiset and std::multimap, the standard does not impose any order guarantee on equivalent elements (ie, those which compare equal)

In C++11:

• std::set, std::multiset, std::map and std::multimap are guaranteed to be ordered according to the keys (and the criterion supplied)
• in std::multiset and std::multimap, the Standard imposes that equivalent elements (those which compare equal) are ordered according to their insertion order (first inserted first)
• std::unordered_* containers are, as the name imply, not ordered. Most notably, the order of elements may change when the container is modified (upon insertion/deletion).

When the Standard says that elements are ordered in a way, it means that:

• when iterating, you see the elements in the order defined
• when iterating in reverse, you see the elements in the opposite order

I hope this clears up any confusion.

Is this guaranteed to print 234 or it's implementation defined?

Yes, std::map is a sorted container, ordered by the Key with the supplied Comparator. So it is guaranteed.

I'd like go iterate through all elements, with key, greater than a concrete int value.

That is surely possible.

Yes ... the elements in a std::map have a strict weak-ordering, meaning that the elements will be composed of a set (i.e., there will be no repeats of keys that are "equal"), and equality is determined by testing on any two keys A and B, that if key A is not less than key B, and B is not less than A, then key A is equal to key B.

That being said, you cannot properly sort the elements of a std::map if the weak-ordering for that type is ambiguous (in your case, where you are using integers as the key-type, that is not a problem). You must be able to define a operation that defines a total order on the type you are using for the keys in your std::map, otherwise you will only have a partial order for your elements, or poset, which has property where A may not be comparable to B. What will typically happen in this scenario is that you'll be able to insert the key/value pairs, but you may end up with duplicate key/value pairs if you iterate through the entire map, and/or detect "missing" key/value pairs when you attempt to perform a std::map::find() of a specific key/value pair in the map.