The Comparison Criterion

The default comparison criterion of the ordered associative containers is std::less. If we want to use a user-defined type as the key, we have to overload the operator <. It’s sufficient to overload the operator < for our data type because the C++ runtime compares, with the help of the relation (! (elem1<elem2 || elem2<elem1)), two elements for equality.

We can specify the sorting criterion as a template argument that must implement a strict weak ordering.

ℹ️ Strict weak ordering
Strict weak ordering for a sorting criterion on a set S is given if the following requirements are met:

• For every s from S it has to hold that s < s is not possible.
• For all s1 and s2 from S it must hold: If s1 < s2, then s2 < s1 is not possible.
• For all s1, s2 and s3 with s1 < s2 and s2 < s3 the following must hold: s1 < s3.
• For all s1, s2 and s3 with s1 not comparable with s2 and s2 not comparable with s3 the following must hold: s1 is not comparable with s3.

In contrast to the definition of the strict weak ordering, the usage of a comparison criterion with strict weak ordering is a lot simpler for an std::map.