The Comparison Criterion

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

You can specify the sorting criterion as a template argument. This sorting criterion 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 s from S has to hold, that s < s is not possible.
• For all s1 and s2 from S must hold: If s1 < s2, then s2 < s1 is not possible.
• For all s1, s2 and s3 with s1 < s2 and s2 < s3 must hold: s1 < s3.
• For all s1, s2 and s3 with s1 not comparable with s2 and s2 not comparable with s3 must hold: s1 is not comparable with s3.

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