What is the preferred/idiomatic way to insert into a map?

First of all, operator[] and insert member functions are not functionally equivalent :

• The operator[] will search for the key, insert a default constructed value if not found, and return a reference to which you assign a value. Obviously, this can be inefficient if the mapped_type can benefit from being directly initialized instead of default constructed and assigned. This method also makes it impossible to determine if an insertion has indeed taken place or if you have only overwritten the value for an previously inserted key
• The insert member function will have no effect if the key is already present in the map and, although it is often forgotten, returns an std::pair<iterator, bool> which can be of interest (most notably to determine if insertion has actually been done).

From all the listed possibilities to call insert, all three are almost equivalent. As a reminder, let's have look at insert signature in the standard :

typedef pair<const Key, T> value_type;

  /* ... */

pair<iterator, bool> insert(const value_type& x);

So how are the three calls different ?

• std::make_pair relies on template argument deduction and could (and in this case will) produce something of a different type than the actual value_type of the map, which will require an additional call to std::pair template constructor in order to convert to value_type (ie : adding const to first_type)
• std::pair<int, int> will also require an additional call to the template constructor of std::pair in order to convert the parameter to value_type (ie : adding const to first_type)
• std::map<int, int>::value_type leaves absolutely no place for doubt as it is directly the parameter type expected by the insert member function.

In the end, I would avoid using operator[] when the objective is to insert, unless there is no additional cost in default-constructing and assigning the mapped_type, and that I don't care about determining if a new key has effectively inserted. When using insert, constructing a value_type is probably the way to go.

As of C++11, you have two major additional options. First, you can use insert() with list initialization syntax:

function.insert({0, 42});

This is functionally equivalent to

function.insert(std::map<int, int>::value_type(0, 42));

but much more concise and readable. As other answers have noted, this has several advantages over the other forms:

• The operator[] approach requires the mapped type to be assignable, which isn't always the case.
• The operator[] approach can overwrite existing elements, and gives you no way to tell whether this has happened.
• The other forms of insert that you list involve an implicit type conversion, which may slow your code down.

The major drawback is that this form used to require the key and value to be copyable, so it wouldn't work with e.g. a map with unique_ptr values. That has been fixed in the standard, but the fix may not have reached your standard library implementation yet.

Second, you can use the emplace() method:

function.emplace(0, 42);

This is more concise than any of the forms of insert(), works fine with move-only types like unique_ptr, and theoretically may be slightly more efficient (although a decent compiler should optimize away the difference). The only major drawback is that it may surprise your readers a little, since emplace methods aren't usually used that way.