I'm a bit confused about if and when I should use typedef in C++. I feel it's a balancing act between readability and clarity.

Here's a code sample without any typedefs:

int sum(std::vector<int>::const_iterator first, 
        std::vector<int>::const_iterator last)
{
    static std::map<std::tuple<std::vector<int>::const_iterator,
                               std::vector<int>::const_iterator>,
                    int> lookup_table;

    std::map<std::tuple<std::vector<int>::const_iterator,
                        std::vector<int>::const_iterator>, int>::iterator lookup_it =
        lookup_table.find(lookup_key);

    if (lookup_it != lookup_table.end())
        return lookup_it->second;            

    ...
}

Pretty ugly IMO. So I'll add some typedefs within the function to make it look nicer:

int sum(std::vector<int>::const_iterator first, 
        std::vector<int>::const_iterator last)
{
    typedef std::tuple<std::vector<int>::const_iterator,
                       std::vector<int>::const_iterator> Lookup_key;
    typedef std::map<Lookup_key, int> Lookup_table;

    static Lookup_table lookup_table;

    Lookup_table::iterator lookup_it = lookup_table.find(lookup_key);

    if (lookup_it != lookup_table.end())
        return lookup_it->second;            

    ...
}

The code is still a bit clumsy, but I get rid of most nightmare material. But there's still the int vector iterators, this variant gets rid of those:

typedef std::vector<int>::const_iterator Input_iterator;

int sum(Input_iterator first, Input_iterator last)
{
    typedef std::tuple<Input_iterator, Input_iterator> Lookup_key;
    typedef std::map<Lookup_key, int> Lookup_table;

    static Lookup_table lookup_table;

    Lookup_table::iterator lookup_it = lookup_table.find(lookup_key);

    if (lookup_it != lookup_table.end())
        return lookup_it->second;            

    ...
}

This looks clean, but is it still readable?

When should I use a typedef? As soon as I have a nightmare type? As soon as it occurs more than once? Where should I put them? Should I use them in function signatures or keep them to the implementation?