Iterator categories

Let's revisit the count and count_if functions that we introduced inChapter 1, Classical Polymorphism and Generic Programming. Compare the function template definition in this next example to the similar code from that chapter; you'll see that it's identical except for the substitution of a pair of Iterators (that is, an implicitly defined range) for the Container& parameter--and except that I've changed the name of the first function from count to distance. That's because you can find this function, almost exactly as described here, in the Standard Template Library under the name std::distance and you can find the second function under the name std::count_if:

    template<typename Iterator>
    int distance(Iterator begin, Iterator end) 
    {
      int sum = 0;
      for (auto it = begin; it != end; ++it) {
        sum += 1;
      }
      return sum;
    }

    template<typename Iterator, typename Predicate>
    int count_if(Iterator begin, Iterator end...