The problem with integer indices

In the previous chapter, we implemented several generic algorithms that operated on containers. Consider one of those algorithms again:

    template<typename Container>
    void double_each_element(Container& arr) 
    {
      for (int i=0; i < arr.size(); ++i) {
        arr.at(i) *= 2;
      }
    }

This algorithm is defined in terms of the lower-level operations .size() and .at(). This works reasonably well for a container type such as array_of_ints or std::vector, but it doesn't work nearly so well for, say, a linked list such as the previous chapter's list_of_ints:

    class list_of_ints {
      struct node {
        int data;
        node *next;
      };
      node *head_ = nullptr;
      node *tail_ = nullptr;
      int size_ = 0;
    public:
      int size() const { return size_; }
      int& at(int i) {
        if (i >= size_...