Range for loop with const container problem

Question

I am implementing an example from the book "A Tour of C ++" by Bjarne Straustrup. I have a template function for calculating the sum of elements (copied from a book):

template<typename Container, typename Value>
Value sum(const Container& c, Value v)
{   
  for (auto x : c)
    v+=x;
  return v;
}

I want to apply it to the Vector template (defined in the book), which has the functions "begin" and "end" to support the for-for loop (copied from the book):

   template<typename T>
   T∗ begin(Vector<T>& x)
   {
    return x.size() ? &x[0] : nullptr;
   }
   template<typename T>
   T∗ end(Vector<T>& x)
   {
    return begin(x)+x.size();
   }

when applied to Vector, for example:

Vector<int> v={1,2,3,4};
int s=sum(v, 0);

this leads to a compilation error. However, when I remove const from the sum template function

 template<typename Container, typename Value>
 Value sum( Container& c, Value v)

it compiles.

1- why it did not work with "const"? If this is a problem with the implementation of "begin", "end", how to implement them?

Answer 1

begin end? , const. sum, const :

template<typename T>
const T∗ begin(const Vector<T>& x)
{
  return x.size() ? &x[0] : nullptr;
}

template<typename T>
const T∗ end(const Vector<T>& x)
{
  return begin(x)+x.size();
}

, Vector const operator[]. ; Vector (), .