Template default init, if there no default constructor in a class - c++

Question

I'm pretty new in C++. I have wrote a function template to sum all elements in a vector like this:
template<typename T>
inline T sumator(const std::vector<T> &sequence) {
T init = T{};
return accumulate(sequence.begin(), sequence.end(), init);
}
All work well until the default constructor is not declare, but declare constructor from, for example, 2 arguments.
Like this:
class A {
private:
int a;
int b;
public:
// A() = default;
A(int aa, int bb) : a(aa),b(bb){};
A operator+(const A &right) const {
return {a + right.a, b + right.b};
}
bool operator==(const A &right) const {
return (a == right.a && b == right.b);
}
};
vector<A> bc = {{3,5},{5,5}};
A res = Adder::sumator(works);
A result = {8,10};
assert(result,res);
Now I get an error like : error: no matching constructor for initialization of 'A'
T init = T{};
How can I avoid this situation, not using https://en.cppreference.com/w/cpp/types/is_default_constructible
UPD: I have many classes, some of them with default constructor, some without but with constructor for 2 arg, some for 3, e.t.c. And I want to accumulate every situation well

Answer 1

Possible solutions that I can think of.
Let users rely on std::accumulate by providing an initial vlaue.
Provide an overload of sumator with an initial value. Users can call the overload with an initial value if they have a type that does not have default constructor.
Insist that the type for which the function is invoked have a default consructor.
template<typename T>
inline T sumator(const std::vector<T> &sequence, T init) {
return accumulate(sequence.begin(), sequence.end(), init);
}
template<typename T>
inline T sumator(const std::vector<T> &sequence) {
return accumulate(sequence.begin(), sequence.end(), {});
}

Answer 2

You can add another parameter with default argument.
template<typename T>
inline T sumator(const std::vector<T> &sequence, const T& init = T{}) {
return accumulate(sequence.begin(), sequence.end(), init);
}
For types could be default-constructed you can still
sumator(some_vector);
And specify the default value when T can't be default-constructed. e.g.
sumator(some_vector, A{0, 0});

Answer 3

You can split it in two overloads and add a static_assert to provide a nice compilation error message if someone tries to use it the wrong way.
One overload would be valid only if the type is default constructible and one overload would be valid for types that is not as well as for those that are:
#include <type_traits>
#include <vector>
template<typename T>
T sumator(const std::vector<T>& sequence) {
static_assert(std::is_default_constructible_v<T>);
return std::accumulate(sequence.begin(), sequence.end(), T{});
}
template<typename T>
T sumator(const std::vector<T>& sequence, const T& init) {
return std::accumulate(sequence.begin(), sequence.end(), init);
}
Another option is to add a default argument that can be used for types that are default constructible - and you could also make it more generic to make it work with not only vectors but with lists etc.
template<template<class, class...> class C, class T, class... Ts>
T sumator(const C<T, Ts...>& sequence, const T& init = T{}) {
return std::accumulate(sequence.begin(), sequence.end(), init);
}