Avoid copy construction by std::transform - c++

Question

I'm calling std::transform with a lambda that takes by reference and gives back a reference to the vector element. However, according to my program output, the copy constructor is called and the objects are NOT the same.
Code:
#include <algorithm>
#include <iostream>
#include <vector>
class Math
{
private:
int val_ = 5;
public:
Math(const Math& m) {
std::cout << "Copy constructor, our address: " << this << ", his address: " << &m << std::endl;
}
Math(int val) : val_(val) {
std::cout << "Object constructed with " << val << std::endl;
}
};
int main()
{
std::vector<Math> v_math = { { 5 }, { 10 } };
std::transform(
begin(v_math),
end(v_math),
begin(v_math),
[](const Math& m)-> const Math& {
return m;
});
}
Output (Godbolt):
Object constructed with 5
Object constructed with 10
Copy constructor, our address: 0x23d7ec0, his address: 0x7fff9dc499a8
Copy constructor, our address: 0x23d7ec4, his address: 0x7fff9dc499ac
So three things are unclear to me right now:
Why are the objects different? Shouldn't they be the same?
Why is one object's address bigger than the other? Is this because the copied-to object remains on the stack which has offset-pointers?
How can I avoid copy construction as well (actually I just "misuse" std::transform for a declarative way of invoking a lambda on every std::vector element)?

Answer 1

The copies have nothing to do with your usage of std::transform. They happen when you construct your v_math std::vector, because you're using a std::initializer_list constructor, which forces copies during construction.
In your std::transform call, operator=(const Math&) is called, change your code to the following to see this.
class Math
{
private:
int val_ = 5;
public:
Math(const Math& m) {
std::cout << "Copy constructor, our address: " << this << ", his address: " << &m << std::endl;
}
Math(int val) : val_(val) {
std::cout << "Object constructed with " << val << std::endl;
}
Math& operator=(const Math& other) {
val_ = other.val_;
std::cout << "Operator=(const Math&) called!\n";
return *this;
}
};
int main()
{
std::vector<Math> v_math = { { 5 }, { 10 } };
std::cout << "After constructing v_math!\n";
std::transform(
begin(v_math),
end(v_math),
begin(v_math),
[](const Math& m)-> const Math& {
return m;
});
std::cout << "After std::transform call!\n";
}