How to initialize const member requiring computations to be performed?

Use a function call inside a delegating (if avaliable, not neccessarily) constructor’s member initialization list:

A::A(std::string const& yourstring) : A(compute_myint(yourstring)) {};

^{Pass std::string by const&, not just const, while you’re at it.}

compute_myint can be non-member, static member, possibly not accessible from outside the class, whichever makes the most sense.