I am studying some chess and others AI algorithms and the majority of these implementations are made in C and C++, my question is, if I make a chess board and all the graphic thing in Unity, can I make it run with my algorithm written in C++? And how can I make this interface?
Sorry if is it a noob question, I'm just starting at this whole gamedev world.
It might be silly, but you could make a small C++ program around the chess library, that takes a simple text board state or movelist as input and returns the AI's selected move. I don't know .net's system libraries off hand, but you can probably start it as a subprocess, send to its stdin and then poll its stdout for a reply. Local sockets are also a possibility..
There are a variety of ways to run code written in other languages in Unity. Most of these are platform specific.
iOS: Since xCode will also compile C++ code, you could add the C++ code to the plugins directory and it will be built when you build the iOS app. You'd then define the function prototypes in C# so they are accessible from Unity. Documentation is here.
The official documentation for a variety of platforms is covered here.