parsing math expression in c++

Question

I have a question about Parsing Trees:

I have a string (math expresion estring), for example: (a+b)*c-(d-e)*f/g. I have to parse that expression in a Tree:

class Exp{};
class Term: public Exp{
    int n_;
}

class Node: Public Exp{
    Exp* loperator_;
    Exp* roperator_;
    char operation; // +, -, *, /
}

What algorithm can I use to build a tree which represents the expresion string above?

Answer 1

Use the Shunting-yard algorithm. The wikipedia description is quite comprehensive, I hope it will suffice.

You can also try to write a formal grammar, for example a parsing-expression grammar, and use a tool to generate a parser. This site about PEGs lists 3 C/C++ libraries for PEG parsing.