在 C++ 中解析数学表达式

2021-12-12 00:00:00 parsing tree c++

我有一个关于解析树的问题:

I have a question about Parsing Trees:

我有一个字符串(数学表达式 estring)，例如:(a+b)*c-(d-e)*f/g.我必须在树中解析该表达式:

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; // +, -, *, /
}

我可以使用什么算法来构建表示上述表达式字符串的树?

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

推荐答案

使用 Shunting-yard 算法.维基百科的描述相当全面，我希望它足够了.

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

您也可以尝试编写形式化语法，例如解析表达式语法，并使用工具生成解析器.这个关于 PEG 的站点列出了 3 个用于 PEG 解析的 C/C++ 库.

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.

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