math - Shunting Yard Algorithm with Variables

Question

I'm currently working on a modified version of the Shunting Yard Algorithm that would work with variables, but I cant figure out how to get it to work. For example, I would want the algorithm to re-write 2 * (2x + 5) - 5 to 4x + 5. Any ideas / links to already implemented algorithms that does this already?

Answer 1

1. 取表达式：2 * (2x + 5) - 5
2. 添加 * 符号以使其更易于计算机理解：2 * (2*x + 5) - 5
3. 使用 Shutting Yard 算法对其进行解析，它变为：（2 2 x * 5 + * 5 -每个字符都可以看作是数组的一个元素）。
4. 使用解析后的表达式，创建二叉树：

- / \ * 5 / \ 2 + / \ * 5 / \ 2 x 5. 定义代数规则并将其应用于树。例如，能够将2节点与2 * x + 5子树“相乘”的规则。