带变量的调车场算法 [英] Shunting Yard Algorithm with Variables
问题描述
我目前正在开发Shunting Yard Algorithm的修改版本，该版本可以使用变量，但是我不知道如何使它起作用.例如，我希望算法重新编写2 *(2x + 5)-5到4x +5.是否有任何想法/指向已经实现的算法的链接?
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?
推荐答案
- 采用表达式:
2 *(2x + 5)-5 - 添加*符号，使计算机更易理解:
2 *(2 * x + 5)-5 - 使用Shunting Yard算法对其进行解析，结果变为:
2 2 x * 5 + * 5-(每个字符都可以看作是数组的元素). - 使用已解析的表达式，创建二叉树:
- Take the expression:
2 * (2x + 5) - 5 - Add the * symbol to make it more understandable for the computer:
2 * (2*x + 5) - 5 - Parse it using the Shunting Yard Algorithm, it becomes:
2 2 x * 5 + * 5 -(Each character could be seen as an element of an array). - With the parsed expression, create the binary tree:
<代码>--/\* 5/\2 +/\* 5/\2倍5.定义代数规则并将其应用于树.例如，一条规则能够将 2 节点与 2 * x + 5 子树相乘".
-
/ \
* 5
/ \
2 +
/ \
* 5
/ \
2 x
5. Define and apply algebraic rules to the tree. For example, a rule to be able to 'multiply' the 2 node with the 2 * x + 5 subtree.
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