分流码验证前pression [英] Shunting-Yard Validate Expression

问题描述

我们使用调度场算法来评估EX pressions。我们可以通过简单地应用算法验证前pression。如果有遗漏的操作数，错过匹配的括号，和其他的东西它失败。然而，调度场算法已不仅仅是人类可读缀更大支持的语法。例如，

We use the Shunting-Yard algorithm to evaluate expressions. We can validate the expression by simply applying the algorithm. It fails if there are missing operands, miss-matched parenthesis, and other things. The Shunting-Yard algorithm however has a larger supported syntax than just human readable infix. For example,

1 + 2
+ 1 2
1 2 +

都是可接受的方式来提供1 + 2作为输入到调度场算法。 '+ 1 2和1 2 +是无效的缀，但是标准调度场算法可以处理它们。该算法并不真正关心的秩序，它承precedence抓住了'最近'运算应用的运营商。

are all acceptable ways to provide '1+2' as input to the Shunting-Yard algorithm. '+ 1 2' and '1 2 +' are not valid infix, but the standard Shunting-Yard algorithm can handle them. The algorithm does not really care about the order, it applies operators by order of precedence grabbing the 'nearest' operands.

我们想限制我们输入有效的人类可读的中缀。我正在寻找一种方法来修改调度场算法失败，非有效缀或使用前分流码提供缀验证。

We would like to restrict our input to valid human readable infix. I am looking for a way to either modify the Shunting-Yard algorithm to fail with non-valid infix or provide an infix validation prior to using Shunting-Yard.

是任何人都知道有任何公开的技术来做到这一点？我们必须支持基本的运营商，运营商定制，支架，和功能（使用多个参数）。我还没有看到任何与工作超过了基本的运营商网络。

Is anyone aware of any published techniques to do this? We must support both basic operator, custom operators, brackets, and functions (with multiple arguments). I haven't seen anything that works with more than the basic operators online.

感谢

推荐答案

解决我的问题是，以加强贴的维基百科，并建议RICI 的状态机。我张贴的伪code在这里，因为它可能是利用他人。

The solution to my problem was to enhance the algorithm posted on Wikipedia with the state machine recommended by Rici. I am posting the pseudo code here because it may be of use to others.

Support two states, ExpectOperand and ExpectOperator.

Set State to ExpectOperand
While there are tokens to read:
    If token is a constant (number)
        Error if state is not ExpectOperand.
        Push token to output queue.
        Set state to ExpectOperator.
    If token is a variable.
        Error if state is not ExpectOperand.
        Push token to output queue.
        Set state to ExpectOperator.
    If token is an argument separator (a comma).
        Error if state is not ExpectOperator.
        Until the top of the operator stack is a left parenthesis  (don't pop the left parenthesis).
            Push the top token of the stack to the output queue.
            If no left parenthesis is encountered then error.  Either the separator was misplaced or the parentheses were mismatched.
        Set state to ExpectOperand.
    If token is a unary operator.
        Error if the state is not ExpectOperand.
        Push the token to the operator stack.
        Set the state to ExpectOperand.
    If the token is a binary operator.
        Error if the state is not ExpectOperator.
        While there is an operator token at the top of the operator stack and either the current token is left-associative and of lower then or equal precedence to the operator on the stack, or the current token is right associative and of lower precedence than the operator on the stack.
            Pop the operator from the operator stack and push it onto the output queue.
        Push the current operator onto the operator stack.
        Set the state to ExpectOperand. 
    If the token is a Function.
        Error if the state is not ExpectOperand.  
        Push the token onto the operator stack.
        Set the state to ExpectOperand.
    If the token is a open parentheses.
        Error if the state is not ExpectOperand.
        Push the token onto the operator stack.
        Set the state to ExpectOperand.
    If the token is a close parentheses.
         Error if the state is not ExpectOperator.
         Until the token at the top of the operator stack is a left parenthesis.
             Pop the token off of the operator stack and push it onto the output queue.
         Pop the left parenthesis off of the operator stack and discard.
         If the token at the top of the operator stack is a function then pop it and push it onto the output queue.
         Set the state to ExpectOperator.
At this point you have processed all the input tokens.
While there are tokens on the operator stack.
    Pop the next token from the operator stack and push it onto the output queue.
    If a parenthesis is encountered then error.  There are mismatched parenthesis.

您可以一元和二元运算符（我专门谈到负preFIX和减法运算符）之间通过查看previous令牌很容易区分。如果没有previous的道理，previous令牌是一个开放的括号，或者previous令牌是一个操作符，那么你曾经遇到过一个一元preFIX运营商，否则你所遇到的二元运算符

You can easily differentiate between unary and binary operators (I'm specifically speaking about the negative prefix and subtraction operator) by looking at the previous token. If there is no previous token, the previous token is an open parenthesis, or the previous token is an operator then you have encountered a unary prefix operator, else you have encountered the binary operator.

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