How to parse math expressions in C#?

Question

Possible Duplicate:
Is there a string math evaluator in .NET?

Can C# parse mathematical expressions such as y=3*x + 3 into string? If so, ho? I appreciate your help.

Solution

Here's a bit of code I wrote a while ago to parse infix (operator operand operator) equations. There are some small classes and helper functions missing, but it should be fairly easy to implement them. If you need them or any help with it, let me know and I can upload them somewhere.

It's a basic implementation of Dijkstra's Shunting-yard algorithm

public Operand ExpressionTree
{
    get;
    private set;
}

private Stack<Operands.Operand> stack = new Stack<InfixParser.Operands.Operand>();
private Queue<Operands.Operand> outputQueue = new Queue<InfixParser.Operands.Operand>();

private void ParseFormulaString()
{
    //Dijkstra's Shunting Yard Algorithm
    Regex re = new Regex(@"([\+\-\*\(\)\^\/\ ])");
    List<String> tokenList = re.Split(formulaString).Select(t => t.Trim()).Where(t => t != "").ToList();

    for (int tokenNumber = 0; tokenNumber < tokenList.Count(); ++tokenNumber)
    {
        String token = tokenList[tokenNumber];
        TokenClass tokenClass = GetTokenClass(token);

        switch (tokenClass)
        {
            case TokenClass.Value:
                outputQueue.Enqueue(new Value(token));
                break;
            case TokenClass.Function:
                stack.Push(new Function(token, 1));
                break;
            case TokenClass.Operator:
                if (token == "-" && (stack.Count == 0 || tokenList[tokenNumber - 1] == "("))
                {
                    //Push unary operator 'Negative' to stack
                    stack.Push(new Negative());
                    break;
                }
                if (stack.Count > 0)
                {
                    String stackTopToken = stack.Peek().Token;
                    if (GetTokenClass(stackTopToken) == TokenClass.Operator)
                    {
                        Associativity tokenAssociativity = GetOperatorAssociativity(token);
                        int tokenPrecedence = GetOperatorPrecedence(token);
                        int stackTopPrecedence = GetOperatorPrecedence(stackTopToken);

                        if (tokenAssociativity == Associativity.Left && tokenPrecedence <= stackTopPrecedence ||
                            tokenAssociativity == Associativity.Right && tokenPrecedence < stackTopPrecedence)
                        {
                            outputQueue.Enqueue(stack.Pop());
                        }
                    }
                }
                stack.Push(new BinaryOperator(token, Operator.OperatorNotation.Infix));
                break;
            case TokenClass.LeftParen:
                stack.Push(new LeftParenthesis());
                break;
            case TokenClass.RightParen:
                while (!(stack.Peek() is LeftParenthesis))
                {
                    outputQueue.Enqueue(stack.Pop());
                }
                stack.Pop();

                if (stack.Count > 0 && stack.Peek() is Function)
                {
                    outputQueue.Enqueue(stack.Pop());
                }
                break;
        }

        if (tokenClass == TokenClass.Value || tokenClass == TokenClass.RightParen)
        {
            if (tokenNumber < tokenList.Count() - 1)
            {
                String nextToken = tokenList[tokenNumber + 1];
                TokenClass nextTokenClass = GetTokenClass(nextToken);
                if (nextTokenClass != TokenClass.Operator && nextTokenClass != TokenClass.RightParen)
                {
                    tokenList.Insert(tokenNumber + 1, "*");
                }
            }
        }
    }

    while (stack.Count > 0)
    {
        Operand operand = stack.Pop();
        if (operand is LeftParenthesis || operand is RightParenthesis)
        {
            throw new ArgumentException("Mismatched parentheses");
        }

        outputQueue.Enqueue(operand);
    }

    String foo = String.Join(",", outputQueue.Select(t => t.Token).ToArray());
    String bar = String.Join("", tokenList.ToArray());

    Stack<Operand> expressionStack = new Stack<Operand>();
    while (outputQueue.Count > 0)
    {
        Operand operand = outputQueue.Dequeue();

        if (operand is Value)
        {
            expressionStack.Push(operand);
        }
        else
        {
            if (operand is BinaryOperator)
            {
                BinaryOperator op = (BinaryOperator)operand;
                Operand rightOperand = expressionStack.Pop();
                Operand leftOperand = expressionStack.Pop();
                op.LeftOperand = leftOperand;
                op.RightOperand = rightOperand;
            }
            else if (operand is UnaryOperator)
            {
                ((UnaryOperator)operand).Operand = expressionStack.Pop();
            }
            else if (operand is Function)
            {
                Function function = (Function)operand;
                for (int argNum = 0; argNum < function.NumArguments; ++argNum)
                {
                    function.Arguments.Add(expressionStack.Pop());
                }
            }

            expressionStack.Push(operand);
        }
    }

    if (expressionStack.Count != 1)
    {
        throw new ArgumentException("Invalid formula");
    }

    ExpressionTree = expressionStack.Pop();
}

private TokenClass GetTokenClass(String token)
{
    double tempValue;
    if (double.TryParse(token, out tempValue) ||
        token.Equals("R", StringComparison.CurrentCultureIgnoreCase) ||
        token.Equals("S", StringComparison.CurrentCultureIgnoreCase))
    {
        return TokenClass.Value;
    }
    else if (token.Equals("sqrt", StringComparison.CurrentCultureIgnoreCase))
    {
        return TokenClass.Function;
    }
    else if (token == "(")
    {
        return TokenClass.LeftParen;
    }
    else if (token == ")")
    {
        return TokenClass.RightParen;
    }
    else if (binaryInfixOperators.Contains(token))
    {
        return TokenClass.Operator;
    }
    else
    {
        throw new ArgumentException("Invalid token");
    }
}

private Associativity GetOperatorAssociativity(String token)
{
    if (token == "^")
        return Associativity.Right;
    else
        return Associativity.Left;
}

private int GetOperatorPrecedence(String token)
{
    if (token == "+" || token == "-")
    {
        return 1;
    }
    else if (token == "*" || token == "/")
    {
        return 2;
    }
    else if (token == "^")
    {
        return 3;
    }
    else
    {
        throw new ArgumentException("Invalid token");
    }
}