Equation (expression) parser with precedence?

Question

I\'ve developed an equation parser using a simple stack algorithm that will handle binary (+, -, |, &, *, /, etc) operators, unary (!) operators, and parenthesis.

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Answer 1

Actually there's a way to do this without recursion, which allows you to go through the entire expression once, character by character. This is O(n) for time and space. It takes all of 5 milliseconds to run even for a medium-sized expression.

First, you'd want to do a check to ensure that your parens are balanced. I'm not doing it here for simplicity. Also, I'm acting as if this were a calculator. Calculators do not apply precedence unless you wrap an expression in parens.

I'm using two stacks, one for the operands and another for the operators. I increase the priority of the operation whenever I reach an opening '(' paren and decrease the priority whenever I reach a closing ')' paren. I've even revised the code to add in numbers with decimals. This is in c#.

NOTE: This doesn't work for signed numbers like negative numbers. Probably is just a simple revision.

  internal double Compute(string sequence)
    {
        int priority = 0;
        int sequenceCount = sequence.Length;            
        for (int i = 0; i < sequenceCount; i++) {
            char s = sequence[i];                
            if (Char.IsDigit(s)) {
                double value = ParseNextNumber(sequence, i);
                numberStack.Push(value);
                i = i + value.ToString().Length - 1;
            } else if (s == '+' || s == '-' || s == '*' || s == '/')  {                
               Operator op = ParseNextOperator(sequence, i, priority);
                CollapseTop(op, numberStack, operatorStack);
                operatorStack.Push(op);
            } if (s == '(') { priority++; ; continue; }
            else if (s == ')') { priority--; continue; }
        }
        if (priority != 0) { throw new ApplicationException("Parens not balanced"); }
        CollapseTop(new Operator(' ', 0), numberStack, operatorStack);
        if (numberStack.Count == 1 && operatorStack.Count == 0) {
            return numberStack.Pop();
        }
        return 0;
    }    

Then to test this out:

Calculator c = new Calculator();
double value = c.Compute("89.8+((9*3)+8)+(9*2)+1");
Console.WriteLine(string.Format("The sum of the expression is: {0}", (float)value));
//prints out The sum of the expression is: 143.8