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

As you put your question there is no need for recursion whatsoever. The answer is three things: Postfix notation plus Shunting Yard algorithm plus Postfix expression evaluation:

1). Postfix notation = invented to eliminate the need for explicit precedence specification. Read more on the net but here is the gist of it: infix expression ( 1 + 2 ) * 3 while easy for humans to read and process not very efficient for computing via machine. What is? Simple rule that says "rewrite expression by caching in precedence,then always process it left-to-right". So infix ( 1 + 2 ) * 3 becomes a postfix 12+3*. POST because operator is placed always AFTER the operands.

2). Evaluating postfix expression. Easy. Read numbers off postfix string. Push them on a stack until an operator is seen. Check operator type - unary? binary? tertiary? Pop as many operands off stack as needed to evaluate this operator. Evaluate. Push result back on stack! And u r almost done. Keep doing so until stack has only one entry = value u r looking for.

Let's do ( 1 + 2 ) * 3 which is in postfix is "12+3*". Read first number = 1. Push it on stack. Read next. Number = 2. Push it on stack. Read next. Operator. Which one? +. What kind? Binary = needs two operands. Pop stack twice = argright is 2 and argleft is 1. 1 + 2 is 3. Push 3 back on stack. Read next from postfix string. Its a number. 3.Push. Read next. Operator. Which one? *. What kind? Binary = needs two numbers -> pop stack twice. First pop into argright, second time into argleft. Evaluate operation - 3 times 3 is 9.Push 9 on stack. Read next postfix char. It's null. End of input. Pop stack onec = that's your answer.

3). Shunting Yard is used to transform human (easily) readable infix expression into postfix expression (also human easily readable after some practice). Easy to code manually. See comments above and net.