C++ Calculator using Stacks and Queues

Question

I'm trying to understand a topic in class about using stacks and queues as a means of programming a calculator. I understand what infix and postfix expression is but how does it make it easier for a program to evaluate an expression and why are queues and stacks ideal in this situation? Thanks

Answer 1

It makes the order of operations simpler to handle, for example:

+ * - 4 2 5 3

Can only mean

((4 - 2) * 5) + 3

Which might be more readable for us, but we need to know the order of operations and match parentheses to figure it out.

As for implementing: if you had a stack, you could handle the expression above as follows:

1. Read + (an operation), push it onto the stack,
2. Read * (an operation), push it onto the stack,
3. Read - (an operation), push it onto the stack,
4. Read 4 (a number), the top of the stack is not a number, so push it onto the stack.
5. Read 2 (a number), the top of the stack is a number, so pop from the stack twice, you get 4 - 2 , calculate it ( 2 ), and push the result ( 2 ) onto the stack.
6. Read 5 (a number), the top of the stack is a number, so pop from the stack twice, you get 2 * 5 , push the result ( 10 ) onto the stack.
7. Read 3 (a number), the top of the stack is a number, so pop from the stack twice, you get 3 + 10 , push the result ( 13 ) onto the stack.
8. Nothing left to read, pop from the stack and return the result ( 13 ).

So as you can see, the expression was evaluated using a few simple rules and without having to search through the entire string for parentheses or having to decide whether multiplication has priority over addition and subtraction.