Java: Evaluate postfix expression

This is a theoretical one:

I have to evaluate an expression which I already have transformed from infix to postfix. The postfix is saved inside a Queue, since I wanted to avoid working with a String. This way I know where are the divisions between numbers and I can access it in the "right" order.

It looks like this:

// Original expression: 2+(3+1)-(5-3)^2*3-1
Queue: [2.0, 3.0, 1.0, +, +, 5.0, 3.0, -, 2.0, ^, 3.0, *, -,1.0, -]

Now I thought using two stacks:

origin stack (which has been filled up with the queue contents beforehand)
and destination stack

passing the postfix expression from one to the other, at the same time asking whether the current element is a number o an operator and counting the consecutive numbers.

If I reach an operator and the number count is at least 2 I'll do the operation and push it onto the destination stack. Reaching the end of the origin stack (empty now) I would pass everything back to it and start all over until there would be only the result left.

I am asking me now:

Is this a good approach or should I rather try to detect all patterns of the type NumberNumberOperator and process them in one go?
And if the second option is the way to go, how could this be done?

Solution

No. You only need one stack, and when you're done there is nothing left to 'start all over' with.

When you dequeue a number, push it: when you dequeue an operator, pop two values, evaluate the operator with those two operands, and push the result. When you reach the end of the input there should be exactly one value in the stack, the result. Otherwise the input was ill-formed.