Parentheses

Parentheses serve a dual role: they dictate the order of operations, and in more complex scenarios, they could also signify multiplication. But we're ignoring multiplication for now. So, what's the big deal?

Why Are Parentheses Tricky?

Parentheses create a new "scope" for our calculations. Think of them like those Russian nesting dolls; what happens inside the innermost doll shouldn't affect the outer dolls directly. Parentheses introduce a hierarchical structure to the expression, which complicates our otherwise linear flow of calculations.

The Mighty Stack Data Structure

The classic way to handle this hierarchical structure is by using a stack. Imagine a stack of books; you can only add or remove a book from the top. Similarly, a stack in computer science is a data structure where you can add elements to the top and remove them from the top.

We'll use two stacks for our calculator:

1. Result Stack: To keep track of intermediate results.
2. Operation Stack: To store the sign (either + or -) before and within the parentheses.

Logic for Handling Parentheses

The stack will help us remember the result and sign right before we enter a new set of parentheses. When we close the parentheses, we can pop the top elements from our stacks to restore the previous state and correctly compute the result.

1if (curr === '(') {
2  stack.push(result);
3  result = 0;
4  operationStack.push(sign);
5  sign = 1;
6} else if (curr === ')') {
7  result = operationStack.pop() * result + stack.pop();
8  sign = 1;
9}

By using stacks to manage the state inside parentheses, we can effectively simplify our calculations while respecting the order of operations. So, are you ready to integrate this into our calculator code?