Q.For the following arithmetic expression:
((2+3)*(4/2))+2
Show step-by-step process for matching parentheses using stack data structure.

Infix to Postfix Conversion: A First Look

Imagine you're giving someone directions. You might say, "Go to the market, then turn left, then buy vegetables." That's a natural, step-by-step order. But sometimes, instructions come in a different style: "After you've turned left at the market, buy vegetables." The meaning is the same, but the order of words has changed.

Infix and postfix are two different ways of writing the same mathematical or logical expression — just like those two sets of directions. The word "infix" means the operator (like +, –, ×) sits in between the numbers or variables. For example, A + B is infix. "Postfix" means the operator comes after the numbers: A B +. That's all.

Why does this matter?

In everyday life, we use infix without thinking. But computers and calculators find infix confusing because of operator precedence — the rule that multiplication happens before addition, and brackets override everything. A human reads 3 + 4 × 2 and knows to multiply first. A simple computer, reading left to right, might add 3 and 4 first and get the wrong answer.

Postfix removes this confusion entirely. In postfix, there are no brackets and no precedence rules. The order of operators already tells you exactly what to do, step by step. This makes it much easier for a machine to evaluate an expression quickly and without error.

How conversion works (the idea, not the algorithm)

Converting infix to postfix is like rewriting a sentence so that every action (operator) comes right after its objects (operands). The key rule is: operands keep their order, operators move to the right, and brackets are used to decide which operator moves first.

Consider a simple infix expression: A + B. In postfix, it becomes A B +. The + moves to the end.

Now consider A + B × C. In infix, multiplication has higher precedence, so it's as if the expression is A + (B × C). In postfix, the multiplication happens first, so we write A B C × +. Notice: B and C are together, then ×, then finally +. The addition waits until after the multiplication is done.

What about brackets? (A + B) × C means addition first. In postfix, that becomes A B + C ×. The + comes right after A and B, before the ×.

So the core idea is: operators are delayed until their operands are fully listed, and the delay is determined by precedence and brackets.

Why you should care (even if you never write code)

• It teaches logical sequencing. You learn to think in steps: what must happen first, second, third. That skill is useful in planning, budgeting, and decision-making. …