Evaluate the following Postfix expression, showing the stack contents: 250,45,9,/,5,+,20,*,- OR Convert the fo

Question

Q. Evaluate the following Postfix expression, showing the stack contents: 250,45,9,/,5,+,20,*,-

(OR)

Convert the following Infix expression to its equivalent Postfix expression, showing the stack contents for each step of conversion: A + B * C ^ D - E

CBSECBSE Class XII Board 2019Subjective· 2mImportance★★★★★

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Part (a)Concept understanding — Stack

The Stack: A Simple but Powerful Idea

Think about a stack of plates in a cafeteria. You place a clean plate on top. When someone needs a plate, they take the one from the top — the last one you put there. You cannot pull a plate from the middle or the bottom without causing a mess. That everyday action is the exact logic of a stack in computing.

A stack is a collection of items that follows one strict rule: the last item added is the first item removed. This is often called LIFO — Last In, First Out. The only item you can access at any moment is the one on top. To get to anything below, you must first remove everything above it.

How It Works

A stack has two fundamental operations:

Push: Add an item to the top of the stack.
Pop: Remove the item from the top of the stack.

That is all. There is no way to peek at the middle, no way to remove from the bottom. The stack only cares about what is on top.

Note

Some systems also allow a Peek operation — you look at the top item without removing it. But the core idea remains: only the top is visible.

Why Does This Matter?

You might wonder: why would anyone want such a restrictive structure? The answer is that many real-world processes naturally work this way.

Consider the Undo feature in a word processor. Every action you perform — typing a word, deleting a sentence, changing a font — is pushed onto a stack. When you press Undo, the most recent action is popped off and reversed. You cannot undo an action from an hour ago without first undoing everything that came after it. That is the stack at work.

Another example is a web browser's Back button. Each page you visit is pushed onto a stack. Clicking Back pops the current page and takes you to the previous one. You retrace your steps in reverse order — exactly LIFO.

Important

The stack is not just a data structure; it is a model for how many systems manage order and priority. Whenever you need to remember a sequence of events and later reverse through them, a stack is the natural choice. …

Part (b)Concept understanding — Infix to Postfix Conversion

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.

Note

Postfix notation is also called Reverse Polish Notation (RPN). Some old calculators and programming languages (like Forth) use it. It's not just a textbook concept — it's a real-world tool.

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. …

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Part (a)

Evaluate the postfix expression 250,45,9,/,5,+,20,*,- with a stack: push operands; on an operator pop two operands (the first popped is the right operand), apply, and push the result.

Token  Action              Stack (top at right)
250    push                [250]
45     push                [250, 45]
9      push                [250, 45, 9]
/      45 / 9  = 5         [250, 5]
5      push                [250, 5, 5]
+      5 + 5   = 10        [250, 10]
20     push                [250, 10, 20]
*      10 * 20 = 200       [250, 200]
-      250 - 200 = 50      [50] …

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Part (a): the postfix expression 250,45,9,/,5,+,20,*,- evaluates to 50.

Part (b): A + B * C ^ D - E converts to the postfix A B C D ^ * + E -.

Part (a)

A postfix (Reverse Polish) expression carries operator order inside the sequence, so no precedence rules or parentheses are needed. Scan left to right: push every operand; when an operator appears, pop the top two values (the first popped is the right operand, the second is the left), apply the operator, and push the result back. At the end one value remains — the answer.

Token  Action              Stack (top at right)
250    push                [250]
45     push                [250, 45]
9      push                [250, 45, 9]
/      45 / 9  = 5         [250, 5]
5      push                [250, 5, 5]
+      5 + 5   = 10        [250, 10]
20     push                [250, 10, 20]
*      10 * 20 = 200       [250, 200]
-      250 - 200 = 50      [50]
``` …

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Same / Similar Concept — real previous-year questions on the same or a closely similar concept, not this exact question.

CBSE 2023Set 91/11 markMCQ
$Q. Q. 17 and 18 are Assertion (A) and Reasoning (R) based questions. Mark the correct choice as$
(a) Both (A) and (R) are true and (R) is the correct explanation for (A).
(b) Both (A) and (R) are true and (R) is not the correct explanation for (A).
(c) (A) is true but (R) is false.
(d) (A) is false but (R) is true. Assertion (A): A stack is a LIFO structure. Reason (R): Any new element pushed into the stack always gets positioned at the index after the last existing element in the stack.
›Reveal solutionSolution

A stack is indeed LIFO, but the reason given confuses implementation detail (index positioning) with the defining principle (last-in, first-out access), so both are true yet the reasoning does not explain the assertion.

A stack is one of the most elegant data structures in computer science, defined entirely by how you interact with it rather than how it is built underneath. The assertion calls it a LIFO structure—Last In, First Out—which captures the essence perfectly. Imagine a stack of plates: you add a new plate on top, and when you need one, you take from the top. The last plate you placed is the first one you remove. That access discipline, that rule of engagement, is what makes a stack a stack.

The reason statement shifts the conversation to implementation. It says that when you push a new element, it gets positioned at the index after the last existing element. This is true if you implement a stack using an array or list, where elements occupy consecutive indices and the "top" pointer advances with each push. But here is the subtle disconnect: the LIFO nature of a stack is not because elements are stored sequentially in memory. LIFO is a logical property, a contract about the order of retrieval. You could implement a stack with a linked list where elements are scattered across memory, each pointing to the one below it, and it would still be LIFO. The sequential indexing is an artifact of one common implementation, not the reason the structure behaves as last-in, first-out.

Note

The defining characteristic of a stack is the restriction on access—only the top element is reachable for removal. Whether that top is tracked by an index, a pointer, or any other mechanism is secondary. …

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Q.Evaluate the following Postfix expression, showing the stack contents: 250,45,9,/,5,+,20,*,-

Part (a)

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