Stack in Python: CBSE Class 12 Computer Science Notes and Programs

What Stack is about

Weightage: This chapter is part of Unit 1, Computational Thinking and Programming - 2, which carries 40 of the 70 theory marks together with Revision of Python Topics from Class XI, Functions, Exception Handling in Python and File Handling in Python.Source: CBSE Computer Science (083) syllabus 2026-27, distribution of marks, Unit 1 Computational Thinking and Programming - 2

Key concepts

Data structures and the stack

NCERT section NCERT 3.1, 3.2

A data structure is a way of organising data in memory so that certain operations are easy, for example a list, a tuple or a dictionary. A stack is a linear data structure in which insertion and deletion happen at the same end, called the top. The item that went in last comes out first: LIFO (Last In, First Out). Think of a pile of plates: you put a plate on the top and take the top plate off; you cannot pull one out from the middle.

Worked example

Books are placed on a pile in the order Physics, Chemistry, Maths, CS. Two books are taken off. Which books remain, and which is now on top?

Try it first, then show the solutionSolution

1. The pile is a stack; CS went on last, so it is on top.
2. Two removals take CS, then Maths (LIFO).
3. Physics and Chemistry remain; Chemistry is on top.

Answer: Physics and Chemistry remain; Chemistry is on top.

Applications of a stack

NCERT section NCERT 3.2.1

A stack is used wherever the latest action must be handled first: the undo feature of a text editor (the last change is undone first), the back button of a web browser (the last page visited is shown first), reversing a string or list (push all, then pop all), checking whether brackets are balanced in an expression, and the way a program keeps track of function calls (the function called last returns first).

Worked example

Use a stack to reverse the string 'CBSE'.

Try it first, then show the solutionSolution

1. Push each character: the stack holds C, B, S, E with E on top.

2. s = []
   for ch in 'CBSE':
       s.append(ch)
   r = ''
   while s:
       r += s.pop()
   print(r)

3. Pop until empty: E, S, B, C.

Answer: ESBC

Push and pop; overflow and underflow

NCERT section NCERT 3.3, 3.3.1

Push adds an item at the top; pop removes and returns the top item. Trying to pop from an empty stack is underflow; trying to push onto a stack that is full (when the stack has a fixed size) is overflow. A Python list grows as needed, so with a list only underflow is a practical concern: [].pop() raises IndexError: pop from empty list, so a pop function must check for an empty stack first.

Worked example

Starting with an empty stack, perform: push 5, push 8, pop, push 3, push 9, pop, pop, push 1. Show the stack (bottom to top) at the end and the popped items in order.

Try it first, then show the solutionSolution

1. push 5: [5]; push 8: [5, 8]; pop removes 8: [5].
2. push 3: [5, 3]; push 9: [5, 3, 9]; pop removes 9; pop removes 3: [5].
3. push 1: [5, 1].

Answer: Final stack [5, 1] (1 on top); popped in order: 8, 9, 3.

Implementing a stack with a Python list

NCERT section NCERT 3.4

Take the end of the list as the top. Then every operation is quick and simple:

Operation	Python
create	stack = []
push x	stack.append(x)
pop	stack.pop() (only if not empty)
peek / top	stack[-1] (only if not empty)
isEmpty	len(stack) == 0 (or not stack)
size	len(stack)

Using the front of the list as the top (insert(0, x) and pop(0)) also works but is slower and easy to get wrong, so the board's answers use the end.

Worked example

Write isEmpty(st) and peek(st), where peek returns the top item, or 'Underflow' if the stack is empty. What do peek([]) and peek([4, 7]) return?

Try it first, then show the solutionSolution

1. def isEmpty(st):
       return len(st) == 0
   def peek(st):
       if isEmpty(st):
           return 'Underflow'
       return st[-1]
   print(peek([]), peek([4, 7]))

2. [] is empty, so 'Underflow'; in [4, 7] the top is the last item, 7.

Answer: Underflow 7

Board pattern: push items that meet a condition, then pop all

NCERT section NCERT 3.4 (Program 3-1 pattern)

The usual 3-mark question gives a list, tuple or dictionary and asks for two functions: one that pushes only the items meeting a condition, and one that pops and displays items until the stack is empty, then prints a message such as 'Stack Empty'. Write the stack as a global list or pass it as a parameter, exactly as the question says. Pop in a while loop (while st: or while len(st) != 0:), not a for loop over the stack, because the stack shrinks while you pop.

Worked example

Write PushEven(N, st) to push the even numbers of list N onto stack st, and PopEven(st) to pop and display them, then print 'Stack Empty'. Show the output for N = [12, 7, 18, 5, 4].

Try it first, then show the solutionSolution

1. def PushEven(N, st):
       for x in N:
           if x % 2 == 0:
               st.append(x)
   def PopEven(st):
       while st:
           print(st.pop(), end=' ')
       print('Stack Empty')
   S = []
   PushEven([12, 7, 18, 5, 4], S)
   print(S)
   PopEven(S)

2. Even numbers pushed in order: 12, 18, 4 (4 on top).
3. Popping gives them in reverse: 4, 18, 12.

Answer: [12, 18, 4]
4 18 12 Stack Empty

Stacks of records

NCERT section NCERT 3.4

A stack item can be any object: a number, a string, a list or a tuple. Board questions often push a part of a record, for example the name and price of each book costing more than 400, taken from a list of tuples or from a dictionary. Build the item first ([b[0], b[1]]) and push it as one element; popping returns the whole item.

Worked example

books = [('B1', 'Python', 450), ('B2', 'SQL', 300), ('B3', 'Networks', 520)]. Push [code, title] for each book priced above 400, then pop and print each, and print 'Empty' at the end.

Try it first, then show the solutionSolution

1. books = [('B1', 'Python', 450), ('B2', 'SQL', 300), ('B3', 'Networks', 520)]
   BS = []
   for b in books:
       if b[2] > 400:
           BS.append([b[0], b[1]])
   while BS:
       print(BS.pop())
   print('Empty')

2. Pushed: ['B1', 'Python'], then ['B3', 'Networks'] (top).
3. Popped: B3 first, then B1.

Answer: ['B3', 'Networks']
['B1', 'Python']
Empty

Stack in real life

Each concept, met in an everyday situation. Read the situation, answer the question in your own words, then compare with the model answer. The one-line hook is what to remember.

Topics in this chapter

• Conditional Push and Pop ProgramsComing soon
• Push and Pop OperationsComing soon
• Implementing a Stack Using a ListComing soon
• Stack Programs: Conditional Push and Pop All
• Push and Pop Operations on a Stack Using a List
• Stack: LIFO Principle and Applications

Stack: syntax and key facts

Stack principle

LIFO: Last In, First Out; all insertions and deletions at the top

Contrast: a queue is FIFO (not in the 2026-27 syllabus).

List operations

push st.append(x); pop st.pop(); peek st[-1]; empty len(st) == 0; size len(st)

The end of the list is the top.

Underflow and overflow

Underflow: pop or peek on an empty stack. Overflow: push on a full fixed-size stack.

[].pop() raises IndexError: pop from empty list.

Pop-all loop

while st: / while len(st) != 0: then print(st.pop()); after the loop print the empty message

Never pop inside for x in st:; the list shrinks while you loop.

How the board asks Stack

The question patterns to expect, and the method that works for each.

Tricks to remember Stack

Short memory aids. Say each one aloud once, then use it on a question the same day.

• LIFO = plates in the canteen

  The last plate washed goes on top and is the first one picked up.

  Use it when: Defining a stack and tracing pushes and pops.

• append is push, pop is pop

  Python already names one of the two operations for you; the other is append().

  Use it when: Writing the list implementation quickly.

• Under = nothing under your hand

  Underflow: you reach for the top plate and there is none. Overflow: the shelf is full.

  Use it when: Defining underflow and overflow.

• Pop with while, never with for

  "While there is something, take it" - while st: st.pop().

  Use it when: The pop-and-display function.

Stack: board-level solved questions

Ordered from board level to HOTS. Cover the solution, write your own, then compare step by step.

st = []
for n in [4, 9, 16, 25, 36]:
    if n % 2 == 0:
        st.append(n)
    elif st:
        st.pop()
print(st)

Case-study practice (Section E style)

Read the situation, then answer every part. In the board paper this is a 4-mark question split into 1 + 1 + 2 marks.

Where the marks are

How a typical answer is split into step marks. Show every step: a right final answer alone rarely earns full marks.

Where students lose marks in Stack

The slips examiners see most often, and what to write instead.

• ✗Mistake: Popping without checking for an empty stack

  pop() on an empty list raises IndexError, and the question usually asks for a message instead.

  Wrong working

  def POP(st):
  return st.pop()

  Right working

  def POP(st):
  if len(st) == 0:
  print('Underflow')
  else:
  return st.pop()

  ✓Do this: Check if st: (or len(st) == 0) before every pop or peek.

  Usually costs: Half to 1 mark

• ✗Mistake: Using pop(0) or insert(0, x) with append()

  Mixing ends turns the stack into a queue: pop(0) removes the first item pushed (FIFO).

  Wrong working

  st.append(x) ... st.pop(0)

  Right working

  st.append(x) ... st.pop()

  ✓Do this: Use one end only: the end of the list.

  Usually costs: 1 mark

• ✗Mistake: Popping inside a for loop over the same stack

  The list shrinks while the for loop walks it, so about half the items are skipped.

  Wrong working

  for x in st:
  print(st.pop())

  Right working

  while st:
  print(st.pop())

  ✓Do this: Always pop in a while loop that runs until the stack is empty.

  Usually costs: 1 mark

• ✗Mistake: Printing the message inside the loop or forgetting it

  The question asks for 'Stack Empty' (or 'None') once, after all items are popped.

  ✓Do this: Put the message after the while loop, at the function's indentation level.

  Usually costs: Half a mark

• ✗Mistake: Pushing the wrong part of a record

  Questions such as "push the name and price of items above 400" need a two-item list or tuple, not the whole record or two separate pushes.

  ✓Do this: Build the item exactly as asked (e.g. [rec[0], rec[2]]) and push it once.

  Usually costs: Half a mark

NCERT exercise guide: Stack

What each exercise in the NCERT chapter tests, how to approach it, and a question of the same kind solved step by step. Questions here are written in our own words.

Practice questions on Stack

Write each answer on paper first. Open the hint only if you are stuck, and the answer only when you have finished.

1. Q1 · 1 mark · MCQBoard level

   Which principle does a stack follow? (a) FIFO (b) LIFO (c) Random access (d) Sorted order

   Hint

   Pile of plates.

   Answer

   (b) LIFO

2. Q2 · 1 mark · Very short answerBoard level

   Which list method is used to push an element onto a stack implemented as a list?

   Hint

   Adds at the end.

   Answer

   append()

3. Q3 · 1 mark · Very short answerBoard level

   Show the stack (bottom to top) after: push 'X', push 'Y', push 'Z', pop, pop, push 'W'.

   Hint

   Z and then Y are removed.

   Answer

   ['X', 'W']

4. Q4 · 3 marks · Short answerHarder board level

   Write PushOdd(N) to push the odd numbers greater than 10 from list N onto a global stack ODD, and PopOdd() to pop and display them followed by 'Stack Underflow'. Show the output for N = [11, 4, 23, 7, 15].

   Hint

   Two conditions: odd and > 10.

   Answer

   ODD = []
   def PushOdd(N):
       for x in N:
           if x % 2 == 1 and x > 10:
               ODD.append(x)
   def PopOdd():
       while ODD:
           print(ODD.pop(), end=' ')
       print('Stack Underflow')
   PushOdd([11, 4, 23, 7, 15])
   PopOdd()

   Output: 15 23 11 Stack Underflow

5. Q5 · 2 marks · Short answerHarder board level

   Predict the output:

   s = [1, 2, 3, 4]
   t = []
   while s:
       x = s.pop()
       if x % 2 == 0:
           t.append(x * 10)
   print(s, t)

   Hint

   Popping starts from 4.

   Answer

   [] [40, 20]

6. Q6 · 2 marks · Short answerHOTS / competency

   A list of dictionaries holds {'name': ..., 'city': ...}. Write PUSH_CITY(L, st, c) that pushes the names of people from city c onto st. What is st after PUSH_CITY([{'name': 'A', 'city': 'Pune'}, {'name': 'B', 'city': 'Agra'}, {'name': 'C', 'city': 'Pune'}], S, 'Pune')?

   Hint

   Each item is a dictionary.

   Answer

   def PUSH_CITY(L, st, c):
       for d in L:
           if d['city'] == c:
               st.append(d['name'])
   S = []
   PUSH_CITY([{'name': 'A', 'city': 'Pune'}, {'name': 'B', 'city': 'Agra'}, {'name': 'C', 'city': 'Pune'}], S, 'Pune')
   print(S)

   Output: ['A', 'C']

7. Q7 · 1 mark · Assertion-reasonHOTS / competency

   Assertion (A): Popping items inside for x in st: empties the stack completely.
   Reason (R): Removing items from a list while a for loop walks it makes the loop skip items.

   Hint

   Try it with 4 items.

   Answer

   (d) A is false but R is true: with [1, 2, 3, 4] only two pops happen, leaving [1, 2].

8. Q8 · 2 marks · Short answerBoard level

   Give two real-life situations where a stack is used and explain why LIFO fits each.

   Hint

   Think of the most recent action.

   Answer

   Undo in an editor: the most recent change must be undone first. Browser back button: the page visited last is the first one to return to. (Other valid answers: reversing a word, bracket matching, function calls.)

9. Q9 · 3 marks · Short answerHOTS / competency

   Write a program that uses a stack to check whether a word is a palindrome. Test with 'level' and 'stack'.

   Hint

   Popping gives the word reversed.

   Answer

   def is_pal(w):
       st = []
       for ch in w:
           st.append(ch)
       rev = ''
       while st:
           rev += st.pop()
       return rev == w
   print(is_pal('level'), is_pal('stack'))

   Output: True False

Test your recall

Answer in your head or on paper first, then open the card. Pulling an answer out of memory makes it stick far better than re-reading.

1. 1.What does LIFO stand for?Show answer

   Last In, First Out.

2. 2.Which end of a Python list is used as the top in the usual implementation?Show answer

   The end (last item); push with append(), pop with pop().

3. 3.What is underflow?Show answer

   An attempt to pop (or peek) from an empty stack.

4. 4.What does [].pop() raise?Show answer

   IndexError: pop from empty list.

5. 5.Give two applications of a stack.Show answer

   Any two: undo in an editor, browser back button, reversing a string, matching brackets, function calls.

6. 6.How do you see the top item without removing it?Show answer

   st[-1] (after checking that the stack is not empty).

7. 7.Push 1, 2, 3, then pop twice. What remains?Show answer

   [1].

Quick revision checklist

The night before the exam: can you do each of these without looking?

• ☐Stack: linear data structure; insert and delete at the top only; LIFO.
• ☐Push adds at the top; pop removes and returns the top item.
• ☐Underflow: pop/peek on an empty stack. Overflow: push on a full fixed-size stack.
• ☐List as stack: top = end; append() push; pop() pop; st[-1] peek; len(st) == 0 empty.
• ☐[].pop() raises IndexError, so check before popping.
• ☐Pop all with while st: and print the empty message after the loop.
• ☐Applications: undo, browser back, reversing, bracket matching, function calls.

Stack: frequently asked questions