Stack operations (push, pop, peek) in Data Structures Theory - Step-by-Step Execution

Concept Flow - Stack operations (push, pop, peek)

Start

↓

Check Operation

↓

Push?

Yes→Add item on top

↓

Update top pointer

↓

Done

↓

Pop?

Yes→Remove item from top

↓

Update top pointer

↓

Return removed item

↓

Peek?

Yes→Look at top item

↓

Return top item

The stack operation flow checks which operation is requested: push adds an item on top, pop removes the top item, and peek returns the top item without removing it.

Execution Sample

Data Structures Theory

stack = []
stack.append(10)
stack.append(20)
top = stack[-1]
item = stack.pop()

This code adds two items to the stack, looks at the top item, then removes the top item.

Analysis Table

Step	Operation	Stack State	Top Pointer	Output/Return
1	Initialize stack	[]	None	None
2	Push 10	[10]	10	None
3	Push 20	[10, 20]	20	None
4	Peek	[10, 20]	20	20
5	Pop	[10]	10	20
6	End	[10]	10	No more operations

💡 No more operations to perform, stack remains with one item [10]

State Tracker

Variable	Start	After Step 2	After Step 3	After Step 4	After Step 5	Final
stack	[]	[10]	[10, 20]	[10, 20]	[10]	[10]
top pointer	None	10	20	20	10	10
output	None	None	None	20	20	None

Key Insights - 3 Insights

Why does peek not remove the top item from the stack?

Peek only looks at the top item without changing the stack, as shown in step 4 of the execution_table where the stack remains [10, 20] after peek.

What happens to the top pointer after a pop operation?

After pop (step 5), the top pointer updates to the next item below the removed one, changing from 20 to 10, reflecting the new top.

Can we pop from an empty stack?

No, popping from an empty stack is invalid and would cause an error; the execution_table starts with an empty stack and only pops after items are pushed.

Visual Quiz - 3 Questions

Look at the execution_table at step 3, what is the top pointer value?

A None

B 10

C 20

D 30

💡 Hint

Check the 'Top Pointer' column at step 3 in the execution_table.

At which step does the stack change from [10, 20] to [10]?

A Step 4

B Step 5

C Step 2

D Step 6

💡 Hint

Look at the 'Stack State' column in the execution_table to see when the stack size decreases.

If we perform another pop after step 5, what would be the new top pointer?

A None

B 20

C 10

D Error

💡 Hint

After popping the last item, the stack becomes empty, so the top pointer is None.

Concept Snapshot

Stack operations:
- push(item): add item on top
- pop(): remove and return top item
- peek(): return top item without removing
Top pointer always points to the last added item
Cannot pop from empty stack

Full Transcript

A stack is a data structure where items are added and removed from the top only. The main operations are push, which adds an item on top; pop, which removes the top item; and peek, which looks at the top item without removing it. The top pointer always points to the current top item. Popping from an empty stack is not allowed. This visual trace shows how the stack changes step-by-step with these operations.

Practice

1. What does the pop operation do in a stack?

easy

A. Shows the bottom item without removing it

B. Adds a new item to the bottom of the stack

C. Removes and returns the top item from the stack

D. Clears all items from the stack

Solution

1. Step 1: Understand the pop operation

   The pop operation removes the last item added to the stack, which is the top item.

2. Step 2: Confirm the behavior of pop

   It returns this top item and removes it from the stack, following last-in, first-out order.

3. Final Answer:

   Removes and returns the top item from the stack -> Option C

4. Quick Check:

   pop = remove top item [OK]

Hint: Pop always removes the last item added [OK]

Common Mistakes:

• Thinking pop adds an item
• Confusing pop with peek
• Assuming pop removes bottom item

2. Which of the following is the correct way to add an item 5 to a stack named s using the push operation?

easy

A. s.pop(5)

B. s.push(5)

C. s.peek(5)

D. s.add(5)

Solution

1. Step 1: Identify the push syntax

   Push adds an item to the top of the stack, usually called with push(item).

2. Step 2: Match the correct method call

   Only s.push(5) correctly adds 5 to the stack.

3. Final Answer:

   s.push(5) -> Option B

4. Quick Check:

   push = add item [OK]

Hint: Push means add, so look for push() method [OK]

Common Mistakes:

• Using pop instead of push
• Using peek to add items
• Using add which is not standard for stacks

3. Given the following stack operations:

s.push(10)
s.push(20)
s.pop()
s.push(30)
top = s.peek()

What is the value of top after these operations?

medium

A. 30

B. 20

C. None

D. 10

Solution

1. Step 1: Trace the stack changes step-by-step

   After push(10), stack = [10]. After push(20), stack = [10, 20]. After pop(), top 20 is removed, stack = [10]. After push(30), stack = [10, 30].

2. Step 2: Determine the top item with peek

   Peek returns the top item without removing it, so top = 30.

3. Final Answer:

   30 -> Option A

4. Quick Check:

   Last pushed after pop is 30 [OK]

Hint: Track stack after each operation carefully [OK]

Common Mistakes:

• Forgetting pop removes top
• Assuming peek removes item
• Mixing order of operations

4. Consider this code snippet for a stack:

stack = []
stack.push(1)
stack.push(2)
item = stack.pop()

What is the error in this code?

medium

A. stack is not initialized correctly

B. pop() does not return the top item

C. stack.pop() removes the bottom item, not top

D. push() is not a method of list in Python

Solution

1. Step 1: Check stack initialization

   The stack is initialized as an empty list, which is correct in Python.

2. Step 2: Verify method usage on list

   Python lists use append() to add items, not push(). Using push() causes an error.

3. Final Answer:

   push() is not a method of list in Python -> Option D

4. Quick Check:

   Python list uses append(), not push() [OK]

Hint: Remember Python list uses append(), not push() [OK]

Common Mistakes:

• Assuming push() works on Python lists
• Confusing pop() behavior
• Thinking stack initialization is wrong

5. You want to reverse a list [1, 2, 3] using a stack. Which sequence of stack operations correctly reverses the list?

hard

A. Push all items in order, then pop all items to get reversed list

B. Pop all items first, then push them back in order

C. Peek all items, then push them again

D. Push items in reverse order, then pop all items

Solution

1. Step 1: Understand stack reversal logic

   Pushing items in original order stores them with last item on top. Popping all items removes them in reverse order.

2. Step 2: Apply push then pop to reverse list

   Push 1, then 2, then 3. Popping returns 3, 2, 1, which is the reversed list.

3. Final Answer:

   Push all items in order, then pop all items to get reversed list -> Option A

4. Quick Check:

   Push then pop reverses order [OK]

Hint: Push in order, pop all to reverse list [OK]

Common Mistakes:

• Pushing in reverse order first
• Using peek to reverse
• Popping before pushing