Stack Concept and LIFO Principle in DSA C++ - Execution Trace

Concept Flow - Stack Concept and LIFO Principle

Start with empty stack

↓

Push element

→Add element on top

↓

Stack grows upwards

↓

Pop element

→Remove top element

↓

Stack shrinks

↓

Repeat push/pop as needed

↓

End with current stack state

Stack works by adding elements on top and removing from top, following Last In First Out (LIFO) order.

Execution Sample

DSA C++

stack.push(10);
stack.push(20);
stack.push(30);
stack.pop();
stack.push(40);

Push 10, 20, 30; pop top (30); push 40 on stack.

Execution Table

Step	Operation	Nodes in Stack	Pointer Changes	Visual State
1	push(10)	10	top -> 10	10 -> null
2	push(20)	20 -> 10	top -> 20	20 -> 10 -> null
3	push(30)	30 -> 20 -> 10	top -> 30	30 -> 20 -> 10 -> null
4	pop()	20 -> 10	top -> 20	20 -> 10 -> null
5	push(40)	40 -> 20 -> 10	top -> 40	40 -> 20 -> 10 -> null

💡 Operations complete; final stack top is 40 with elements 40, 20, 10.

Variable Tracker

Variable	Start	After 1	After 2	After 3	After 4	After 5
top	null	10	20	30	20	40
stack size	0	1	2	3	2	3

Key Moments - 3 Insights

Why does pop remove the last pushed element and not the first?

Because the stack follows LIFO, the last element pushed (step 3) is on top and is removed first at step 4, as shown in execution_table rows 3 and 4.

What happens to the popped element in memory?

The popped element (30) is removed from the stack top pointer at step 4, so it is no longer accessible in the stack, effectively discarded from the structure.

Why does the stack grow and shrink only at the top?

Stack operations push and pop only affect the top pointer, adding or removing elements there, as seen in pointer changes column in execution_table.

Visual Quiz - 3 Questions

Look at the execution_table, what is the stack top after step 3?

A 10

B 30

C 20

D 40

💡 Hint

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

At which step does the stack size decrease?

A Step 2

B Step 3

C Step 4

D Step 5

💡 Hint

Look at 'stack size' in variable_tracker between steps; it decreases after step 4.

If we pop twice after step 3, what would be the new top?

A 10

B 20

C 30

D 40

💡 Hint

After popping twice from 30 -> 20 -> 10, top moves down two elements; see execution_table for pop behavior.

Concept Snapshot

Stack stores elements in LIFO order.
Push adds element on top.
Pop removes element from top.
Only top element is accessible.
Stack size changes with push/pop.
Used for undo, recursion, expression evaluation.

Full Transcript

A stack is a data structure where elements are added and removed from the top only. This follows the Last In First Out principle, meaning the last element added is the first to be removed. In the example, we push 10, 20, and 30 onto the stack, making 30 the top. When we pop, 30 is removed, and the top becomes 20. Then pushing 40 places it on top. The stack grows and shrinks only at the top pointer. This behavior is shown step-by-step in the execution table and variable tracker.

Practice

1. What does the LIFO principle mean in the context of a stack?

easy

A. Last In, First Out - the last element added is removed first

B. First In, First Out - the first element added is removed first

C. Elements are removed randomly

D. Elements are removed based on their value

Solution

1. Step 1: Understand LIFO principle

   LIFO means the last element added to the stack is the first one to be removed.

2. Step 2: Match with stack behavior

   Stacks follow LIFO, so the last pushed element is popped first.

3. Final Answer:

   Last In, First Out - the last element added is removed first -> Option A

4. Quick Check:

   LIFO = Last In, First Out [OK]

Hint: Remember stack removes newest item first [OK]

Common Mistakes:

• Confusing LIFO with FIFO
• Thinking stack removes oldest element first
• Assuming random removal order

2. Which of the following is the correct way to push an integer 10 onto a stack named s in C++ STL?

easy

A. s.add(10);

B. s.insert(10);

C. push(s, 10);

D. s.push(10);

Solution

1. Step 1: Recall C++ STL stack push syntax

   In C++ STL, the method to add an element to stack is push() called on the stack object.

2. Step 2: Verify correct method usage

   Using s.push(10); correctly pushes 10 onto stack s.

3. Final Answer:

   s.push(10); -> Option D

4. Quick Check:

   Stack push method = push() [OK]

Hint: Use s.push(value) to add in C++ STL stack [OK]

Common Mistakes:

• Using non-existent methods like add or insert
• Calling push as a free function
• Confusing vector methods with stack

3. What will be the output of the following C++ code?

std::stack<int> s;
s.push(5);
s.push(10);
s.push(15);
int x = s.top();
s.pop();
int y = s.top();
std::cout << x << " " << y << std::endl;

medium

A. 15 10

B. 5 10

C. 10 5

D. 15 5

Solution

1. Step 1: Trace stack push operations

   Elements pushed in order: 5 (bottom), 10, 15 (top).

2. Step 2: Check top and pop operations

   First, x = s.top() gives 15. Then s.pop() removes 15. Next, y = s.top() gives 10.

3. Final Answer:

   15 10 -> Option A

4. Quick Check:

   Top after push = 15, after pop = 10 [OK]

Hint: Top shows last pushed; pop removes it [OK]

Common Mistakes:

• Confusing order of elements after pop
• Assuming pop returns value
• Mixing bottom and top elements

4. Identify the error in the following C++ code snippet using stack:

std::stack<int> s;
s.pop();
s.push(20);

medium

A. Syntax error in stack declaration

B. Cannot pop from an empty stack; causes runtime error

C. push should come before pop always

D. No error; code runs fine

Solution

1. Step 1: Analyze stack operations order

   The code calls pop() on an empty stack before pushing any element.

2. Step 2: Understand pop behavior on empty stack

   Calling pop() on empty stack is undefined and causes runtime error.

3. Final Answer:

   Cannot pop from an empty stack; causes runtime error -> Option B

4. Quick Check:

   Pop empty stack = runtime error [OK]

Hint: Never pop before pushing any element [OK]

Common Mistakes:

• Ignoring empty stack before pop
• Assuming pop returns value
• Thinking push order fixes pop error

5. Given a stack with elements pushed in this order: 3, 7, 9, 2, 5. Which sequence of pop() operations will produce the output 5 2 9 when printing popped elements?

hard

A. Pop twice, push 1, then pop once

B. Pop once, push 4, then pop twice

C. Pop three times consecutively

D. Pop once, pop again, then push 6 and pop

Solution

1. Step 1: Understand stack order after pushes

   Stack top to bottom: 5 (top), 2, 9, 7, 3 (bottom).

2. Step 2: Pop three times consecutively

   First pop: 5, second pop: 2, third pop: 9. This matches output sequence.

3. Final Answer:

   Pop three times consecutively -> Option C

4. Quick Check:

   Pop order matches output 5 2 9 [OK]

Hint: Pop in order to get last pushed elements first [OK]

Common Mistakes:

• Adding extra pushes changes output
• Popping fewer times than needed
• Confusing push/pop order