Stack Concept and LIFO Principle in DSA C++ - Time & Space Complexity

Time Complexity: Stack Concept and LIFO Principle

O(1)

Understanding Time Complexity

We want to understand how fast stack operations run as the stack grows.

How does the time to add or remove items change when the stack gets bigger?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

#include <iostream>
#include <stack>

int main() {
    std::stack<int> s;
    s.push(10);  // Add item
    s.push(20);
    s.pop();     // Remove item
    return 0;
}
    

This code adds two items to a stack and then removes one, following the last-in, first-out rule.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: push and pop actions on the stack.
• How many times: Each operation happens once here, but in general, each push or pop works on one item at a time.

How Execution Grows With Input

Each push or pop takes the same short time no matter how many items are in the stack.

Input Size (n)	Approx. Operations
10	10 push or pop steps
100	100 push or pop steps
1000	1000 push or pop steps

Pattern observation: The time grows directly with the number of push or pop actions, but each action itself is quick and does not depend on stack size.

Final Time Complexity

Time Complexity: O(1)

This means each push or pop operation takes a constant amount of time, no matter how big the stack is.

Common Mistake

[X] Wrong: "Removing an item from the stack takes longer if the stack is bigger."

[OK] Correct: The stack only removes the top item, so it does not need to look through all items. The time stays the same.

Interview Connect

Understanding that stack operations are fast and simple helps you explain why stacks are useful in many programs and algorithms.

Self-Check

"What if we changed the stack to a queue? How would the time complexity of adding and removing items change?"

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