Stack Concept and LIFO Principle in DSA Javascript - 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 these stack operations.

class Stack {
  constructor() {
    this.items = [];
  }
  push(element) {
    this.items.push(element);
  }
  pop() {
    return this.items.pop();
  }
}
    

This code adds (push) and removes (pop) items from the stack following the last-in, first-out rule.

Identify Repeating Operations

Look at what repeats when we use the stack.

• Primary operation: Adding or removing one item at the end of the array.
• How many times: Each push or pop happens once per call, no loops inside.

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	1 operation per push or pop
100	1 operation per push or pop
1000	1 operation per push or pop

Pattern observation: The time stays the same no matter how big the stack is.

Final Time Complexity

Time Complexity: O(1)

This means adding or removing an item takes a constant, quick step regardless of stack size.

Common Mistake

[X] Wrong: "Push or pop takes longer as the stack grows because there are more items."

[OK] Correct: Push and pop only work at the top, so they do not check or move other items, keeping time constant.

Interview Connect

Knowing stack operations run in constant time shows you understand efficient data handling, a key skill in coding interviews.

Self-Check

"What if we used an array but added items at the start instead of the end? How would the time complexity change?"

Practice

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

easy

A. Elements are removed based on their value

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

C. Elements are removed randomly

D. Last In, First Out - the last element added is the first to be removed

Solution

1. Step 1: Understand the LIFO principle

   LIFO means the last element you put in is the first one you take out.

2. Step 2: Apply to stack behavior

   Stacks follow LIFO, so the newest item is removed first.

3. Final Answer:

   Last In, First Out - the last element added is the first to be removed -> Option D

4. Quick Check:

   LIFO = Last In, First Out [OK]

Hint: Remember stack like a stack of plates, last added removed first [OK]

Common Mistakes:

• Confusing LIFO with FIFO
• Thinking elements are removed randomly
• Assuming removal depends on element value

2. Which of the following is the correct way to push an element '5' onto a stack named stack in JavaScript?

easy

A. stack.insert(5);

B. stack.add(5);

C. stack.push(5);

D. stack.enqueue(5);

Solution

1. Step 1: Recall JavaScript stack operations

   JavaScript arrays use push() to add elements at the end (top of stack).

2. Step 2: Match method to stack push

   push() adds element to stack top, so stack.push(5); is correct.

3. Final Answer:

   stack.push(5); -> Option C

4. Quick Check:

   Push method adds element to stack [OK]

Hint: Use push() to add elements to stack in JavaScript [OK]

Common Mistakes:

• Using add() or insert() which are not array methods
• Confusing enqueue() with queue operation
• Trying to use non-existent methods

3. What will be the output of the following JavaScript code?

const stack = [];
stack.push(10);
stack.push(20);
const popped = stack.pop();
console.log(popped);
console.log(stack);

medium

A. 20
[10]

B. 10
[20]

C. 10
[10, 20]

D. 20
[20]

Solution

1. Step 1: Trace push operations

   stack.push(10) adds 10, stack.push(20) adds 20. Stack is now [10, 20].

2. Step 2: Trace pop operation

   stack.pop() removes last element 20 and returns it. Stack becomes [10].

3. Final Answer:

   20 [10] -> Option A

4. Quick Check:

   Pop returns last pushed element 20 [OK]

Hint: Pop returns last pushed element, stack shrinks by one [OK]

Common Mistakes:

• Thinking pop returns first element
• Confusing push and pop order
• Expecting stack unchanged after pop

4. Identify the error in the following code snippet that tries to implement a stack using an array:

const stack = [];
stack.push(1);
stack.push(2);
const top = stack.pop;
console.log(top);

medium

A. pop is used without parentheses, so it returns the function, not the popped value

B. push method is incorrect, should be pushElement

C. stack should be initialized as an object, not an array

D. console.log cannot print stack elements

Solution

1. Step 1: Check pop usage

   stack.pop is a function reference; missing () means no call, so top is function, not value.

2. Step 2: Understand effect on output

   console.log(top) prints function code, not popped element. Correct usage is stack.pop().

3. Final Answer:

   pop is used without parentheses, so it returns the function, not the popped value -> Option A

4. Quick Check:

   Call pop() with () to get value [OK]

Hint: Always use parentheses to call pop() method [OK]

Common Mistakes:

• Forgetting parentheses on pop()
• Thinking push method is wrong
• Confusing array with object for stack

5. You have a stack initially empty. You perform these operations in order:

push(1), push(2), pop(), push(3), pop(), pop()

What is the final output of each pop operation in sequence?

hard

A. [2, 3, 3]

B. [2, 3, 1]

C. [2, 3, undefined]

D. [1, 3, 2]

Solution

1. Step 1: Perform push(1) and push(2)

   Stack becomes [1, 2].

2. Step 2: pop() removes last pushed element

   pop() returns 2, stack is now [1].

3. Step 3: push(3)

   Stack becomes [1, 3].

4. Step 4: pop() returns 3, stack is [1]

5. Step 5: pop() returns 1, stack is empty

6. Final Answer:

   [2, 3, 1] -> Option B

7. Quick Check:

   Pop returns last pushed elements in reverse order [OK]

Hint: Track stack after each operation to find pop outputs [OK]

Common Mistakes:

• Mixing order of popped elements
• Assuming pop returns undefined when stack not empty
• Confusing push and pop effects