Push Operation on Stack in DSA Javascript - Time & Space Complexity

Time Complexity: Push Operation on Stack

O(1)

Understanding Time Complexity

We want to understand how the time needed to add an item to a stack changes as the stack grows.

How does the push operation behave when the stack size increases?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

class Stack {
  constructor() {
    this.items = [];
  }

  push(element) {
    this.items.push(element);
  }
}
    

This code adds an element to the top of the stack using an array's push method.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: Adding one element to the end of the array.
• How many times: Exactly once per push call.

How Execution Grows With Input

Each push adds one element without scanning or moving other elements.

Input Size (n)	Approx. Operations
10	10 pushes = 10 operations
100	100 pushes = 100 operations
1000	1000 pushes = 1000 operations

Pattern observation: Operations grow directly with the number of pushes, one per push.

Final Time Complexity

Time Complexity: O(1)

This means adding an element takes the same short time no matter how big the stack is.

Common Mistake

[X] Wrong: "Push takes longer as the stack grows because it has to move all elements."

[OK] Correct: The push operation adds only to the end without moving existing elements, so time stays constant.

Interview Connect

Knowing push is quick and constant time helps you explain stack efficiency clearly in interviews.

Self-Check

"What if the stack was implemented using a linked list instead of an array? How would the time complexity of push change?"

Practice

1. What does the push operation do in a stack data structure?

easy

A. Checks if the stack is empty

B. Removes the top element from the stack

C. Returns the bottom element of the stack

D. Adds an element to the top of the stack

Solution

1. Step 1: Understand stack operations

   A stack follows Last In First Out (LIFO). The push operation adds an element on top.

2. Step 2: Identify the role of push

   It inserts a new element at the top, increasing stack size by one.

3. Final Answer:

   Adds an element to the top of the stack -> Option D

4. Quick Check:

   Push = Add top element [OK]

Hint: Push means add on top of stack [OK]

Common Mistakes:

• Confusing push with pop operation
• Thinking push removes elements
• Mixing stack with queue operations

2. Which of the following is the correct syntax to push an element 5 into a stack array named stack in JavaScript?

easy

A. stack.add(5);

B. stack.push(5);

C. push.stack(5);

D. stack.insert(5);

Solution

1. Step 1: Recall JavaScript array push syntax

   JavaScript arrays use push() method to add elements at the end.

2. Step 2: Match correct method call

   stack.push(5); correctly calls push on the array named stack.

3. Final Answer:

   stack.push(5); -> Option B

4. Quick Check:

   Array push method = stack.push(value) [OK]

Hint: Use arrayName.push(value) to add element [OK]

Common Mistakes:

• Using non-existent methods like add or insert
• Reversing method and object like push.stack()
• Forgetting parentheses after push

3. What will be the output after executing the following code?

const stack = [];
stack.push(10);
stack.push(20);
stack.push(30);
console.log(stack);

medium

A. [10, 20]

B. [30, 20, 10]

C. [10, 20, 30]

D. Error: push is not a function

Solution

1. Step 1: Trace push operations on empty stack

   Initially stack is empty []. After push(10), stack = [10]. After push(20), stack = [10, 20]. After push(30), stack = [10, 20, 30].

2. Step 2: Understand console.log output

   Logging stack prints the array as is: [10, 20, 30].

3. Final Answer:

   [10, 20, 30] -> Option C

4. Quick Check:

   Push adds at end, so stack = [10,20,30] [OK]

Hint: Push adds at end, array grows left to right [OK]

Common Mistakes:

• Assuming push adds at start (top as front)
• Confusing stack order with queue
• Expecting reversed array output

4. Identify the error in the following code snippet that tries to push an element into a stack:

let stack = 5;
stack.push(10);

medium

A. stack is not an array, so push method is undefined

B. push method requires two arguments

C. stack.push should be stack.add

D. No error, code runs fine

Solution

1. Step 1: Check variable type of stack

   stack is assigned number 5, not an array. Numbers do not have push method.

2. Step 2: Understand push method applicability

   push is an array method. Calling push on a number causes error: push is not a function.

3. Final Answer:

   stack is not an array, so push method is undefined -> Option A

4. Quick Check:

   push only works on arrays [OK]

Hint: Only arrays have push method [OK]

Common Mistakes:

• Assuming push works on numbers
• Thinking push needs multiple arguments
• Confusing push with add method

5. Given a stack implemented as an array, how would you push multiple elements [1, 2, 3] onto it so that 3 is on top after all pushes?
Choose the correct code snippet.

hard

A. stack.push(1); stack.push(2); stack.push(3);

B. stack.push(3); stack.push(2); stack.push(1);

C. stack.push([1, 2, 3]);

D. stack = [1, 2, 3];

Solution

1. Step 1: Understand push order for stack

   Push adds elements on top. To have 3 on top, push 1 first, then 2, then 3.

2. Step 2: Analyze options

   Sequential pushes of 1 then 2 then 3 add elements individually with 3 on top. Pushing [1,2,3] adds a single array element with [1,2,3] on top. Reverse pushes put 1 on top. Assignment replaces the stack entirely.

3. Final Answer:

   stack.push(1); stack.push(2); stack.push(3); -> Option A

4. Quick Check:

   Push in order to have last element on top [OK]

Hint: Push elements in order, last pushed is top [OK]

Common Mistakes:

• Pushing array [1,2,3] as single element
• Pushing in reverse order
• Replacing stack instead of pushing