Stack Implementation Using Array in DSA Javascript - Time & Space Complexity

Time Complexity: Stack Implementation Using Array

O(1)

Understanding Time Complexity

We want to understand how fast stack operations run when using an array.

Specifically, how the time changes as the stack grows.

Scenario Under Consideration

Analyze the time complexity of the following stack operations using an array.

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

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

  pop() {
    return this.items.pop();
  }

  peek() {
    return this.items[this.items.length - 1];
  }
}
    

This code shows how to add, remove, and check the top item in a stack using an array.

Identify Repeating Operations

Look at the main actions that repeat when using 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 does a simple action regardless of stack size.

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 calls, not the stack size.

Final Time Complexity

Time Complexity: O(1)

This means each push or pop takes the same small amount of time no matter how big the stack is.

Common Mistake

[X] Wrong: "Push or pop takes longer as the stack grows because the array gets bigger."

[OK] Correct: Arrays add or remove items at the end in constant time, so time does not depend on size.

Interview Connect

Knowing stack operations are quick helps you choose the right tool for problems needing last-in-first-out order.

Self-Check

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

Practice

1. What is the main characteristic of a stack data structure implemented using an array?

easy

A. Sorted Order

B. Last In, First Out (LIFO)

C. Random Access

D. First In, First Out (FIFO)

Solution

1. Step 1: Understand stack behavior

   A stack adds and removes elements from the same end, so the last element added is the first to be removed.

2. Step 2: Identify the correct term

   This behavior is called Last In, First Out (LIFO).

3. Final Answer:

   Last In, First Out (LIFO) -> Option B

4. Quick Check:

   Stack = LIFO [OK]

Hint: Stack always removes the last added item first [OK]

Common Mistakes:

• Confusing stack with queue (FIFO)
• Thinking stack allows random access
• Assuming stack keeps elements sorted

2. Which of the following is the correct way to add an element to a stack implemented as an array in JavaScript?

easy

A. stack.push(element);

B. stack.pop(element);

C. stack.shift(element);

D. stack.unshift(element);

Solution

1. Step 1: Identify method to add element at the end

   In JavaScript arrays, push() adds an element to the end of the array.

2. Step 2: Confirm stack push operation

   Stack push means adding element on top, which corresponds to array's end, so push() is correct.

3. Final Answer:

   stack.push(element); -> Option A

4. Quick Check:

   Use push() to add element to stack [OK]

Hint: Use push() to add on top of stack [OK]

Common Mistakes:

• Using pop() which removes element
• Using shift() or unshift() which affect start of array

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

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

medium

A. [10, 20, 30]

B. [30]

C. [20, 30]

D. [10, 30]

Solution

1. Step 1: Trace push and pop operations

   Initially stack = [] push(10) -> [10] push(20) -> [10, 20] pop() removes last element 20 -> [10] push(30) -> [10, 30]

2. Step 2: Check final stack state

   After all operations, stack contains [10, 30].

3. Final Answer:

   [10, 30] -> Option D

4. Quick Check:

   Push and pop update stack correctly [OK]

Hint: Pop removes last pushed, push adds at end [OK]

Common Mistakes:

• Assuming pop removes first element
• Confusing order of elements after pop

4. Identify the error in the following stack implementation code and select the correct fix:

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

medium

A. Use push() instead of unshift() in push method

B. Use shift() instead of pop() in pop method

C. No error, code is correct

D. Use pop() instead of push() in push method

Solution

1. Step 1: Analyze push method

   push uses unshift which adds element at start of array.

2. Step 2: Analyze pop method

   pop removes element from end of array. This causes mismatch because push adds at start but pop removes from end.

3. Step 3: Fix mismatch

   To maintain stack behavior, push should add at end using push(), so pop removes last added element correctly.

4. Final Answer:

   Use push() instead of unshift() in push method -> Option A

5. Quick Check:

   push() and pop() must match ends [OK]

Hint: Push and pop must operate on same array end [OK]

Common Mistakes:

• Mixing unshift with pop causes wrong stack order
• Thinking shift() and pop() are interchangeable
• Ignoring array end consistency

5. You want to implement a stack using an array that also tracks the maximum element at any time efficiently. Which approach is best?

hard

A. Scan entire array to find max after each pop

B. Sort the array after each push to find max

C. Use two stacks: one for elements, one for max values

D. Store max element only in a variable updated on push

Solution

1. Step 1: Understand max tracking challenge

   Finding max after each operation must be efficient, not scanning entire array.

2. Step 2: Evaluate options

   Sorting after each push is costly. Scanning array after pop is slow. Storing max in variable fails if max is popped.

3. Step 3: Use two stacks approach

   One stack stores elements, second stack stores current max at each push. This allows O(1) max retrieval.

4. Final Answer:

   Use two stacks: one for elements, one for max values -> Option C

5. Quick Check:

   Two stacks track max efficiently [OK]

Hint: Use auxiliary stack to track max values [OK]

Common Mistakes:

• Sorting array each time is inefficient
• Single variable max fails when max is popped
• Scanning array after pop is slow