Stack Implementation Using Array in DSA Typescript - 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.

How does the time to push or pop items change as the stack grows?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

class Stack {
  private items: number[] = [];

  push(element: number): void {
    this.items.push(element);
  }

  pop(): number | undefined {
    return this.items.pop();
  }
}
    

This code shows a stack using an array with push and pop methods.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

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

How Execution Grows With Input

Each push or pop does a single action regardless of stack size.

Input Size (n)	Approx. Operations
10	1 per push or pop
100	1 per push or pop
1000	1 per push or pop

Pattern observation: The time stays the same no matter how many items are in the stack.

Final Time Complexity

Time Complexity: O(1)

This means push and pop take the same short time no matter the stack size.

Common Mistake

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

[OK] Correct: The array adds or removes only at the end, so it does not need to move other items, keeping time constant.

Interview Connect

Knowing that stack operations are quick and constant time helps you explain efficient data handling in interviews.

Self-Check

"What if we used an array but added or removed elements 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. It stores elements in sorted order

B. It follows First In First Out (FIFO) order

C. It allows random access to elements

D. It follows Last In First Out (LIFO) order

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 order type

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

3. Final Answer:

   It follows Last In First Out (LIFO) order -> Option D

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 sorts elements
• Assuming random access like arrays

2. Which of the following is the correct way to push an element 'x' onto a stack implemented as an array named stack in TypeScript?

easy

A. stack.insert(x);

B. stack.pop(x);

C. stack.push(x);

D. stack.add(x);

Solution

1. Step 1: Recall array methods for stack push

   In TypeScript, to add an element at the end of an array, use the push method.

2. Step 2: Verify other options

   pop removes elements, insert and add are not valid array methods.

3. Final Answer:

   stack.push(x); -> Option C

4. Quick Check:

   Push uses .push() method [OK]

Hint: Use .push() to add elements to array stack [OK]

Common Mistakes:

• Using pop instead of push
• Using non-existent methods like insert or add
• Confusing push with pop

3. What will be the output of the following TypeScript code implementing a stack using an array?

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

medium

A. [10, 20, 30]

B. [10, 30]

C. [20, 30]

D. [30]

Solution

1. Step 1: Trace stack operations step-by-step

   Initially stack = []. After push(10), stack = [10]. After push(20), stack = [10, 20]. After pop(), top element 20 is removed, stack = [10]. After push(30), stack = [10, 30].

2. Step 2: Determine final stack state

   The console.log prints the current stack array: [10, 30].

3. Final Answer:

   [10, 30] -> Option B

4. Quick Check:

   Push and pop update stack correctly [OK]

Hint: Pop removes last pushed element, then push adds new [OK]

Common Mistakes:

• Forgetting pop removes last element
• Assuming pop removes first element
• Confusing order of push and pop

4. Identify the error in the following TypeScript code for stack pop operation and select the correct fix.

class Stack {
  private items: number[] = [];
  pop(): number {
    return this.items.pop();
  }
}

medium

A. pop() should check if stack is empty before popping

B. items array should be public, not private

C. pop() should return void, not number

D. No error, code is correct

Solution

1. Step 1: Analyze pop method behavior

   The pop() method of array returns number | undefined if empty. Returning directly without check can cause undefined return.

2. Step 2: Identify fix for empty stack

   To avoid returning undefined, pop() should check if items is empty before popping and handle that case.

3. Final Answer:

   pop() should check if stack is empty before popping -> Option A

4. Quick Check:

   Check empty before pop to avoid undefined [OK]

Hint: Always check stack empty before pop to avoid errors [OK]

Common Mistakes:

• Ignoring empty stack check
• Changing return type incorrectly
• Making items public unnecessarily

5. Given a stack implemented using an array, how would you implement a function reverseStack that reverses the elements in the stack without using any extra stack or array? Which approach is correct?

hard

A. Use recursion to pop all elements, then insert them at bottom recursively

B. Use a for loop to swap elements from start and end indices

C. Pop all elements into a new array, then push back in reverse order

D. Use a queue to dequeue and enqueue elements to reverse order

Solution

1. Step 1: Understand constraints

   No extra stack or array allowed, so iterative swapping or extra storage is not possible.

2. Step 2: Use recursion to reverse stack

   Recursion can pop all elements, then insert each element at the bottom of the stack recursively, effectively reversing it.

3. Step 3: Evaluate other options

   Use a for loop to swap elements from start and end indices requires direct index access which is not typical for stack abstraction. Pop all elements into a new array, then push back in reverse order uses extra array. Use a queue to dequeue and enqueue elements to reverse order uses queue, which is extra data structure.

4. Final Answer:

   Use recursion to pop all elements, then insert them at bottom recursively -> Option A

5. Quick Check:

   Recursion reverses stack without extra storage [OK]

Hint: Recursion can reverse stack by inserting at bottom [OK]

Common Mistakes:

• Using extra arrays or stacks against constraints
• Trying to swap elements directly in stack
• Using other data structures like queue