Stack Using Linked List vs Array Stack Trade-offs in DSA Typescript - Complexity Comparison

Time Complexity: Stack Using Linked List vs Array Stack Trade-offs

O(1)

Understanding Time Complexity

We want to understand how fast stack operations run when using linked lists versus arrays.

Which method is faster or slower as the stack grows?

Scenario Under Consideration

Analyze the time complexity of push and pop operations for stacks implemented with linked lists and arrays.

// Linked List Stack push
function pushLinkedList(value: number) {
  const newNode = { value, next: top };
  top = newNode;
}

// Array Stack push
function pushArray(value: number) {
  stackArray.push(value);
}
    

These functions add an item to the top of the stack using two different methods.

Identify Repeating Operations

Both push and pop do a single main action each time.

• Primary operation: Adding or removing one element at the top.
• How many times: Once per push or pop call, no loops involved.

How Execution Grows With Input

Each push or pop takes about the same time no matter how big the stack is.

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

Pattern observation: Time stays steady as stack size grows.

Final Time Complexity

Time Complexity: O(1)

This means each push or pop happens in constant time, no matter how many items are in the stack.

Common Mistake

[X] Wrong: "Array stack push always takes longer as the stack grows because the array size increases."

[OK] Correct: Most array stacks resize occasionally, but each push is still amortized constant time because resizing happens rarely and its cost spreads out.

Interview Connect

Knowing these trade-offs helps you explain why one stack type might be better in certain situations, showing your understanding of data structure choices.

Self-Check

"What if the array stack did not resize dynamically and had a fixed size? How would that affect time complexity and usability?"

Practice

1. Which of the following is a key advantage of using a linked list to implement a stack compared to using an array?

easy

A. Dynamic size without needing to resize

B. Faster access to elements by index

C. Uses less memory per element

D. Simpler syntax to implement

Solution

1. Step 1: Understand stack size behavior

   Arrays have fixed size or require resizing, linked lists grow dynamically.

2. Step 2: Compare memory and access

   Linked lists use extra memory for pointers and have slower indexed access.

3. Final Answer:

   Dynamic size without needing to resize -> Option A

4. Quick Check:

   Linked list stacks grow dynamically = A [OK]

Hint: Linked list stacks grow dynamically, arrays need resizing [OK]

Common Mistakes:

• Thinking arrays always use less memory
• Confusing access speed advantages
• Assuming linked lists have simpler syntax

2. Which TypeScript syntax correctly declares an array-based stack of numbers?

easy

A. let stack = new Stack<number>();

B. const stack: number[] = [];

C. const stack: Array = number[];

D. var stack: number = [];

Solution

1. Step 1: Check array declaration syntax

   TypeScript arrays use type[] or Array<type> syntax.

2. Step 2: Validate each option

   const stack: number[] = []; uses correct syntax: number[] = []. Others have syntax errors or wrong types.

3. Final Answer:

   const stack: number[] = []; -> Option B

4. Quick Check:

   Correct array syntax = C [OK]

Hint: Array type syntax is type[] or Array<type> [OK]

Common Mistakes:

• Using wrong generic syntax
• Assigning array to wrong type variable
• Using var instead of const/let incorrectly

3. Consider this TypeScript code using an array stack:

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

What is the output?

medium

A. [10, 30]

B. [30]

C. [20, 30]

D. [10, 20, 30]

Solution

1. Step 1: Trace stack operations

   Push 10 -> [10], push 20 -> [10,20], pop removes 20 -> [10], push 30 -> [10,30]

2. Step 2: Check final stack content

   Stack contains 10 and 30 in order pushed and popped.

3. Final Answer:

   [10, 30] -> Option A

4. Quick Check:

   Push/pop trace = [10, 30] [OK]

Hint: Pop removes last pushed element, check stack after each step [OK]

Common Mistakes:

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

4. This TypeScript code tries to implement a linked list stack but has an error:

class Node {
  value: number;
  next: Node | null;
  constructor(value: number) {
    this.value = value;
    this.next = null;
  }
}

class Stack {
  top: Node | null = null;
  push(value: number) {
    const newNode = new Node(value);
    newNode.next = this.top;
    this.top = newNode;
  }
  pop(): number | null {
    if (!this.top) return null;
    const val = this.top.value;
    this.top = this.top.next;
    return val;
  }
}

const stack = new Stack();
stack.push(5);
stack.push(10);
console.log(stack.pop());
console.log(stack.pop());
console.log(stack.pop());

What is the error in this code?

medium

A. Node class is missing a constructor

B. push() does not update the top pointer correctly

C. pop() returns null when stack is empty, which is correct behavior

D. Stack class does not initialize top to null

Solution

1. Step 1: Review pop() method behavior

   pop() returns null if stack is empty, which is expected to indicate empty stack.

2. Step 2: Check push() and initialization

   push() correctly updates top; Node has constructor; top initialized to null.

3. Final Answer:

   pop() returns null when stack is empty, which is correct behavior -> Option C

4. Quick Check:

   pop() returns null on empty stack = A [OK]

Hint: pop() returning null on empty stack is expected [OK]

Common Mistakes:

• Thinking pop() should throw error instead
• Believing push() does not update top
• Missing that top is initialized properly

5. You want to implement a stack that can handle millions of push/pop operations efficiently without resizing overhead. Which implementation is better and why?

hard

A. Array stack, because arrays have faster indexed access

B. Linked list stack, because it uses contiguous memory

C. Array stack, because it uses less memory per element

D. Linked list stack, because it avoids costly array resizing

Solution

1. Step 1: Consider resizing overhead in array stacks

   Arrays must resize and copy data when full, causing delays in many operations.

2. Step 2: Evaluate linked list advantages

   Linked lists grow dynamically without resizing, so push/pop remain efficient for large operations.

3. Final Answer:

   Linked list stack, because it avoids costly array resizing -> Option D

4. Quick Check:

   Dynamic growth avoids resizing = B [OK]

Hint: Avoid resizing overhead with linked list stacks for large operations [OK]

Common Mistakes:

• Assuming arrays never resize
• Confusing memory usage with speed
• Thinking linked lists use contiguous memory