Stack Implementation Using Linked List in DSA Typescript - Time & Space Complexity

Time Complexity: Stack Implementation Using Linked List

O(1)

Understanding Time Complexity

We want to understand how fast stack operations work when using a linked list.

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

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

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 poppedValue = this.top.value;
    this.top = this.top.next;
    return poppedValue;
  }
}
    

This code adds and removes items from the top of a stack using a linked list.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: Adding or removing one node at the top of the linked list.
• How many times: Each push or pop does this once, no loops or recursion involved.

How Execution Grows With Input

Each push or pop takes the same small number of steps no matter how many items are in the stack.

Input Size (n)	Approx. Operations
10	About 3 steps per push or pop
100	About 3 steps per push or pop
1000	About 3 steps per push or pop

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

Final Time Complexity

Time Complexity: O(1)

This means each push or pop operation takes a constant amount of time regardless of stack size.

Common Mistake

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

[OK] Correct: Push and pop only change the top node, so they do not need to look at the whole list.

Interview Connect

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

Self-Check

"What if we changed the stack to use an array instead of a linked list? How would the time complexity of push and pop change?"

Practice

1. What is the main advantage of implementing a stack using a linked list instead of an array?

easy

A. It allows random access to elements

B. It uses less memory than an array

C. The stack can grow dynamically without a fixed size limit

D. It is faster to access elements by index

Solution

1. Step 1: Understand stack size limitation in arrays

   Arrays have a fixed size, so stacks implemented with arrays have a maximum capacity.

2. Step 2: Linked list dynamic size

   Linked lists can grow or shrink dynamically by adding or removing nodes, so stack size is not fixed.

3. Final Answer:

   The stack can grow dynamically without a fixed size limit -> Option C

4. Quick Check:

   Linked list stacks grow dynamically = A [OK]

Hint: Linked list stacks grow dynamically, arrays do not [OK]

Common Mistakes:

• Thinking linked lists use less memory always
• Confusing stack with queue behavior
• Assuming random access is possible in linked lists

2. Which of the following is the correct TypeScript syntax to define a node class for a linked list stack?

easy

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

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

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

D. class Node { value: number; next: any; constructor(value: number) { this.value = value; this.next = undefined; } }

Solution

1. Step 1: Check next pointer type

   In a linked list, next can be another node or null if it's the last node.

2. Step 2: Verify constructor initialization

   The constructor sets value and initializes next to null.

3. Final Answer:

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

4. Quick Check:

   next can be Node or null = B [OK]

Hint: next must allow null for last node [OK]

Common Mistakes:

• Not allowing next to be null
• Initializing next as undefined
• Using incorrect type for next

3. Given the following TypeScript code for a stack push operation, what will be the top node's value after pushing 10, then 20?

medium

A. undefined

B. 10

C. null

D. 20

Solution

1. Step 1: Understand push operation

   Push adds a new node at the top, so the last pushed value becomes the top.

2. Step 2: Trace pushing 10 then 20

   First push 10: top.value = 10; then push 20: top.value = 20 (new node).

3. Final Answer:

   20 -> Option D

4. Quick Check:

   Last pushed value is top = 20 [OK]

Hint: Top always holds last pushed value [OK]

Common Mistakes:

• Assuming bottom value is top
• Confusing push with pop
• Not updating top pointer

4. Identify the error in this pop method of a linked list stack implementation:

pop(): number | null {
  if (!this.top) return null;
  const value = this.top.value;
  this.top = this.top.next;
  return this.top.value;
}

medium

A. Returns the new top value instead of popped value

B. Does not check if stack is empty

C. Does not update top pointer

D. Throws error when stack is empty

Solution

1. Step 1: Analyze return value

   The method returns this.top.value after updating top, which is the new top, not the popped value.

2. Step 2: Correct return value

   It should return the saved value before updating top to return the popped element.

3. Final Answer:

   Returns the new top value instead of popped value -> Option A

4. Quick Check:

   Pop must return popped value, not new top [OK]

Hint: Return saved value before updating top [OK]

Common Mistakes:

• Returning top after update instead of popped value
• Not handling empty stack
• Forgetting to update top pointer

5. You want to implement a method peek() in your linked list stack that returns the top value without removing it. Which is the correct implementation?

hard

A. peek(): number | null { return this.top ? this.top.value : null; }

B. peek(): number | null { const val = this.top.value; this.top = this.top.next; return val; }

C. peek(): number | null { if (!this.top) return null; this.top = this.top.next; return this.top.value; }

D. peek(): number | null { return this.top.next ? this.top.next.value : null; }

Solution

1. Step 1: Understand peek operation

   Peek returns the top value without changing the stack.

2. Step 2: Check each option

   peek(): number | null { return this.top ? this.top.value : null; } returns top value if exists, else null, without modifying stack. Others modify top or return wrong node.

3. Final Answer:

   peek(): number | null { return this.top ? this.top.value : null; } -> Option A

4. Quick Check:

   Peek returns top value without removal = C [OK]

Hint: Peek returns top value without changing stack [OK]

Common Mistakes:

• Modifying top pointer in peek
• Returning next node's value
• Not handling empty stack