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

Time Complexity: Stack Implementation Using Linked List

O(1)

Understanding Time Complexity

We want to understand how fast stack operations run 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 stack push operation.

class Node {
    int data;
    Node next;
    Node(int data) { this.data = data; this.next = null; }
}

class Stack {
    Node top;
    void push(int data) {
        Node newNode = new Node(data);
        newNode.next = top;
        top = newNode;
    }
}
    

This code adds a new item on top of the stack using a linked list.

Identify Repeating Operations

Look for loops or repeated steps in the push operation.

• Primary operation: Creating a new node and linking it to the top.
• How many times: Exactly once per push call, no loops involved.

How Execution Grows With Input

Each push does the same small set of steps no matter how big the stack is.

Input Size (n)	Approx. Operations
10	3 steps (create node, link, update top)
100	3 steps
1000	3 steps

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

Final Time Complexity

Time Complexity: O(1)

This means pushing an item takes the same short time no matter how big the stack is.

Common Mistake

[X] Wrong: "Pushing takes longer as the stack grows because we have to move through all nodes."

[OK] Correct: We only change the top pointer and link the new node; we never walk through the list.

Interview Connect

Knowing that stack push and pop are quick helps you explain why stacks are good for fast temporary storage.

Self-Check

"What if we used an array instead of a linked list for the stack? How would the time complexity of push change?"

Practice

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

easy

A. It uses less memory than an array

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

C. It allows random access to elements

D. It is easier to sort the elements

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 advantage

   Linked lists can grow or shrink dynamically by adding or removing nodes, so the stack size is limited only by memory.

3. Final Answer:

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

4. Quick Check:

   Dynamic size = Advantage of linked list stack [OK]

Hint: Linked list stacks grow dynamically, arrays don't [OK]

Common Mistakes:

• Thinking linked list uses less memory always
• Assuming stacks allow random access
• Confusing sorting with stack operations

2. Which of the following is the correct way to declare a node class for a linked list stack in Java?

easy

A. class Node { int data; int next; }

B. class Node { int data; Node prev; }

C. class Node { Node data; Node next; }

D. class Node { int data; Node next; }

Solution

1. Step 1: Identify node structure for linked list stack

   A node should store data and a reference to the next node.

2. Step 2: Check each option

   class Node { int data; Node next; } correctly uses 'int data' and 'Node next'. class Node { int data; Node prev; } uses 'prev' which is for doubly linked lists. class Node { int data; int next; } wrongly uses 'int next'. class Node { Node data; Node next; } wrongly uses 'Node data'.

3. Final Answer:

   class Node { int data; Node next; } -> Option D

4. Quick Check:

   Node stores data + next pointer [OK]

Hint: Node must have data and next pointer for stack [OK]

Common Mistakes:

• Using 'prev' pointer in singly linked list
• Declaring next as int instead of Node
• Using Node type for data field

3. What will be the output after the following operations on an empty linked list stack?

push(10); push(20); push(30); pop(); push(40);

Print the stack from top to bottom.

medium

A. 40 -> 30 -> 20 -> 10 -> null

B. 30 -> 20 -> 10 -> null

C. 40 -> 20 -> 10 -> null

D. 20 -> 10 -> null

Solution

1. Step 1: Trace push and pop operations

   push(10) -> stack: 10
   push(20) -> stack: 20 -> 10
   push(30) -> stack: 30 -> 20 -> 10
   pop() removes 30 -> stack: 20 -> 10
   push(40) -> stack: 40 -> 20 -> 10

2. Step 2: Write final stack order

   Top is 40, then 20, then 10, then null.

3. Final Answer:

   40 -> 20 -> 10 -> null -> Option C

4. Quick Check:

   Stack top after ops = 40 -> 20 -> 10 [OK]

Hint: Push adds top, pop removes top [OK]

Common Mistakes:

• Forgetting pop removes top element
• Appending instead of prepending on push
• Confusing order of elements after operations

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

public int pop() {
  if (top == null) {
    System.out.println("Stack Underflow");
  }
  int value = top.data;
  top = top.next;
  return value;
}

medium

A. It does not handle empty stack properly before accessing top.data

B. It should return void instead of int

C. It should update top.next instead of top

D. It should print "Stack Overflow" instead of "Stack Underflow"

Solution

1. Step 1: Check empty stack condition handling

   The method prints "Stack Underflow" but continues to access top.data without stopping or returning.

2. Step 2: Consequence of missing return or exception

   Accessing top.data when top is null causes NullPointerException. Proper handling requires returning or throwing after printing.

3. Final Answer:

   It does not handle empty stack properly before accessing top.data -> Option A

4. Quick Check:

   Null check must prevent access [OK]

Hint: Check for empty stack before accessing data [OK]

Common Mistakes:

• Not returning or throwing after underflow message
• Confusing overflow with underflow
• Updating wrong pointer in pop

5. You want to implement a method reverseStack() that reverses the elements of a linked list stack without using extra data structures. Which approach is best?

hard

A. Use recursion to pop all elements and push them back in reverse order

B. Traverse the linked list and swap data of nodes pairwise

C. Create a new linked list and copy elements in reverse order

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

Solution

1. Step 1: Understand constraints of no extra data structures

   Options C and D use extra structures (new list or queue), so they are invalid.

2. Step 2: Evaluate recursion and swapping

   Swapping data pairwise is complex and error-prone for linked list stack. Recursion can pop all elements and push back in reverse order naturally.

3. Final Answer:

   Use recursion to pop all elements and push them back in reverse order -> Option A

4. Quick Check:

   Recursion reverses stack without extra storage [OK]

Hint: Recursion can reverse stack without extra space [OK]

Common Mistakes:

• Using extra data structures despite constraints
• Trying to swap node data instead of nodes
• Confusing queue operations with stack reversal