Stack Implementation Using Linked List in DSA C - 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.

Specifically, 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.

// Push operation in stack using linked list
void push(Node** top, int value) {
    Node* newNode = (Node*)malloc(sizeof(Node));
    newNode->data = value;
    newNode->next = *top;
    *top = newNode;
}

// Pop operation in stack using linked list
int pop(Node** top) {
    if (*top == NULL) return -1; // stack empty
    Node* temp = *top;
    int val = temp->data;
    *top = temp->next;
    free(temp);
    return val;
}
    

This code adds or removes items at the start of the linked list to simulate stack push and pop.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

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

How Execution Grows With Input

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

Input Size (n)	Approx. Operations
10	5 steps (allocate, assign, link, update pointer, free)
100	5 steps (same as above)
1000	5 steps (same as above)

Pattern observation: The number of steps stays the same regardless of stack size.

Final Time Complexity

Time Complexity: O(1)

This means push and pop operations take constant time no matter how big the stack is.

Common Mistake

[X] Wrong: "Push or pop takes longer as the stack grows because more nodes exist."

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

Interview Connect

Knowing that stack operations with linked lists run in constant time shows you understand efficient data structure design.

Self-Check

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

Practice

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

easy

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

B. It uses less memory than an array

C. It allows random access to elements

D. It is easier to sort the stack elements

Solution

1. Step 1: Understand stack size limitation in arrays

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

2. Step 2: Linked list dynamic size

   Linked lists allocate memory dynamically, so the stack can grow as needed without fixed size.

3. Final Answer:

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

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
• Confusing stack with queue behavior
• Assuming random access is possible in stack

2. Which of the following is the correct way to declare a node structure for a stack implemented using a linked list in C?

easy

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

B. struct Node { int data; int next; };

C. struct Node { int data; struct Node* next; };

D. struct Node { int* data; struct Node* next; };

Solution

1. Step 1: Understand node structure for linked list

   A node must hold data and a pointer to the next node.

2. Step 2: Check pointer types

   Next must be a pointer to struct Node, not an int or struct Node itself.

3. Final Answer:

   struct Node { int data; struct Node* next; }; -> Option C

4. Quick Check:

   Node has data + pointer to next [OK]

Hint: Next pointer must be struct Node* not int or struct Node [OK]

Common Mistakes:

• Using int instead of pointer for next
• Declaring next as struct Node instead of pointer
• Using pointer for data unnecessarily

3. Consider the following C code snippet for pushing elements onto a stack implemented using a linked list:

void push(struct Node** top_ref, int new_data) {
  struct Node* new_node = (struct Node*) malloc(sizeof(struct Node));
  new_node->data = new_data;
  new_node->next = *top_ref;
  *top_ref = new_node;
}

// Initial stack is empty (top_ref = NULL)
push(&top, 10);
push(&top, 20);
push(&top, 30);

What will be the order of elements in the stack from top to bottom after these pushes?

medium

A. 10 -> 20 -> 30 -> NULL

B. 30 -> 20 -> 10 -> NULL

C. 20 -> 30 -> 10 -> NULL

D. NULL -> 10 -> 20 -> 30

Solution

1. Step 1: Trace first push(10)

   Stack top points to node with data 10, next is NULL.

2. Step 2: Trace second push(20) and third push(30)

   Each new node becomes top, so order is 30 (top) -> 20 -> 10 -> NULL.

3. Final Answer:

   30 -> 20 -> 10 -> NULL -> Option B

4. Quick Check:

   Last pushed is top = 30 [OK]

Hint: Last pushed is always on top in linked list stack [OK]

Common Mistakes:

• Assuming order is insertion order (FIFO)
• Confusing next pointer direction
• Forgetting top points to last pushed node

4. The following code snippet is intended to pop an element from a stack implemented using a linked list. Identify the error:

int pop(struct Node** top_ref) {
  struct Node* temp;
  int popped;
  if (*top_ref == NULL) {
    printf("Stack Underflow\n");
    return -1;
  }
  temp = *top_ref;
  popped = temp->data;
  *top_ref = temp->next;
  free(temp);
  return popped;
}

medium

A. Should update temp->next to NULL before freeing

B. Missing check for NULL before accessing temp->data

C. Should not free temp after popping

D. No error, code correctly pops the top element

Solution

1. Step 1: Check for empty stack

   Code correctly checks if *top_ref is NULL and returns underflow error.

2. Step 2: Pop operation correctness

   It saves top node, retrieves data, updates top to next node, frees old top, and returns data.

3. Final Answer:

   No error, code correctly pops the top element -> Option D

4. Quick Check:

   Pop code with free and update top is correct [OK]

Hint: Pop frees top node and updates pointer correctly [OK]

Common Mistakes:

• Forgetting to free popped node causing memory leak
• Not checking for empty stack before pop
• Incorrectly updating top pointer

5. You want to implement a function reverseStack that reverses the elements of a stack implemented using a linked list without using any extra stack or array. Which approach is correct?

hard

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

B. Traverse the linked list and swap data of first and last nodes repeatedly

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

   No extra stack or array allowed, so iterative copying or extra data structures are not allowed.

2. Step 2: Use recursion to reverse

   Recursion can pop all elements, then push them back in reverse order naturally using call stack.

3. Step 3: Other options use extra data or incorrect method

   Swapping data repeatedly is complex and error-prone; copying creates extra list; queue uses extra structure.

4. Final Answer:

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

5. Quick Check:

   Recursion reverses stack without extra data structures [OK]

Hint: Recursion uses call stack to reverse without extra structures [OK]

Common Mistakes:

• Trying to swap node data instead of rearranging nodes
• Using extra arrays or stacks against constraints
• Confusing queue usage for stack reversal