Push Using Linked List Node in DSA C++ - Time & Space Complexity

Time Complexity: Push Using Linked List Node

O(1)

Understanding Time Complexity

We want to understand how long it takes to add a new node at the start of a linked list.

How does the time needed change as the list grows?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

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

void push(Node*& head, int value) {
    Node* newNode = new Node();
    newNode->data = value;
    newNode->next = head;
    head = newNode;
}
    

This code adds a new node with a given value at the start of the linked list.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: Creating and linking one new node.
• How many times: Exactly once per push call, no loops or recursion.

How Execution Grows With Input

Adding a node always takes the same steps, no matter how big the list is.

Input Size (n)	Approx. Operations
10	4 steps (create node, assign data, link, update head)
100	4 steps (same as above)
1000	4 steps (same as above)

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

Final Time Complexity

Time Complexity: O(1)

This means adding a node at the start takes a constant amount of time no matter how long the list is.

Common Mistake

[X] Wrong: "Adding a node at the start takes longer as the list grows because we have to move through the list."

[OK] Correct: We only change the first node's pointer; we never walk through the list, so time does not grow with list size.

Interview Connect

Knowing that pushing a node at the start is quick helps you design efficient linked list operations and shows you understand how pointers work.

Self-Check

"What if we changed push to add the node at the end of the list? How would the time complexity change?"

Practice

1. What does the push operation do in a linked list when using nodes?

easy

A. Deletes the entire linked list

B. Removes the last node from the list

C. Searches for a node with a specific value

D. Adds a new node at the beginning of the list

Solution

1. Step 1: Understand push operation in linked list

   The push operation inserts a new node at the start (head) of the linked list.

2. Step 2: Effect of push on list structure

   The new node becomes the head, and its next pointer points to the previous head node.

3. Final Answer:

   Adds a new node at the beginning of the list -> Option D

4. Quick Check:

   Push means insert at head = D [OK]

Hint: Push always adds node at the start (head) [OK]

Common Mistakes:

• Confusing push with pop (removal)
• Thinking push adds at the end
• Mixing push with search or delete

2. Which of the following is the correct syntax to create a new node and push it at the head in C++ linked list?

easy

A. Node* newNode = new Node(data); newNode->next = head; head = newNode;

B. Node newNode = Node(data); head = newNode.next;

C. newNode = Node(data); newNode.next = head; head = newNode;

D. Node* newNode = Node(data); head = newNode->next;

Solution

1. Step 1: Create new node dynamically

   Use new Node(data) to allocate memory and initialize node.

2. Step 2: Link new node to current head and update head

   Set newNode->next = head and then head = newNode to push at front.

3. Final Answer:

   Node* newNode = new Node(data); newNode->next = head; head = newNode; -> Option A

4. Quick Check:

   Dynamic allocation + pointer update = B [OK]

Hint: Use pointer and 'new' keyword to create and link node [OK]

Common Mistakes:

• Not using pointer (*) for new node
• Using dot (.) instead of arrow (->) for pointers
• Assigning head incorrectly

3. What will be the output linked list after executing this code?

struct Node {
  int data;
  Node* next;
  Node(int val) : data(val), next(nullptr) {}
};

Node* head = nullptr;

// Push 10
Node* newNode1 = new Node(10);
newNode1->next = head;
head = newNode1;

// Push 20
Node* newNode2 = new Node(20);
newNode2->next = head;
head = newNode2;

// Push 30
Node* newNode3 = new Node(30);
newNode3->next = head;
head = newNode3;

// Print list
Node* temp = head;
while(temp != nullptr) {
  std::cout << temp->data << " -> ";
  temp = temp->next;
}
std::cout << "null";

medium

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

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

C. 20 -> 30 -> 10 -> null

D. null

Solution

1. Step 1: Trace push operations

   First push 10: list is 10 -> null. Then push 20: list becomes 20 -> 10 -> null. Then push 30: list becomes 30 -> 20 -> 10 -> null.

2. Step 2: Print linked list

   Printing from head prints 30, then 20, then 10, then null.

3. Final Answer:

   30 -> 20 -> 10 -> null -> Option B

4. Quick Check:

   Push adds at head, last pushed is first = C [OK]

Hint: Last pushed node appears first in list [OK]

Common Mistakes:

• Assuming push adds at tail
• Mixing order of nodes
• Not updating head pointer correctly

4. Identify the error in this push function for a singly linked list:

void push(Node* head, int data) {
  Node* newNode = new Node(data);
  newNode->next = head;
  head = newNode;
}

medium

A. head is passed by value, so original list head is not updated

B. newNode is not allocated dynamically

C. newNode->next should be nullptr

D. Function should return void* instead of void

Solution

1. Step 1: Analyze parameter passing

   head is passed by value, so changes inside function do not affect original head pointer.

2. Step 2: Effect on linked list

   Assigning head = newNode only changes local copy; original list head remains unchanged.

3. Final Answer:

   head is passed by value, so original list head is not updated -> Option A

4. Quick Check:

   Pass pointer by reference or pointer to pointer [OK]

Hint: Pass head by reference or pointer to update original [OK]

Common Mistakes:

• Ignoring parameter passing method
• Not returning new head if passed by value
• Incorrect pointer usage

5. You want to implement a stack using a singly linked list with push operation. Which approach correctly maintains the stack's LIFO order?

hard

A. Push new nodes at the tail and update head pointer

B. Push new nodes at the tail of the linked list without tail pointer

C. Push new nodes at the head of the linked list

D. Insert new nodes randomly in the list

Solution

1. Step 1: Understand stack LIFO behavior

   Stack requires last-in, first-out order, so newest element must be accessed first.

2. Step 2: Push at head maintains LIFO

   Adding new nodes at head means newest node is always at front, enabling O(1) push and pop.

3. Step 3: Problems with tail insertion

   Inserting at tail without tail pointer is inefficient and does not maintain LIFO easily.

4. Final Answer:

   Push new nodes at the head of the linked list -> Option C

5. Quick Check:

   Stack push = insert at head = A [OK]

Hint: Stack push uses head insertion for O(1) LIFO [OK]

Common Mistakes:

• Pushing at tail without tail pointer (slow)
• Not maintaining LIFO order
• Inserting nodes randomly