Insert at Beginning Head Insert in DSA C - Time & Space Complexity

Time Complexity: Insert at Beginning Head Insert

O(1)

Understanding Time Complexity

We want to understand how long it takes to add a new item 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;
    struct Node* next;
};

void insertAtBeginning(struct Node** head, int newData) {
    struct Node* newNode = (struct Node*)malloc(sizeof(struct Node));
    newNode->data = newData;
    newNode->next = *head;
    *head = newNode;
}
    

This code adds a new node at the start of a linked list by adjusting pointers.

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 insertion, no loops or recursion.

How Execution Grows With Input

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

Input Size (n)	Approx. Operations
10	4 steps (allocate, 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 at the start takes a fixed amount of time no matter how big the list is.

Common Mistake

[X] Wrong: "Adding at the beginning takes longer as the list grows because we have to move all nodes."

[OK] Correct: We only change the head pointer and the new node's next pointer; no nodes are moved or visited.

Interview Connect

Knowing that inserting at the start is quick helps you choose the right method for fast updates in linked lists.

Self-Check

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

Practice

1. What does the "Insert at Beginning" operation do in a singly linked list?

easy

A. Deletes the first node of the list

B. Adds a new node at the end of the list

C. Adds a new node at the start of the list

D. Deletes the last node of the list

Solution

1. Step 1: Understand the operation

   Inserting at the beginning means placing a new node before the current first node.

2. Step 2: Effect on the list

   The new node becomes the head, pushing the old head to second position.

3. Final Answer:

   Adds a new node at the start of the list -> Option C

4. Quick Check:

   Insert at beginning = Add new head [OK]

Hint: New node becomes head, old head moves next [OK]

Common Mistakes:

• Confusing insert at beginning with insert at end
• Thinking it deletes nodes
• Assuming it inserts in the middle

2. Which of the following is the correct syntax to insert a new node at the beginning in C for a singly linked list?

easy

A. newNode->next = head; head = newNode;

B. head = newNode->next; newNode = head;

C. head->next = newNode; newNode = head;

D. newNode = head; head->next = newNode;

Solution

1. Step 1: Assign newNode's next to current head

   This links the new node to the existing list.

2. Step 2: Update head to newNode

   Now the new node is the first node in the list.

3. Final Answer:

   newNode->next = head; head = newNode; -> Option A

4. Quick Check:

   Link newNode to head, then update head [OK]

Hint: Point newNode->next to head, then head to newNode [OK]

Common Mistakes:

• Swapping assignments order
• Assigning head to newNode->next incorrectly
• Not updating head pointer

3. What will be the linked list after inserting nodes with values 10, then 20, then 30 at the beginning in that order? Assume the list was initially empty.

medium

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

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

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

D. 30 -> 20 -> 10 -> null

Solution

1. Step 1: Insert 10 at beginning

   List becomes 10 -> null.

2. Step 2: Insert 20 at beginning

   List becomes 20 -> 10 -> null.

3. Step 3: Insert 30 at beginning

   List becomes 30 -> 20 -> 10 -> null.

4. Final Answer:

   30 -> 20 -> 10 -> null -> Option D

5. Quick Check:

   Last inserted is new head [OK]

Hint: Last inserted node is always head [OK]

Common Mistakes:

• Assuming insertion at end
• Reversing insertion order
• Confusing node values order

4. Given the following code snippet, what is the error that prevents correct insertion at the beginning?

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

void insertAtBeginning(struct Node** head, int val) {
  struct Node* newNode = malloc(sizeof(struct Node));
  newNode->data = val;
  newNode->next = NULL;
  *head = newNode;
}

medium

A. malloc size is incorrect

B. newNode->next should point to current head before updating head

C. newNode->data is not assigned

D. head pointer should not be double pointer

Solution

1. Step 1: Check newNode->next assignment

   It is set to NULL, losing the existing list.

2. Step 2: Correct linking

   newNode->next should point to current head before head is updated.

3. Final Answer:

   newNode->next should point to current head before updating head -> Option B

4. Quick Check:

   Link newNode->next to old head before head update [OK]

Hint: Link newNode->next to old head before head update [OK]

Common Mistakes:

• Setting newNode->next to NULL always
• Not using double pointer for head
• Forgetting to assign data

5. You have a singly linked list with nodes: 5 -> 15 -> 25 -> null. You want to insert a new node with value 10 at the beginning. After insertion, what will be the correct sequence of nodes?

hard

A. 10 -> 5 -> 15 -> 25 -> null

B. 5 -> 10 -> 15 -> 25 -> null

C. 10 -> 15 -> 25 -> 5 -> null

D. 5 -> 15 -> 25 -> 10 -> null

Solution

1. Step 1: Current list is 5 -> 15 -> 25 -> null

   This is the starting list before insertion.

2. Step 2: Insert 10 at beginning

   New node 10 points to current head (5), then head updated to 10.

3. Final Answer:

   10 -> 5 -> 15 -> 25 -> null -> Option A

4. Quick Check:

   New node becomes head, old head follows [OK]

Hint: New node points to old head, becomes new head [OK]

Common Mistakes:

• Inserting at wrong position
• Not updating head pointer
• Linking nodes incorrectly