Insert at Beginning of Doubly Linked List in DSA C - Time & Space Complexity

Time Complexity: Insert at Beginning of Doubly Linked List

O(1)

Understanding Time Complexity

We want to understand how the time needed to insert a new node at the start of a doubly linked list changes as the list grows.

Specifically, how does the work change when the list gets longer?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

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

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

This code creates a new node and inserts it at the start of the doubly linked list.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: Creating and linking one new node.
• How many times: Only once per insertion, no loops or repeated traversals.

How Execution Grows With Input

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

Input Size (n)	Approx. Operations
10	About 5 steps
100	About 5 steps
1000	About 5 steps

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

Final Time Complexity

Time Complexity: O(1)

This means inserting at the beginning takes a constant amount of time no matter how big the list is.

Common Mistake

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

[OK] Correct: We only change a few pointers at the start; we do not move or visit other nodes.

Interview Connect

Knowing that insertion at the start is quick helps you explain efficient list operations clearly and confidently.

Self-Check

"What if we changed this to insert at the end of the doubly linked list without a tail pointer? How would the time complexity change?"

Practice

1. What is the main purpose of inserting a node at the beginning of a doubly linked list?

easy

A. To add a new node after the tail node

B. To add a new node before the current head node

C. To delete the first node of the list

D. To reverse the entire list

Solution

1. Step 1: Understand the structure of a doubly linked list

   A doubly linked list has nodes connected both forward and backward, with a head and tail.

2. Step 2: Identify what inserting at the beginning means

   Inserting at the beginning means adding a new node before the current head node, making it the new head.

3. Final Answer:

   To add a new node before the current head node -> Option B

4. Quick Check:

   Insert at beginning = add before head [OK]

Hint: Insert at beginning means new node becomes the head [OK]

Common Mistakes:

• Confusing insertion at beginning with insertion at end
• Thinking insertion deletes nodes
• Mixing up head and tail positions

2. Which of the following is the correct way to update the previous pointer of the old head node when inserting a new node at the beginning in C?

easy

A. new_node->prev = old_head;

B. old_head->next = new_node;

C. new_node->next = old_head->prev;

D. old_head->prev = new_node;

Solution

1. Step 1: Identify pointer updates when inserting at beginning

   The new node's next points to old head, and old head's prev points back to new node.

2. Step 2: Choose correct pointer update for old head

   We must set old_head->prev = new_node to link backward to new node.

3. Final Answer:

   old_head->prev = new_node; -> Option D

4. Quick Check:

   Old head prev points to new node [OK]

Hint: Old head's prev points to new node after insertion [OK]

Common Mistakes:

• Setting old_head->next instead of prev
• Assigning new_node->prev incorrectly
• Forgetting to update old head's prev pointer

3. What will be the output of the following code snippet after inserting a node with value 10 at the beginning of the doubly linked list?

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

Node* head = NULL;

void insertAtBeginning(int val) {
  Node* new_node = (Node*)malloc(sizeof(Node));
  new_node->data = val;
  new_node->prev = NULL;
  new_node->next = head;
  if (head != NULL) {
    head->prev = new_node;
  }
  head = new_node;
}

int main() {
  insertAtBeginning(20);
  insertAtBeginning(10);
  Node* temp = head;
  while (temp != NULL) {
    printf("%d ", temp->data);
    temp = temp->next;
  }
  return 0;
}

medium

A. 10

B. 20 10

C. 10 20

D. 20

Solution

1. Step 1: Trace first insertion insertAtBeginning(20)

   List is empty, new node with 20 becomes head: 20 -> NULL

2. Step 2: Trace second insertion insertAtBeginning(10)

   New node with 10 points next to old head (20), old head prev points to new node, head updated to 10: 10 <-> 20

3. Final Answer:

   10 20 -> Option C

4. Quick Check:

   List after insertions = 10 20 [OK]

Hint: New node becomes head, old head shifts right [OK]

Common Mistakes:

• Printing nodes in reverse order
• Not updating head pointer
• Forgetting to update old head's prev pointer

4. Identify the error in the following code snippet for inserting a node at the beginning of a doubly linked list:

void insertAtBeginning(int val) {
  Node* new_node = (Node*)malloc(sizeof(Node));
  new_node->data = val;
  new_node->prev = NULL;
  new_node->next = head;
  if (head != NULL) {
    head->next = new_node;
  }
  head = new_node;
}

medium

A. head->next should be head->prev when updating old head

B. new_node->prev should not be NULL

C. head pointer should not be updated

D. malloc size is incorrect

Solution

1. Step 1: Check pointer updates for old head

   When inserting at beginning, old head's prev pointer must point to new node, not next.

2. Step 2: Identify incorrect line

   Code uses head->next = new_node; which wrongly sets old head's next pointer instead of prev.

3. Final Answer:

   head->next should be head->prev when updating old head -> Option A

4. Quick Check:

   Old head prev must point to new node [OK]

Hint: Old head prev, not next, points to new node [OK]

Common Mistakes:

• Updating old head's next pointer instead of prev
• Not updating head pointer
• Incorrect malloc size usage

5. You have a doubly linked list with nodes: 5 <-> 15 <-> 25. You want to insert a new node with value 1 at the beginning. After insertion, what will be the correct sequence of node values when traversing from head to tail?

medium

A. 1 <-> 5 <-> 15 <-> 25

B. 5 <-> 15 <-> 25 <-> 1

C. 25 <-> 15 <-> 5 <-> 1

D. 1 <-> 15 <-> 5 <-> 25

Solution

1. Step 1: Understand insertion at beginning

   New node with value 1 becomes new head, pointing next to old head (5).

2. Step 2: Update pointers and traverse list

   Sequence after insertion: 1 (head) <-> 5 <-> 15 <-> 25 (tail).

3. Final Answer:

   1 <-> 5 <-> 15 <-> 25 -> Option A

4. Quick Check:

   New head is 1, followed by old nodes [OK]

Hint: New node becomes head, old head shifts right [OK]

Common Mistakes:

• Appending new node at end instead of beginning
• Mixing node order after insertion
• Not updating head pointer