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

Time Complexity: Insert at End of Doubly Linked List

O(n)

Understanding Time Complexity

We want to understand how the time needed to add a new item at the end of a doubly linked list changes as the list grows.

How does the number of steps grow 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 insertAtEnd(struct Node** head, int value) {
    struct Node* newNode = malloc(sizeof(struct Node));
    newNode->data = value;
    newNode->next = NULL;

    if (*head == NULL) {
        newNode->prev = NULL;
        *head = newNode;
        return;
    }

    struct Node* temp = *head;
    while (temp->next != NULL) {
        temp = temp->next;
    }

    temp->next = newNode;
    newNode->prev = temp;
}
    

This code adds a new node at the end of a doubly linked list by walking through the list to find the last node.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: The while loop that moves through the list nodes to find the last node.
• How many times: It runs once for each node in the list until the last one is found, so roughly n times for a list of size n.

How Execution Grows With Input

As the list gets longer, the time to find the end grows roughly in a straight line with the number of nodes.

Input Size (n)	Approx. Operations
10	About 10 steps to reach the end
100	About 100 steps to reach the end
1000	About 1000 steps to reach the end

Pattern observation: The steps increase directly with the number of nodes, so doubling the list size roughly doubles the work.

Final Time Complexity

Time Complexity: O(n)

This means the time to insert at the end grows linearly with the list size because we must walk through all nodes to find the end.

Common Mistake

[X] Wrong: "Inserting at the end is always fast and takes the same time no matter the list size."

[OK] Correct: Without a pointer to the last node, we must walk through the whole list, so bigger lists take more time.

Interview Connect

Understanding this helps you explain how linked lists work and why keeping track of the last node can speed up insertions.

Self-Check

"What if we kept a pointer to the last node? How would the time complexity change?"

Practice

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

easy

A. To add a new element after the last node

B. To remove the first node

C. To reverse the list

D. To find the middle node

Solution

1. Step 1: Understand the list structure

   A doubly linked list has nodes connected forward and backward, allowing traversal in both directions.

2. Step 2: Purpose of insertion at end

   Inserting at the end means adding a new node after the last node, extending the list.

3. Final Answer:

   To add a new element after the last node -> Option A

4. Quick Check:

   Insert at end = add after last node [OK]

Hint: Insert at end means add after last node [OK]

Common Mistakes:

• Confusing insertion at end with deletion
• Thinking insertion happens at the start
• Mixing up singly and doubly linked list operations

2. Which of the following is the correct way to update the 'next' pointer of the last node when inserting a new node at the end in C?

easy

A. last->next = newNode;

B. newNode->next = last;

C. last->prev = newNode;

D. newNode->prev = NULL;

Solution

1. Step 1: Identify the last node's next pointer

   The last node's 'next' pointer should point to the new node to link it at the end.

2. Step 2: Correct pointer assignment

   Assigning 'last->next = newNode;' correctly links the new node after the last node.

3. Final Answer:

   last->next = newNode; -> Option A

4. Quick Check:

   Last node's next points to new node [OK]

Hint: Last node's next points to new node [OK]

Common Mistakes:

• Assigning newNode->next to last (wrong direction)
• Changing last->prev instead of last->next
• Setting newNode->prev to NULL instead of last

3. What will be the output of the following code snippet after inserting a node with value 5 at the end of the doubly linked list 1 <-> 3 <-> 4?

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

void insertEnd(struct Node** head, int val) {
  struct Node* newNode = malloc(sizeof(struct Node));
  newNode->data = val;
  newNode->next = NULL;
  if (*head == NULL) {
    newNode->prev = NULL;
    *head = newNode;
    return;
  }
  struct Node* temp = *head;
  while (temp->next != NULL) {
    temp = temp->next;
  }
  temp->next = newNode;
  newNode->prev = temp;
}

void printList(struct Node* head) {
  while (head != NULL) {
    printf("%d ", head->data);
    head = head->next;
  }
}

int main() {
  struct Node* head = malloc(sizeof(struct Node));
  head->data = 1; head->prev = NULL;
  struct Node* second = malloc(sizeof(struct Node));
  second->data = 3; second->prev = head; head->next = second;
  struct Node* third = malloc(sizeof(struct Node));
  third->data = 4; third->prev = second; second->next = third; third->next = NULL;
  insertEnd(&head, 5);
  printList(head);
  return 0;
}

medium

A. 1 3 4 0

B. 1 3 4 5

C. 1 3 4

D. 5 1 3 4

Solution

1. Step 1: Understand initial list and insertion

   The list is 1 <-> 3 <-> 4. The function inserts 5 at the end by traversing to last node (4) and linking new node after it.

2. Step 2: Trace printList output

   After insertion, list is 1 <-> 3 <-> 4 <-> 5. Printing nodes in order outputs "1 3 4 5 "

3. Final Answer:

   1 3 4 5 -> Option B

4. Quick Check:

   List after insertEnd = 1 3 4 5 [OK]

Hint: Traverse to last, link new node, print all nodes [OK]

Common Mistakes:

• Not setting newNode->prev correctly
• Forgetting to set last node's next to newNode
• Printing before insertion

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

void insertEnd(struct Node** head, int val) {
  struct Node* newNode = malloc(sizeof(struct Node));
  newNode->data = val;
  newNode->next = NULL;
  if (*head == NULL) {
    *head = newNode;
    return;
  }
  struct Node* temp = *head;
  while (temp->next != NULL) {
    temp = temp->next;
  }
  temp->next = newNode;
}

medium

A. Wrong condition in while loop

B. Incorrect malloc size

C. Missing setting newNode->prev pointer

D. Not updating head pointer

Solution

1. Step 1: Check pointer assignments for doubly linked list

   In doubly linked list, newNode->prev must point to the last node (temp) after insertion.

2. Step 2: Identify missing pointer update

   The code sets temp->next = newNode but does not set newNode->prev = temp, breaking backward link.

3. Final Answer:

   Missing setting newNode->prev pointer -> Option C

4. Quick Check:

   newNode->prev must be set [OK]

Hint: Always set newNode->prev to last node [OK]

Common Mistakes:

• Forgetting newNode->prev assignment
• Assuming singly linked list logic applies
• Not handling empty list case

5. Given a doubly linked list with nodes 10 <-> 20 <-> 30, write the sequence of pointer changes when inserting a new node with value 40 at the end. Which of the following correctly describes the final connections?

hard

A. newNode->prev = NULL; newNode->next = NULL; last->next = NULL

B. newNode->next = last; last->prev = newNode; newNode->prev = NULL

C. last->prev = newNode; newNode->next = last; newNode->prev = NULL

D. last->next = newNode; newNode->prev = last; newNode->next = NULL

Solution

1. Step 1: Identify last node and new node pointers

   Last node is 30. New node 40 should be linked after 30 with next NULL.

2. Step 2: Correct pointer assignments

   Set last->next = newNode to link forward, newNode->prev = last for backward link, and newNode->next = NULL as it is new end.

3. Final Answer:

   last->next = newNode; newNode->prev = last; newNode->next = NULL -> Option D

4. Quick Check:

   New node linked after last with proper prev and next [OK]

Hint: New node's prev = last; last's next = new node; new node's next = NULL [OK]

Common Mistakes:

• Reversing prev and next pointers
• Setting newNode->prev to NULL incorrectly
• Not setting last->next to newNode