Let P be a singly linked list. Let Q be the pointer to an intermediate node x in the list. What is the worst-case time complexity of the best known algorithm to delete the node x from the list?a)0(n)b)0(log2 n)c)0(logn)d)0(1)Correct answer is option 'D'. Can you explain this answer?

Question

Answer

A simple solution is to traverse the linked list until you find the node you want to delete. But this solution requires pointer to the head node which contradicts the problem statement.

Fast solution is to copy the data from the next node to the node to be deleted and delete the next node. Something like following.

// Find next node using next pointer
struct node *temp = node_ptr->next;

// Copy data of next node to this node
node_ptr->data = temp->data;

// Unlink next node
node_ptr->next = temp->next;

// Delete next node
free(temp);

Time complexity of this approach is O(1)

Answer

Worst-case Time Complexity of Deleting a Node x from a Singly Linked List

To understand the worst-case time complexity of deleting a node x from a singly linked list, let's analyze the steps involved in the process.

Traversing to the Node x
1. Initially, we have a pointer Q pointing to the node x in the list.
2. To delete node x, we need to find its previous node (let's call it prev).
3. We can traverse the linked list starting from the head until we find the node whose next node is x.
4. This traversal requires iterating through all the nodes until we reach the node x or the end of the list.

Deleting the Node x
1. Once we have the previous node (prev) of x, we can update the next pointer of prev to skip the node x.
2. This operation involves changing the next pointer of prev to point to the node after x.
3. We also need to free the memory occupied by the node x.

Worst-case Time Complexity
The worst-case time complexity of the best known algorithm to delete the node x from a singly linked list is O(1).

- Traversing to the Node x: The time complexity of this step is O(n) in the worst case, as we may need to traverse the entire linked list to reach the node x.
- Deleting the Node x: Once we have the previous node (prev) of x, deleting the node x and updating the pointers can be done in constant time, regardless of the size of the linked list.

Since the second step (deleting the node x) can be done in constant time, it dominates the time complexity. Therefore, the overall worst-case time complexity is O(1).

Conclusion
The best known algorithm to delete a node x from a singly linked list has a worst-case time complexity of O(1). This means that the time taken to delete the node x is constant and does not depend on the size of the linked list.

Top Courses for Computer Science Engineering (CSE)View all

GATE Computer Science Engineering(CSE) 2025 Mock Test Series

Question Bank for GATE Computer Science Engineering

General Aptitude for GATE

Computer Networks

Programming and Data Structures

Top Courses for Computer Science Engineering (CSE)

Top Courses for Computer Science Engineering (CSE)

Suggested Free Tests

Related Content

Mock Test Series

Subject-wise Courses

Subject-wise Courses

Other Engg Branches

Company