Circular single linked list conceptual

Question

Please explain how to approach this problem?

Comments

If the linked list is not circular then we can insert the element in the beginning by just :

link.new=start;

start=new;

This is O(1) operation.

But as the linked list is circular, in addition to the above operation we also need to search for the last element {$\Theta$(n) operation} & then update:

link.new=start;

start=new;

// reach to last node in $\Theta$(n) time

link.last=start; 

Answer 1

Thus inserting when only 1 node is present is best case while when there are n nodes then to connect last pointer to start of new node we need time O(n) hence average case is $\Theta(n)$

Answer 2

If you have pointer to the first node

Insertion at beginning: O(n)

Insertion at the end: O(n) // As you have to traverse till the end. 

If you have pointer to the last node

Insertion at beginning: O(1)

Insertion at end: O(1)

In GATE question they will most likely clearly mention to which nodes we have the pointer to. 

Check this: https://gateoverflow.in/1033/gate2004-36