N items are stored in a sorted doubly linked list. For a delete operation, a pointer is provided

to the record to be deleted. For a decrease-key operation, a pointer is provided to the record on

which the operation is to be performed.

An algorithm performs the following operations on the list in this order: Θ(N) delete, O(log N)

insert, O(log N) find, and Θ(N) decrease-key. What is the time complexity of all these

operations put together?

(A) O(log^2 N)

(B) O(N)

© O(N^2)

(D) Θ(N^2 log N)

I request a easy to understand explanation and also would like to know the reason for the option to be incorrect.