GATE CS 2016 Set 2 — Question 25
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Programming & Data Structures → Linked Lists → Doubly Linked Lists
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Question
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: delete, insert, find, and decrease-key. What is the time complexity of all these operations put together?
An algorithm performs the following operations on the list in this order: delete, insert, find, and decrease-key. What is the time complexity of all these operations put together?
Correct answer
(C) O(N²)
Solution
We analyze the cost of each set of operations on a sorted doubly linked list:
1. delete operations: Since a pointer to the node is provided, deletion in a doubly linked list is . Total cost: .
2. insert operations: To insert into a sorted linked list, we must find the correct position. In a linked list, we cannot perform binary search, so we must linearly scan. Worst case per insert is
O(N). Total cost: .3. find operations: Similar to insert, finding an element in a sorted linked list requires a linear scan,
O(N). Total cost: .4. decrease-key operations: A pointer is given, but after decreasing the key, the sorted order must be maintained. The node might need to be moved to a new position. In the worst case, it moves
Summing these up: .The dominant term is .O(N) steps. Total cost: .Continue learning with Success Tracker
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