Data-Structures
April 17, 2024Question 9065 – Data-Structures
April 18, 2024Question 8117 – Data-Structures
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(logN) insert, O(logN) find, and Θ(N) decrease-key. What is the time complexity of all these operations put together?
Correct Answer: C
Question 31 Explanation:
In Doubly linked list (sorted)
→ Delete needs O(1) time
→ Insert takes O(N) time
→ Find takes O(N) time
→ Decrease by takes O(N) time
Now number of each operation performed is given, so finally total complexity,
→ Delete = O(1) × O(N) = O(N)
→ Find = O(N) × O(log N) = O(N log N)
→ Insert = O(N) × O(log N) = O(N log N)
→ Decrease key = O(N) × O(N) = O(N2)
So, overall time complexity is, O(N2).
→ Delete needs O(1) time
→ Insert takes O(N) time
→ Find takes O(N) time
→ Decrease by takes O(N) time
Now number of each operation performed is given, so finally total complexity,
→ Delete = O(1) × O(N) = O(N)
→ Find = O(N) × O(log N) = O(N log N)
→ Insert = O(N) × O(log N) = O(N log N)
→ Decrease key = O(N) × O(N) = O(N2)
So, overall time complexity is, O(N2).
O(log2 N)
O(N)
O(N2)
Θ(N2 logN)