GATE CS 2015 Set 1 — Question 60
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Algorithms → Asymptotic Analysis → Asymptotic Notations
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Question
An algorithm performs find operations, insert operations, delete operations, and decrease-key operations on a set of data items with keys drawn from a linearly ordered set. For a delete operation, a pointer is provided to the record that must be deleted. For the decrease-key operation, a pointer is provided to the record that has its key decreased. Which one of the following data structures is the most suited for the algorithm to use, if the goal is to achieve the best total asymptotic complexity considering all the operations?
Correct answer
(A) Unsorted array
Solution
Let's analyze the cost for each operation in an Unsorted Array:
- Insert: (append to end). Total cost for inserts:
O(N). - Find:
O(N)(linear search). Total cost for finds: . - Delete: (since a pointer is provided, we can swap with the last element and decrement size). Total cost: .
- Decrease-key: (direct access via pointer). Total cost: .
- Insert: . Total cost: .
- Find:
O(N). Total cost: . - Delete: . Total cost: .
- Decrease-key: . Total cost: .
O(N) insertion cost, leading to total complexity, which is much worse.Continue learning with Success Tracker
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