Suppose that the two Rank methods below are added to the Skip List class on Blackboard. public int Rank(T item) Returns the rank of the given item. public T Rank(int i) Returns the item with the given rank i. Requirements 1. Describe in a separate Design Document what additional data is needed and how that data is used to support an expected time complexity of O(log n) for each of the Rank methods. Show as well that the methods Insert and Remove can efficiently maintain this data as items are inserted and removed. (7 marks) 2. Re-implement the methods Insert and Remove of the Skip List class to maintain the augmented data in expected O(log n) time. Using the Contains method, ensure that added items are distinct. (6 marks) 3. Implement the two Rank methods. (8 marks) 4. Test your new methods thoroughly. Include your test cases and results in a Test Document. (4 marks)
Suppose that the two Rank methods below are added to the Skip List class on Blackboard.
public int Rank(T item)
Returns the rank of the given item.
public T Rank(int i)
Returns the item with the given rank i.
Requirements
1. Describe in a separate Design Document what additional data is needed and how that data is used to
support an expected time complexity of O(log n) for each of the Rank methods. Show as well that the
methods Insert and Remove can efficiently maintain this data as items are inserted and removed. (7
marks)
2. Re-implement the methods Insert and Remove of the Skip List class to maintain the augmented data in
expected O(log n) time. Using the Contains method, ensure that added items are distinct. (6 marks)
3. Implement the two Rank methods. (8 marks)
4. Test your new methods thoroughly. Include your test cases and results in a Test Document. (4 marks)
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