Introduction To Algorithms, Third Edition (international Edition)
3rd Edition
ISBN: 9780262533058
Author: Thomas H. Cormen, Charles E. Leiserson, Ronald L. Rivest, Clifford Stein
Publisher: TRILITERAL
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Chapter 9.3, Problem 9E
Program Plan Intro
To describe the way to pick the optimal location of the main pipeline that minimizes the total length of the spurs and also shows the method to determine the optimal location in linear time.
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Suppose that the MinGap method below is added to the Treap class on Blackboard.
public int MinGap ( )
Returns the absolute difference between the two closest numbers in the treap. For example, if the
numbers are {2, 5, 7, 11, 12, 15, 20} then MinGap would returns 1, the absolute difference between 11
and 12.
Requirements
1. Describe in a separate Design Document what additional data is needed and how that data is used to
support an time complexity of O(1) for the MinGap method. Show as well that the methods Add and
Remove can efficiently maintain this data as items are added and removed. (6 marks)
2. Re-implement the methods Add and Remove of the Treap class to maintain the augmented data in
expected O(log n) time. (6 marks)
3. Implement the MinGap method. (4 marks)
4. Test your new method 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)
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)
Chapter 9 Solutions
Introduction To Algorithms, Third Edition (international Edition)
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