Licensed software: The licensed software is the legalized software that includes zero errors and bugs. The copyright and patent rights of the software lie within the hands of the owner. He/she has all the rights to create the copies of the software. The software will be protected in both source code and object code.

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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)

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Chapter 12, Problem 17SG

Program Plan Intro

Licensed software:

The licensed software is the legalized software that includes zero errors and bugs.

The copyright and patent rights of the software lie within the hands of the owner.

He/she has all the rights to create the copies of the software. The software will be protected in both source code and object code.

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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)

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