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Unformatted text preview: COMP 271H Design and Analysis of Algorithms 2006 Fall Semester Tutorial 11 1. (From textbook) A sequence of n operations is performed on a data structure. The i th operation costs i if i is an exact power of 2, and 1 otherwise. Determine the amortized cost per operation in two ways: (i) using the accounting method; (ii) using the potential method. Possible solution: Define C i be the actual cost for the i th operation, we have: C i = i if i is power of 2 C i = 1 otherwise Accounting method We claim that each operation pays for 3 credits (amortized cost of ANY operation is 3), Case 1: Not the i th operation • Use 1 credit to pay for the actual cost • Save 2 credits into the account for future use Case 2: The i th operation • If i < 3, save i- 3 credits into the account for future use • Otherwise, pay i- 3 credits from the account Question: How to come up with the magic number (3 credits) for any operation?...
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This note was uploaded on 12/09/2010 for the course ENGLISH 1303 taught by Professor May during the Spring '10 term at HKU.
- Spring '10