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IntroductiontoAlgorithms.pdf

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IntroductiontoAlgorithms

Introduction to Algorithms 6.046J/18.401J LECTURE 13 Amortized Analysis ? Dynamic tables ? Aggregate method ? Accounting method ? Potential method Prof. Charles E. Leiserson October 31, 2005 Copyright ? 2001-5 by Erik D. Demaine and Charles E. Leiserson L13.1 How large should a hash table be? Goal: Make the table as small as possible, but large enough so that it won’t overflow (or otherwise become inefficient). Problem: What if we don’t know the proper size in advance? Solution: Dynamic tables. IDEA: Whenever the table overflows, “grow” it by allocating (via malloc or new) a new, larger table. Move all items from the old table into the new one, and free the storage for the old table. October 31, 2005 Copyright ? 2001-5 by Erik D. Demaine and Charles E. Leiserson L13.2 Example of a dynamic table 1. INSERT 2. INSERT 1 overflow October 31, 2005 Copyright ? 2001-5 by Erik D. Demaine and Charles E. Leiserson L13.3 Example of a dynamic table 1. INSERT 2. INSERT 11 overflow October 31, 2005 Copyright ? 2001-5 by Erik D. Demaine and Charles E. Leiserson L13.4 Example of a dynamic table 1. INSERT 2. INSERT 11 2 October 31, 2005 Copyright ? 2001-5 by Erik D. Demaine and Charles E. Leiserson L13.5 Example of a dynamic table 1. INSERT 2. INSERT 3. INSERT 11 22 overflow October 31, 2005 Copyright ? 2001-5 by Erik D. Demaine and Charles E. Leiserson L13.6 Example of a dynamic table 1. INSERT 2. INSERT 3. INSERT overflow 1 2 October 31, 2005 Copyright ? 2001-5 by Erik D. Demaine and Charles E. Leiserson L13.7 Example of a dynamic table 1. INSERT 2. INSERT 3. INSERT 1 2 October 31, 2005 Copyright ? 2001-5 by Erik D. Demaine and Charles E. Leiserson L13.8 Example of a dynamic table 1. INSERT 2. INSERT 3. INSERT 4. INSERT 1 2 3 4 October 31, 2005 Copyright ? 2001-5 by Erik D. Demaine and Charles E. Leiserson L13.9 Example of a dynamic table 1. INSERT 2. INSERT 3. INSERT 4. INSERT 5. INSERT 1 2 3 4 overflow October 31, 2005 Copyright ? 2001-5 by Erik D. Demaine and Charles E. Leiserso