COT5407-Class04

COT5407-Class04 - Master Method Some of the slides are from...

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Unformatted text preview: Master Method Some of the slides are from Prof. Plaisteds resources at University of North Carolina at Chapel Hill COT5407 The Master Method Based on the Master theorem . Cookbook approach for solving recurrences of the form T ( n ) = aT ( n / b ) + f ( n ) a 1, b > 1 are constants. f ( n ) is asymptotically positive. n / b may not be an integer, but we ignore floors and ceilings. Requires memorization of three cases. COT5407 The Master Theorem Theorem 4.1 Let a 1 and b > 1 be constants, let f ( n ) be a function , and Let T ( n ) be defined on nonnegative integers by the recurrence T ( n ) = aT ( n / b ) + f ( n ) , where we can replace n / b by n / b or n / b . T ( n ) can be bounded asymptotically in three cases: 1. If f ( n ) = O ( n ) for some constant > 0, then T ( n ) = ( n ) . COT5407 Recursion tree view (1) f ( n ) f ( n / b ) f ( n / b ) f ( n / b ) f ( n / b 2 ) f ( n / b 2 ) f ( n / b 2 ) f ( n / b 2 ) f ( n / b 2 ) f ( n / b 2 ) f ( n / b 2 ) f ( n / b 2 ) f ( n / b 2 ) a a a a a a a a a a (1) (1) (1) (1) (1) (1) (1) (1) (1) (1) (1)...
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This note was uploaded on 12/03/2011 for the course COT 5407 taught by Professor Staff during the Fall '08 term at FIU.

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COT5407-Class04 - Master Method Some of the slides are from...

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