Lecture6 - Algorithms in Systems Engineering IE170 Lecture...

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Algorithms in Systems Engineering IE170 Lecture 6 Dr. Ted Ralphs
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IE170 Lecture 6 1 References for Today’s Lecture Required reading CLRS Chapter 4 References R. Sedgewick, Algorithms in C++ (Third Edition), 1998.
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IE170 Lecture 6 2 Analyzing Recurrences Last time, we analyzed merge sort using a recursion tree . General methods for analyzing recurrences Note that when we analyze a recurrence, we may not get or need an exact answer. We may prove the running time is in O ( f ) or Θ( f ) for some simpler function f . When taking the ratio of two integers, it usually doesn’t matter whether we round up or down.
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3 A Few Examples This recurrence arises in algorithms that loop through the input to eliminate one item. T ( n ) = ( 1 n = 1 T ( n - 1) + n n > 1 This recurrence arises in algorithms that halve the input in one step. T ( n ) = ( 1 n = 1 T ( n/ 2) + 1 n > 1 This recurrence arises in algorithms that halve the input in one step, but have to scan through the data at each step. T
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This note was uploaded on 02/29/2008 for the course IE 170 taught by Professor Ralphs during the Spring '07 term at Lehigh University .

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Lecture6 - Algorithms in Systems Engineering IE170 Lecture...

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