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Unformatted text preview: n ) = T( α n ) + T((1α ) n ) + n , Where α is a constant in the range 0< α < 1. 5. Prove that T( n ), which is defined by the recurrence relation T( n ) = 2T n /2 . + 2 n log 2 n , T(2) = 4, Satisfies T( n ) = O( n log 2 n ) 6. Compare the following pairs of functions in terms of order of magnitude. In each case, say whether f( n ) = O(g( n ), f( n ) = Ω (g( n )), and/or f( n ) = Θ (g( n )) f( n ) g( n ) a. 100 n +log n n + (log n ) 2 b. log n log( n 2 ) c . n 2 /log n n (log n ) 2 d. (log n ) log n n /log n e . √ n (log n ) 5 f. n 2 n 3 n...
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This document was uploaded on 11/18/2009.
 Spring '09
 Algorithms

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