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2c03-review - 00043 - 10[10 Give tight big-oh and big-omega...

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12 10.[10] Give tight big-oh and big-omega bounds on T(n) defined by the following recurrences. Assume T(1)=1 a.[5] T(n)=2T(n/2)+log n b.[5] T(n)=2T(n/2)+n 2 a.[5] 2 2 3 2 2 3 2 1 1 lg lg lg lg 1 0 lg 1 lg 1 lg 0 0 ( ) 2 ( ) lg 2 2 ( ) 2 ( ) 2lg 2 2 2 2 ( ) 2 ( ) 2 lg 2 2 2 2 ( ) 2 ( ) 2 lg 2 2 2 2 ( ) 2 2 ( ) 2 lg 2 ( ) 2 lg lg 2 lg (2 1) lg lg 2 i i i i i i n n n n i i i n n i i n i i i n T n T n n n n T T n n n T T n n n T T n T n T n n n T n n n n n n n n n n + + = = = = + = + = + = + = = + = +
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