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In: Computer Science

Does the Master theorem apply to the following recurrences. Justify your answer in each case. If...

Does the Master theorem apply to the following recurrences. Justify your answer in each case. If it applies, then also state the case and the solution. (a) T(n) = √ nT(n/2)+logn, (b) T(n) = T(n/2+ 31)+log n, (c) T(n) = T(n−1)+T(n/2)+n and (d) T(n) = T(n/7)+T(5n/13)+n?

Solutions

Expert Solution

(a) T(n) = √nT(n/2)+logn
This is not in the form of T(n) = aT(n/b) + f(n). because a must be a constant but here a is √n
so, we can not apply master's theorem here.

(b) T(n) = T(n/2+ 31)+log n
we can modify T(n) = T(n/2+ 31)+log n to T(n) = T(n/2)+log n
now we can apply the master's theorem here


(c) T(n) = T(n−1)+T(n/2)+n
This is not in the form of T(n) = aT(n/b) + f(n). because there are two T() terms in right hand side of the equation.
so, we can not apply master's theorem here.

(d) T(n) = T(n/7)+T(5n/13)+n
This is not in the form of T(n) = aT(n/b) + f(n). because there are two T() terms in right hand side of the equation.
so, we can not apply master's theorem here.


venereology answered 1 month ago
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