I have to solve this recurrence relation with tree method, because Master theorem does not apply.
T(n) = (2+1/log n) T(n/2)
After a some thoughts I can not come up with an exact solution. Master's theorem does not work here and unrolling the tree has not gave me anything reasonable. So I will just estimate the complexity in the following way.
For any reasonably big n
you can estimate 0 < 1/log n < 1
. So you can get:
T1(n) = 2 * T1(n/2)
T2(n) = 3 * T2(n/2)
and O(T1) < O(T) < O(T2)
. You can find the complexity for both recurrences using master theorem . The complexity of T1
is O(n)
and of T2
is O(n^log2(3))
.
So you can be sure that the complexity of your recurrence is bigger than O(n)
and less than O(n^1.58)
, so less than quadratic.
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