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How to solve this recurrence: T(n) = T(n/2) + T(n/4) + O(1)
It doesn’t seem like Master Method will help, as this is not in the form of T(n) = aT(n/b) + f(n). And I got stuck for quite a while.
Akra Bazzi is a much more powerful method than Master method.
Since the ‘non-recursive’ term is O(1), it amounts to solving the equation
1/2^p + 1/4^p = 1And the answer you get will be
T(n) = Theta(n^p)I believe solving the above (quadratic in
1/2^p) gives usp = log_2 phiwhere phi is the golden ratio.Computing that gives us
T(n) = Theta(n^0.694...)