For parameters \(a\) and \(b\), both of which are \(ω(1)\), \(T(n) =…

GATE · 2020 · CS · Computer Science & IT

For parameters aa and bb, both of which are ω(1)ω(1), T(n)=T(n1/a)+1T(n) = T(n^{1/a})+1, and T(b)=1T(b)=1.

Then T(n)T(n) is

  1. A.

    Θ(log⁡alog⁡bn)\Theta (\log_a \log _b n)

  2. B.

    Θ(log⁡abn)\Theta (\log_{ab} n)

  3. C.

    Θ(log⁡blog⁡a n)\Theta (\log_{b} \log_{a} \: n)

  4. D.

    Θ(log⁡2log⁡2n)\Theta (\log_{2} \log_{2} n)

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