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Recurrence relation and Time Complexity
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VikramRB
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Algorithms
Jan 20, 2019
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Jan 21, 2019
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VikramRB
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Query resolved.
What is the time complexity of the following recurrence relation and step to derive the same
$T(n) = T(\sqrt{n}) + log(logn)$
time-complexity
algorithms
recurrence-relation
VikramRB
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Jan 20, 2019
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Take $n=2^m$ then
$T(2^m)=T(2^{m/2})+\log m$
$\implies S(m)=S(m/2)+\log m$
Solve using master's theorem .$S(m)=O(\log ^2 m)=T(2^m)$
Put $m=logn \implies T(n)=(\log \log n)^2$
Verma Ashish
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Jan 20, 2019
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Verma Ashish
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VikramRB
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Jan 21, 2019
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How did you derive the 3rd step, m = $2^{m}$ is understod but how $2^{m/2}$ written as m/2
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Verma Ashish
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Jan 21, 2019
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We are not replacing $2^m \;by\; m$ but we are changing function T to S.
$T(2^m)\implies$ function of m. (S(m))
$T(2^{m/2})\implies$ function of m/2. (S(m/2))
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Hira Thakur
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Oct 11, 2019
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can you please tell me $log^2(logn)$ and $(loglogn)^2$both are same??
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Verma Ashish
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Oct 11, 2019
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Yes..same
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