Question
Download Solution PDFGive asymptotic upper and lower bound for T(n) given below. Assume T(n) is constant for \(n \le 2.\;T\left( n \right) = 4T\left( {\sqrt n } \right) + lo{g^2}n\)
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDF\(T\left( n \right) = 4T\left( {√ n } \right) + lo{g^2}n\)
Consider n = 2m
m = log2n
n = 2m
Taking square root
√n = 2m/2
T(2m) = 4T(2m/2) + m2
Put S(m) = T (2m/2)
S(m) = 4 S(m/2) + m2
Comparing with
T(m) = a T(m/k) + cmk
a = 4, b = 2, k = 2
a = bk = 4
Now use master’s theorem :
T(m) = O(mklog m)
So, Time complexity will be O(m2log m)
Put the value of m
Time complexity will be : O (log2n log (logn))
Last updated on Jun 6, 2025
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