Question

Solve the recurrence relation T(n)=T(n^1/2)+1 and give a Θ bound. Assume that T (n) is constant for sufficiently small n. Can you show a verification of the recurrence relation? I've not been able to solve the verification part so far

note: n^1/2 is square root(n)

Answer 1

For verification we will use master's theorem

Master's theorem :-

T(n) = aT(n/b) + f(n), a>=1 and b>1

Compare n^log_ba and f(n)

i).if n^log_ba > f(n), greater by polynomial function

Then T(n) = theta(n^log_ba)

ii).If n^log_ba < f(n),greater by polynomial function

Then T(n) = theta(f(n))

iii).if f(n) = n^log_ba

Then T(n) = theta(f(n).logn)

Soling uwing suhsitufin methoe?

theorem:- ers thal is solvable maser's theoneim f n-2 Abve equat on 's solvable maden's teotem Hence, vexitied