Two variables

Computer Science Level pending

T ( x ) = { 8 T ( x 2 ) + Θ ( 1 ) x 2 > K K x 2 ≤ K \large{T(x) = \begin{cases} 8T\left(\dfrac{x}{2}\right) + \Theta(1) & x^2 > K \\ K & x^2 \leq K \\ \end{cases}}

Which of the following is the correct tight bound for the recurrence above?

Assume K K is a variable independent of x x .

Θ ( n 3 M ) \Theta \left(\frac{n^3}{\sqrt{M}} \right ) Θ ( n lg ⁡ ( M 3 ) ) \Theta(n\lg(M^3)) Θ ( M n 3 ) \Theta(Mn^3) Θ ( n 3 M 2.5 ) \Theta\left(\frac{n^3}{M^{2.5}}\right )

Thaddeus Abiy by Thaddeus Abiy , 25, Ethiopia

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