Jian-Wei Zhang wrote: > > Dear Professor: > > I am not clear the question 4-1(p85). What is it mean upper and lower > bounds for T(n)? > If it is $T(n)=\Theta(n^3)$. That's enough? or we need to find > $c_1*n^3 < T(n) < c_2*n^3$ , and find what is c_1 and c_2? > > Regards > > Jianwei Dear Jian-Wei: If you show $T(n)=\Theta(f)$ for any f, this is asymptotically tight. Of course, there are implicit constants, c_1, c_2, n_0. But you need not show them unless we explicitly ask for them (but we did not). That means, for question 4-1, you can use the Master theorem whenever it it appropriate! Of course, to use the Master Theorem, be sure to justify the case that you are invoking. --Chee