Fall 2001
Fundamental Algorithms
Professor Yap

Homework 1 (HINTS)

  •    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