Use a recursion tree to determine a good asymptotic upper bound
on the following recurrences. Use the substitution method to verify
your answer.
T(n) = 3T(n/2) + n.
T(n) = T(n/2) + n2.
Use a recursion tree to determine a good asymptotic upper bound
on the following recurrences. Use the substitution method to verify
your answer.
T(n) = 3T(n/2) + n.
T(n) = T(n/2) + n2.
Give asymptotic upper and lower bounds for T(n). Assume that
T(n) is constant for n <= 2.
Make your bounds as tight as possible, and justify your
answers.
T(n) = T(n-2) + n^2
Use a recursion tree to determine a good asymptotic upper bound
on the recurrence T(n) = 2T(n/3) + 2n.
Use the substitution method to verify your answer
Using Θ-notation, provide asymptotically tight bounds in terms
of n for the solution to each of
the following recurrences. Assume each recurrence has a non-trivial
base case of T(1) = Θ(1).
For example, if asked to solve T(n) = 2T(n/2) + n, then your answer
should be Θ(n log n).
Give a brief explanation for each solution.
(a) T(n) = 5T(n/2) + n
(b) T(n) = 4T(n/2) + n2
(c) T(n) = T(n/4) + T(n/2) + n
Use a recursion tree to determine a good asymptotic upper bound
on the recurrence ?(?) = 3?(?/3) + ?. Use the substitution method
to verify your answer.
Use the recursion tree method to determine the asymptoticupper
bound of T(n).T(n) satisfies the recurrence T(n)=2T(n-1)+ c, where
c is a positive constant, andT(0)=0.
Solve the following recurrences by assuming T(n) is constant for
sufficiently small values of n and find time complexity
?(?) = ?(? − 1) + ? (?/2) + ?
?(?) = 4? (?/3) + ???(?)
?(?)=?(?−2)+ 1/ lg(?)