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 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.
Solve the following recurrence relations: (find an asymptotic
upper bound O(?) for each one)
a. T(n) = T(2n/3)+T(n/3) + n^2
b. T(n) = √nT(√n) + n
c. T(n) = T(n-1)+T(n/2) + n
The base case is that constant size problems can be solved in
constant time (O(1)). You can use the induction, substitution or
recursion tree method
Give asymptotic tight bounds for T(n) in each of the following
recurrences using recursion tree.
a. T(n) = 2T(n − 1) + 1
b. T(n) = t(n − 1) + n
c. T(n) = 2T (n/4) + √n
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
Derive a Θ-bound on the solution to the following recurrence.
using iterative recursion and check your answer with master theorem
result
T(n) = T (1/3 n) + log n