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 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
Write a function divisibleBy3 with 2 positive
integer inputs, a lower bound and an upper bound. Generate a list
of integers from the lower bound to the upper bound and determine
how many numbers in the list have a remainder equal to zero when
dividing by 3.
Hint: Use a loop and the MATLAB built-in function
rem to calculate the remainder after division. The
remainder of N divided by P is rem(N,P).
Write a program in JAVA that prompts the user for a lower bound
and an upper bound. Use a loop to output all of the even integers
within the range inputted by the user on a single line.