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
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 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 recurrence ?(?) = 3?(?/3) + ?. Use the substitution method
to verify your answer.
Determine the p-value for each of the following
situations. (Give your answer bounds exactly.)
(a) Ha: β1 > 0, with
n = 15 and t = 1.23
_____ < p < _____
(b) Ha: β1 ≠ 0, with
n = 25, b1 = 0.3, and
sb1 = 0.11
____ < p < _____
(c) Ha: β1 < 0, with
n = 18, b1 = -1.55, and
sb1 = 0.73
____< p < ____
Using the method of recursion, compute y[n] for n = 0 to 20,
when x[n]=u[n] and y[-1]=2:
?[? + 1] − 0.8?[?] = ?[?]
Find a closed-form expression for your result.
Let T be a binary tree with n positions that is realized with an
array representation A, and let f() be the level numbering function
of the positions of T, as given in Section 8.3.2. Give pseudocode
descriptions of each of the methods root, parent, left, right,
isExternal, and isRoot.