2. The time taken for a sorting algorithm on an input size of n, obeys the following relation 364 Tn+1 = T, + 52 for n20 given To = 1 (a) Calculate the first 4 terms To..T3. (b) Use the unwinding technique to determine the closed form of T,. (c) Show that your closed form expression for T, from part (b) is correct when n = 0. Demonstrate that your closed form expression for T, satisfies the recurrence equation in part (a) (Hint: Substitute your closed form solution into part (a)).
2. The time taken for a sorting algorithm on an input size of n, obeys the following relation 364 Tn+1 = T, + 52 for n20 given To = 1 (a) Calculate the first 4 terms To..T3. (b) Use the unwinding technique to determine the closed form of T,. (c) Show that your closed form expression for T, from part (b) is correct when n = 0. Demonstrate that your closed form expression for T, satisfies the recurrence equation in part (a) (Hint: Substitute your closed form solution into part (a)).
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![2. The time taken for a sorting algorithm on an input size of n, obeys the
following relation
364
Tn+1 = T, +
52
for n20 given To = 1
%3D
(a) Calculate the first 4 terms T...T3.
(b) Use the unwinding technique to determine the closed form of T.
(c) Show that your closed form expression for T, from part (b) is correct
when n = 0. Demonstrate that your closed form expression for T,
satisfies the recurrence equation in part (a) [Hint: Substitute your
closed form solution into part (a)].
(d) The time complexity of an algorithm is given by O(log; n2 – log; n).
If n = 78125, what is the value of k in log, n = k?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6cdae1b3-511b-42a7-83bc-b26c890aa6cb%2Fdf53ecd3-c3a8-4ff6-892e-99659f4a9eac%2Fa9gwze6_processed.jpeg&w=3840&q=75)
Transcribed Image Text:2. The time taken for a sorting algorithm on an input size of n, obeys the
following relation
364
Tn+1 = T, +
52
for n20 given To = 1
%3D
(a) Calculate the first 4 terms T...T3.
(b) Use the unwinding technique to determine the closed form of T.
(c) Show that your closed form expression for T, from part (b) is correct
when n = 0. Demonstrate that your closed form expression for T,
satisfies the recurrence equation in part (a) [Hint: Substitute your
closed form solution into part (a)].
(d) The time complexity of an algorithm is given by O(log; n2 – log; n).
If n = 78125, what is the value of k in log, n = k?
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