Solve each recurrence below using the 2. Recurrences (Master Method). Master Method and write your answer using e-notation. Make sure that you show all your work including the corresponding case and the values of e or k used. If it is not possible to solve a recurrence using the Master Method, prove it by showing that the form is inapplicable or by showing that all 3 cases cannot be satisfied. (a) T(n)=37(n/2) + n² (b) T(n)=257(n/5)+n (e) T(n)= T(3n/10) + n (d) T(n)= n³T(n) + 2n (e) T(n)= 37(n/3) +n¹/3 (f) T(n)=9T(n/3) + n² lg n (g) T(n)=97(n/3) + nlg³n (h) T(n)= T(n/3)+27(n/5)+n (i) Bonus T(n)=27(√n) + log n
Solve each recurrence below using the 2. Recurrences (Master Method). Master Method and write your answer using e-notation. Make sure that you show all your work including the corresponding case and the values of e or k used. If it is not possible to solve a recurrence using the Master Method, prove it by showing that the form is inapplicable or by showing that all 3 cases cannot be satisfied. (a) T(n)=37(n/2) + n² (b) T(n)=257(n/5)+n (e) T(n)= T(3n/10) + n (d) T(n)= n³T(n) + 2n (e) T(n)= 37(n/3) +n¹/3 (f) T(n)=9T(n/3) + n² lg n (g) T(n)=97(n/3) + nlg³n (h) T(n)= T(n/3)+27(n/5)+n (i) Bonus T(n)=27(√n) + log n
Operations Research : Applications and Algorithms
4th Edition
ISBN:9780534380588
Author:Wayne L. Winston
Publisher:Wayne L. Winston
Chapter2: Basic Linear Algebra
Section: Chapter Questions
Problem 15RP
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Question
![2. Recurrences (Master Method).
Solve each recurrence below using the
Master Method and write your answer using e-notation. Make sure that you show all your
work including the corresponding case and the values of e or k used. If it is not possible to
solve a recurrence using the Master Method, prove it by showing that the form is inapplicable
or by showing that all 3 cases cannot be satisfied.
(a) T(n)=37(n/2) + n²
(b) T(n)=25T(n/5)+n
(e) T(n)= T(3n/10)+n
(d) T(n)= n³T(n) + 2n
(e) T(n)= 3T(n/3) +n¹/3
(f) T(n)=9T(n/3) + n² lg n
(g) T(n)=9T(n/3) + nlg²n
(h) T(n)= T(n/3)+27 (n/5)+n
(i) Bonus
T(n) = 27 (√n) +logn](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6dafaef2-7bf1-4b89-a31b-dbaea4355db9%2Ffa866d2d-bf66-4cec-8b13-13e23ec0df76%2Fr52w0g_processed.png&w=3840&q=75)
Transcribed Image Text:2. Recurrences (Master Method).
Solve each recurrence below using the
Master Method and write your answer using e-notation. Make sure that you show all your
work including the corresponding case and the values of e or k used. If it is not possible to
solve a recurrence using the Master Method, prove it by showing that the form is inapplicable
or by showing that all 3 cases cannot be satisfied.
(a) T(n)=37(n/2) + n²
(b) T(n)=25T(n/5)+n
(e) T(n)= T(3n/10)+n
(d) T(n)= n³T(n) + 2n
(e) T(n)= 3T(n/3) +n¹/3
(f) T(n)=9T(n/3) + n² lg n
(g) T(n)=9T(n/3) + nlg²n
(h) T(n)= T(n/3)+27 (n/5)+n
(i) Bonus
T(n) = 27 (√n) +logn
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