Kenneth Rosen Edition 7 Exercise 8.3 Question 12 (Page No. 535)

Question

Find $f (n)$ when $n = 3k,$ where $f$ satisfies the recurrence relation $f (n) = 2f (n/3) + 4 \:\text{with}\: f (1) = 1.$

Answer 1

- Solve the given recurrence relation by backward substitution, This is one approach,

 Reference: http://web.deu.edu.tr/halil.oruc/M100FFA-05.pdf---> Problem 6a with solution

   Hope this helps!

Comments

for me it is also helpful, many thanks!

Answer 2

Use Master Theorem with$ a = 2, b = 3, c = 4, d = 0$.

Since $a > b^{d}, (d<log_{b}a)$

we know that f(n) is $O(n^{ log_{b }a} ) = O(n ^{log_{3} 2} ).$