Chapter 8 - Section 8.3 - Divide-and-Conquer Algorithms and Recurrence Relations - Exercises - Page 535: 7

a) 2 b) 4 c) 7

We are given $$f(n)=f(n/3)+1$$ and $$f(1)=1$$ a) Apply the recurrence relation when $n=3$ $f(3)=f(1)+1$ $=1+1$ $=2$ b) Apply the recurrence relation when $n=27$ $f(27)=f(9)+1$ $=f(3)+2$ $=f(1)+3$ $=1+3$ $=4$ c) Apply the recurrence relation when $n=729$ $f(729)=f(243)+1$ $=f(81)+2$ $=f(27)+3$ $=f(9)+4$ $=f(3)+5$ $=f(1)+6$ $=1+6$ $=7$