Recursion problem T(n)=3T(n/3)+3n

Question

I just need help solving this problem. I know I'm supposed to be using the Master's Theorem but I don't know where to start

The solution is a direct application of the theorem. You just need to read the statement and check which condition applies. — Steven, Mar 06 '22 at 21:47
Does this answer your question? Solving or approximating recurrence relations for sequences of numbers — xskxzr, Mar 07 '22 at 07:07

score 0 · Answer 1 · answered Mar 07 '22 at 11:55

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$$T(n)=3T\left(\frac n3\right)+3n=9T\left(\frac n9\right)+3\frac n3+3n=27T\left(\frac n{27}\right)+3\frac n{27}+3\frac n3+3n=\cdots$$

So for an exact power of $3$, you get

$$nT(1)+3\frac{3n-3}2.$$

answered Mar 07 '22 at 11:55

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Please consider not to encourage undesirable posting behaviour. – Nathaniel Mar 07 '22 at 12:24
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I think you lost a factor 3 at the 3 (n/3) which should be 9 (n/3). And you do that for every recursion level, which means k times if n = 3^k, or a factor of log_3(n) – gnasher729 Mar 07 '22 at 12:30

1 Answers1