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I'm trying to solve this recurrence relation:

$T(n) = T(\frac{n}{2}) + T(\frac{n}{5}) + T(\frac{n}{10}) + c_1n$ ; n > 1
$T(n) = c_2n$ ; n = 1

My first thought was to combine the fractions and solve through the Master Theorem. Would this approach be enough to calculate a tight bound, or are there any other approaches I can take?

  • We discourage "please check whether my answer is correct" questions, as only "yes/no" answers are possible, which won't help you or future visitors. See here and here. Can you edit your post to ask about a specific conceptual issue you're uncertain about? As a rule of thumb, a good conceptual question should be useful even to someone who isn't looking at the problem you happen to be working on. If you just need someone to check your work, you might seek out a friend, classmate, or teacher. – D.W. Oct 19 '22 at 19:49
  • One way to verify the correctness of your answer is to guess explicit constants for the solution and prove it correct, also known as "guess-and-prove" (e.g., guess constants $c_3,c_4$ and prove that $T(n)\le c_3 n + c_4$ by induction, for large enough $n$). See https://cs.stackexchange.com/q/2789/755. – D.W. Oct 19 '22 at 19:50
  • Have you tried tracing the recurrence tree for this? – Rinkesh P Oct 20 '22 at 05:47

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