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I have this recurrence equation:

$T(n) = T(n/4) + T(3n/4) + \mathcal{O}(n)$

$T(1) = 1$

I know that the result is $\mathcal{O}(n \log n)$ but i don't know how to proceed.

A.Schulz
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Federico Ponzi
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    What have you tried so far? What have you looked up? What are you confused about? –  Apr 14 '13 at 19:20
  • Hi jason, i would like to know which are the steps to follow to solve that recurrence equation (and recurrence equation in general). Thanks for help, Federico –  Apr 15 '13 at 11:02
  • The easiest way is to use Master theorem. – Bartosz Przybylski Apr 29 '13 at 12:24
  • If you want to see how to come up with recursion equations, you can see the base question, and read through the answers, to get result for general approach. –  Apr 29 '13 at 12:25
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    Try the reference question: http://cs.stackexchange.com/questions/2789/solving-or-approximating-recurrence-relations-for-sequences-of-numbers – Aryabhata Apr 29 '13 at 16:48
  • Welcome to [cs.SE]! Your question is a basic one. Since you did not include much of an attempt to solve it on your own, we have little to work with. Let me direct you towards our reference questions which cover your problem in detail. Please work through the related questions listed there, try to solve your problem again and edit to include your attempts along with the specific problems you encountered. Your question may then be reopened. Good luck! – Raphael Apr 29 '13 at 18:28

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Construct a recursion tree. The sum of the costs per level is less then $c\cdot n$, for $c$ being the constant in the $O(n)$. The tree has roughly $n\log_4 n$ full levels, and the deepest level is $n \log_{4/3} n$. So, summing up over all levels gives $T(n)=O(n\log n)$.

A.Schulz
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