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I want to calculate O(n log(n)) without using the master theorem.
Does anyone know a mathematical way of calculating O(n log(n)) from the recursive formula T(n) = 2T(n/2) + O(n)?
Draw a recursion tree:
height of the tree will be log n
cost at each level will come out to be constant times n
Hence the total cost will be O(nlogn). http://homepages.ius.edu/rwisman/C455/html/notes/Chapter4/RecursionTree.htm
And you can always prove it by induction if you want.