You don't need an exact, or even close, solution. n is an integer, and a small one at that. You can easily check that by n=8, we already have n > 8 log n [assuming log is base 10]. But it's close

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n log n = c log(n^n) = c n^n = exp(c) Then, this equation has a solution of the form: n = exp(W(c)) where W is Lambert W function (see especially Example 2). It was proved that

n log n is O (n)? T (n) = 3 T (n/2) + n lg n .. I have come to the solution that it belongs to masters theorem case 2 since n lg n is O (n^2) but after referring to the solution

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Apparently the way to answer these is the following 3 identities: f = O(g) if \lim_{n \to \infty} \frac{f}{g} n \to \infty} \frac{f}{g} = 0 f = \Omega(g) if Graph containing every trees of size n as subgraphs

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