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Big-O estimate

  1. Jul 9, 2009 #1
    1. The problem statement, all variables and given/known data
    Hi, I am trying to solve this problem:
    I want the Big-O Estimate for this problem
    (n*logn + 1)^2 + (logn +1)(n^2+1)


    2. Relevant equations
    now only real problem comes when I try to do the square of the first term.

    I just dont know what (n*logn)^2 would be equal, it may be a it stupid, but it completely escapes my memory how to do it.

    Checking on the calculator 2nlogn != (n*logn)^2 neither does n^2logn^2, so although it may be a little stupid, I just cant recall what thats equal to, I have been looking up log rules, but to no avail.


    3. The attempt at a solution
    To me it makes sense that (n*logn)^2 = 2n*log(n)
    Thank You For Your Help.
     
  2. jcsd
  3. Jul 9, 2009 #2
    (n log n)^2 is just n^2 (log n)^2.

    Your best big-O estimate for (n*logn + 1)^2 + (logn +1)(n^2+1) is going to be
    O( n^2 (log n)^2 ).

    Of course, it is also O( n^3), or O( n^8 ), etc., but those aren't best.


    [ You might be confusing yourself with the property log(n^2)=2 log n. This property doesn't come into play in this problem. ]
     
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