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Thread: The Big O Notation
 04232012, 08:12 PM #1Senior Member
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 04232012, 08:23 PM #2
Re: The Big O Notation
What is your actual question? You have already supplied the BigO runtime of mergesort. Are you asking how to get O(n lgn) in the first place, or are you asking how to plug 14 in for n?
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 04232012, 08:27 PM #3Senior Member
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Re: The Big O Notation
Yes how to plug 14 in for n, and to get a result of the amount of steps it took for that algorithm? (But not in code, Just in theory)
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 04232012, 08:27 PM #4
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Re: The Big O Notation
Also note that O(f(n)) == O(c*f(n)) where c is any constant, so if you plug in a (small) value for n, the answer by itself doesn't tell you anything.
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 04232012, 08:31 PM #5Senior Member
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Re: The Big O Notation
Is that another formula for merge or something? I mean can I not just use the basic O(n log n) merge formula to plug in the value?
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 04232012, 08:34 PM #6
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 04232012, 08:39 PM #7Senior Member
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Re: The Big O Notation
Ok, what would be the easiest way to calculate the Big O if you have 14 data records that you want to sort in theory? That's really all my problem?
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 04232012, 09:00 PM #8Senior Member
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Re: The Big O Notation
The bubble sort is an O(n^2) formula, so if the value of n is 14, then :
O(n^2)
= 14^2
=196
So therefore is took the bubble sort 196 steps to complete the sort.
Now I am sure it would be as simple to do a calculation for the merge O(n log n)?
I just can't plot them in?
Any suggestions?
ThanksLast edited by dougie1809; 04232012 at 09:02 PM.
 04232012, 09:10 PM #9
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Re: The Big O Notation
You seem to want to count the number of elementary operations needed by your sorting algorithm; increment a simple counter each time your algorithm performs one of those elementary operations. A compare or a swap or a single append to a list etc. count as simple operations.
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Joscenosillicaphobia: the fear for an empty beer glass
 04232012, 09:14 PM #10Senior Member
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Re: The Big O Notation
Oh yes, I do understand how it may be written in code, but I'd like to be able to write it down as an equation i.e.
: O(n log n)
= 14 log(14)
= ??
Id like to calculate in that kind of sense, the same way the bubble sort O(n^2) can be calculated?
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 04232012, 09:17 PM #11
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Re: The Big O Notation
Well, 14*log(14) == 36.9468026146, but that number doesn't say much (see my first reply in this thread).
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Joscenosillicaphobia: the fear for an empty beer glass
 04232012, 09:21 PM #12Senior Member
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Re: The Big O Notation
Ah ok, that looks promising. Now how did you calculate 36.9468026146? I mean how is log(14) calculated?
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 04232012, 09:33 PM #13
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Re: The Big O Notation
I pressed the 'ln' key on my calculator; if you want the base 2 log, note that alog(x) == blog(x)/blog(a). So 2log(14) == log(14)/log(2) == 3.8073549221. But again, those numbers don't say much in bigOh computations (that's why a 'ln' is as good as any base log).
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 04232012, 09:39 PM #14Senior Member
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