Oh,Oh,Oh,merry analysis!!!

anonimnystefy · 2012-01-23 11:01:32

hi JEF

no no.it's something we've done last year.

hi bobbym

well it would be nice.

bobbym · 2012-01-23 11:07:37

HI;

Prove that n^3+20n -10 is not O(n^2).

anonimnystefy · 2012-01-23 11:12:25

hi

so n^3+20n-10>c*n^2 for any finite real number c>0.so n^3+20n-10 is w(n^2) and W(n^2) if i'm not mistaken.

i think that's enough for today.just tell me if i got this one right.

bobbym · 2012-01-23 11:20:39

I do not remember about little w and Big W. But you are correct in the question.

anonimnystefy · 2012-01-23 21:12:13

hi bobbym

next?

bobbym · 2012-01-24 01:16:48

Describe the growth of

bobbym · 2012-01-24 11:47:03

Hi anonimnystefy;

You have two questions for you to work on.

What does O(1) really mean? Put your answer in terms of a physical problem, something computer related.

anonimnystefy · 2012-01-24 21:33:35

hi bobbym

1.n/((n+1)/2) is O(1)

2.O(1) means that an application with this complexity means that for any input it will take the same time to execute.e.g. the finding of the first element in an array has complexity of (1).

bobbym · 2012-01-25 01:12:43

Correct!

What is the Big(O) of this loop structure;

int x
for(x = 1; x<n; x*=2)
{
cout<< "hello";
}

bobbym · 2012-01-25 06:20:08

Hi anonimnystefy;

What does O(2^n) mean in cumputerese? Would you recommend an algorithm that had this amount of complexity?

anonimnystefy · 2012-01-25 08:04:30

hi bobbym

1.it's O(log n)
2.well it's time doubles when we add one more element.time grow very very quickly,so i would never recommend it.

unfortunately i cannot think of any algorithms that are O(2^n)

bobbym · 2012-01-25 08:07:36

Hi;

Very good!

You probably have never seen an O(2^n) algorithm.

anonimnystefy · 2012-01-25 08:11:30

probably.you?

next?

bobbym · 2012-01-25 08:13:02

When we say O(log(n)), clarify.

anonimnystefy · 2012-01-25 08:25:56

it means that the algorithm execution time grow slower than a linear algorithm.for example if we have 1 element the execution time will be 1,if we have 2 then it's 2,but for 3 it's also 2,for 4 it would be 3,and so on.

example algorithm is binary search algorithm.

bobbym · 2012-01-25 08:26:45

True but there is one more oddity about it. Check the notation for a clue.

anonimnystefy · 2012-01-25 08:42:54

well i don't know what it is.maybe it's that the base needn't be specified.

bobbym · 2012-01-25 08:44:01

Hmmm! You were close. In normal mathematics log(n) means logs to the base e. Here it is in base 2.

TheDude · 2012-01-25 08:52:49

Sorry to be pedantic, but when base isn't specified isn't log(n) usually base 10 and ln(n) base e?

anonimnystefy · 2012-01-25 08:55:50

hi bobbym

i don't agree.somewhere log is used to represent base 10 and ln for base e.

bobbym · 2012-01-25 08:59:46

Hi TheDude and anonimnystefy;

Yes, you are correct. I use ln rather than log, but Mathematica, (Wolfram ) uses the notation log(n) for the natural logarithm. I should have been clearer in making that distinction.

anonimnystefy · 2012-01-25 09:04:57

it's okay.you're just used to it.

next?

bobbym · 2012-01-25 09:07:38

Hold on, because I have answered this question before. If you look here

http://en.wikipedia.org/wiki/Logarithm

in notations near the top you will see that when no base is specified log(x) means the natural log ( base e ) and not the common one at least one branch of math too.

anonimnystefy · 2012-01-25 09:10:09

the writer uses it like that as well and probably doesn't know about the other notation.

bobbym · 2012-01-25 09:13:33

It appears that either way depending on writers and branches of math both are correct.

For the purposes of asymptotic analysis log(n) means to the base 2.

Math Is Fun Forum

#76 2012-01-23 11:01:32

Re: Oh,Oh,Oh,merry analysis!!!

#77 2012-01-23 11:07:37

Re: Oh,Oh,Oh,merry analysis!!!

#78 2012-01-23 11:12:25

Re: Oh,Oh,Oh,merry analysis!!!

#79 2012-01-23 11:20:39

Re: Oh,Oh,Oh,merry analysis!!!

#80 2012-01-23 21:12:13

Re: Oh,Oh,Oh,merry analysis!!!

#81 2012-01-24 01:16:48

Re: Oh,Oh,Oh,merry analysis!!!

#82 2012-01-24 11:47:03

Re: Oh,Oh,Oh,merry analysis!!!

#83 2012-01-24 21:33:35

Re: Oh,Oh,Oh,merry analysis!!!

#84 2012-01-25 01:12:43

Re: Oh,Oh,Oh,merry analysis!!!

#85 2012-01-25 06:20:08

Re: Oh,Oh,Oh,merry analysis!!!

#86 2012-01-25 08:04:30

Re: Oh,Oh,Oh,merry analysis!!!

#87 2012-01-25 08:07:36

Re: Oh,Oh,Oh,merry analysis!!!

#88 2012-01-25 08:11:30

Re: Oh,Oh,Oh,merry analysis!!!

#89 2012-01-25 08:13:02

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#90 2012-01-25 08:25:56

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#91 2012-01-25 08:26:45

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#92 2012-01-25 08:42:54

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#93 2012-01-25 08:44:01

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#94 2012-01-25 08:52:49

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#95 2012-01-25 08:55:50

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#96 2012-01-25 08:59:46

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#97 2012-01-25 09:04:57

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#98 2012-01-25 09:07:38

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#99 2012-01-25 09:10:09

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#100 2012-01-25 09:13:33

Re: Oh,Oh,Oh,merry analysis!!!

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