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#101 2012-01-25 09:14:02

anonimnystefy
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Registered: 2011-05-23
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Re: Oh,Oh,Oh,merry analysis!!!

ok.

next?


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

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#102 2012-01-25 09:17:22

bobbym
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From: Bumpkinland
Registered: 2009-04-12
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Re: Oh,Oh,Oh,merry analysis!!!

But, between us I agree with you and TheDude and will stick to the notation you mentioned.

If two processes have a running time of 1111 log(n) and (1 / 111 )n^3 which one is slower? For what n will they be equal? ( here we are using the computer notation for log(n) )


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#103 2012-01-25 09:51:24

anonimnystefy
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Posts: 15,526

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

hi bobbym

1111log(n) is much better.n^3/111 is slower

i don't know when they are equal.

Last edited by anonimnystefy (2012-01-25 09:51:45)


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

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#104 2012-01-25 09:57:42

bobbym
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From: Bumpkinland
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Re: Oh,Oh,Oh,merry analysis!!!

You have no idea when they are equal?


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#105 2012-01-25 09:58:50

anonimnystefy
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Registered: 2011-05-23
Posts: 15,526

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

nope.i mean i know i have to solve an equation,but i'm not sure it can be done.


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

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#106 2012-01-25 09:59:49

bobbym
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From: Bumpkinland
Registered: 2009-04-12
Posts: 86,771

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

Want to try it?


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#107 2012-01-25 10:03:21

anonimnystefy
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From: The Foundation
Registered: 2011-05-23
Posts: 15,526

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

yup.how?


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

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#108 2012-01-25 10:06:35

bobbym
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From: Bumpkinland
Registered: 2009-04-12
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Re: Oh,Oh,Oh,merry analysis!!!

Enter this into alpha, just as you see it.

Plot[{1111Log[n,2],n^3/111},{n,0,30}]


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#109 2012-01-25 10:09:28

anonimnystefy
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Registered: 2011-05-23
Posts: 15,526

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

hi bobbym

i used "solve" instead.i got a real solution- 29.3544.now i'm not sure if i should take 19 or 30,but i'm more on the side of 29.


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

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#110 2012-01-25 10:12:23

bobbym
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From: Bumpkinland
Registered: 2009-04-12
Posts: 86,771

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

The plot would have shown you a little more. For n< that value you are better off using the slower process!

View Image: 2012-01-25_140642.png

In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#111 2012-01-25 10:14:47

anonimnystefy
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From: The Foundation
Registered: 2011-05-23
Posts: 15,526

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

hi bobbym

i know that.but the big oh gives us results for large enough numbers.i was trying to find the exact value at which they are equal.

btw i looked it up first,but i couldn't see the exact result.

Last edited by anonimnystefy (2012-01-25 10:15:24)


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

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#112 2012-01-25 10:16:53

bobbym
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From: Bumpkinland
Registered: 2009-04-12
Posts: 86,771

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

You can not have n, other than a whole number so 29 and 30 are all you need..


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#113 2012-01-25 10:18:48

anonimnystefy
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From: The Foundation
Registered: 2011-05-23
Posts: 15,526

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

next?


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

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#114 2012-01-25 10:20:09

bobbym
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From: Bumpkinland
Registered: 2009-04-12
Posts: 86,771

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

One more thing first. Did you see the reason for solving graphically or otherwise?


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#115 2012-01-25 10:22:11

anonimnystefy
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From: The Foundation
Registered: 2011-05-23
Posts: 15,526

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

hi bobbym

well not really.i know when the latter will be better and when the first will be better.i just need to know when they are equal.


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

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#116 2012-01-25 10:24:17

bobbym
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From: Bumpkinland
Registered: 2009-04-12
Posts: 86,771

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

Yes, but the exact point tells you which one is best for particular n's, while Big(O) only tells you for gazillions! If those were two different type sorts and you only had 20 objects to sort the n^3 / 111 is the right one to use.


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#117 2012-01-25 10:26:03

anonimnystefy
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From: The Foundation
Registered: 2011-05-23
Posts: 15,526

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

hi

well,duh.i'm saying that using the mixed you can do better than using just one.


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

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#118 2012-01-25 10:30:34

bobbym
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From: Bumpkinland
Registered: 2009-04-12
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Re: Oh,Oh,Oh,merry analysis!!!

f(n) = 100n^2, g(n) = n^4

f(10) = 10000, g(10) = 10000

f(50) = 250000, g(50) = 6250000

f(100) = 1,000,000, g(100)= 100,000,000

The above table and a graph show that f(n) grows more slowly than g(n). Would you agree that f(n) = O(g(n))?


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#119 2012-01-25 10:36:20

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,526

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

hi

it should be g(50)=6250000.

yes.i would say that f(n) is O(g(n))


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

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#120 2012-01-25 10:40:07

bobbym
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From: Bumpkinland
Registered: 2009-04-12
Posts: 86,771

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

Correct! I have fixed the above question.


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#121 2012-01-25 10:40:58

anonimnystefy
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From: The Foundation
Registered: 2011-05-23
Posts: 15,526

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

hi bobbym

4 zeros!

next?


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

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#122 2012-01-25 10:46:23

bobbym
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From: Bumpkinland
Registered: 2009-04-12
Posts: 86,771

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

I see that my cyber pen ran out of cyber ink.

Order these common functions according to growth rate:

1, n^n, 2^n, log(n), n log(n), n^2, n, n^2


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#123 2012-01-25 10:48:55

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,526

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

hi

by what,complexity?

1,log(n),n,n log(n),n^2 (twice?),2^n,n^n


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

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#124 2012-01-25 10:51:40

bobbym
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From: Bumpkinland
Registered: 2009-04-12
Posts: 86,771

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

Kayrect a mundo! You certainly know your Big(O).


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#125 2012-01-25 10:55:31

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,526

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

well it's not mine.

next?and this should be the last one for today.

Last edited by anonimnystefy (2012-01-25 10:55:53)


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

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