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junky_fellow 02-20-2004 06:09 AM

complexity of an algorithm
 
How do we calculate the complexity of an algorithm?

Am i right if i say the complexity of an algorithm
is the number of comparisons done in that algorithm?

thanx in advance .......

Ben Pfaff 02-20-2004 06:12 AM

Re: complexity of an algorithm
 
junky_fellow@yahoo.co.in (junky_fellow) writes:

> How do we calculate the complexity of an algorithm?
>
> Am i right if i say the complexity of an algorithm
> is the number of comparisons done in that algorithm?


Your question is outside the domain of comp.lang.c, which discusses
only the standard C programming language, including the standard C
library. This is a remarkably narrow topic compared to what many
people expect.

For your convenience, the list below contains topics that are not
on-topic for comp.lang.c, and suggests newsgroups for you to explore
if you have questions about these topics. Please do observe proper
netiquette before posting to any of these newsgroups. In particular,
you should read the group's charter and FAQ, if any (FAQs are
available from www.faqs.org and other sources). If those fail to
answer your question then you should browse through at least two weeks
of recent articles to make sure that your question has not already
been answered.

* OS-specific questions, such as how to clear the screen,
access the network, list the files in a directory, or read
"piped" output from a subprocess. These questions should be
directed to OS-specific newsgroups, such as
comp.os.ms-windows.programmer.misc, comp.unix.programmer, or
comp.os.linux.development.apps.

* Compiler-specific questions, such as installation issues and
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comp.lang.asm.x86, embedded system processor questions may
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* ABI-specific questions, such as how to interface assembly
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* Algorithms, except questions about C implementations of
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news.groups.questions is a good place to ask about the appropriate
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Christian Bau 02-20-2004 07:55 AM

Re: complexity of an algorithm
 
In article <8c7d4a6e.0402192209.728d1bfe@posting.google.com >,
junky_fellow@yahoo.co.in (junky_fellow) wrote:

> How do we calculate the complexity of an algorithm?
>
> Am i right if i say the complexity of an algorithm
> is the number of comparisons done in that algorithm?


Function f () calculates the sum of 1/x for x = 1 to 1e12 without any
comparisons:

double f1 (double x) { return 1/x + 1/(x+1) + 1/(x+2) ... + 1/(x+9); }
double f2 (double x) { return f1(x) + f1(x+10) + f1(x+20)...+ f1(x+90); }
double f3 (double x) { return f2(x) + f2(x+100)...+f2 (x+900); }
....
double f12(double x) { return f11(x) + f11(x+1e11) + ... + f11(x+9e11); }

double f (void) { return f12 (1.0); }

So the answer to your question seems to be "no".

Joona I Palaste 02-20-2004 08:02 AM

Re: complexity of an algorithm
 
junky_fellow <junky_fellow@yahoo.co.in> scribbled the following:
> How do we calculate the complexity of an algorithm?


> Am i right if i say the complexity of an algorithm
> is the number of comparisons done in that algorithm?


> thanx in advance .......


This has pretty much nothing to do with any specific programming
language. However, the answer to your question above is "no".
Consider these functions:

int isOneSmallerThanTwo(void) {
if (1<2) return 1; else return 0;
}

int isOneSmallerThanTwo2(void) {
if (1<2) if (1<2) return 1; else return 0; else if (1<2) return 1;
else return 0;
}

Both are of complexity O(1), but still the latter performs one more
comparison than the former.

A more correct statement would be:
"A single atomic operation or a comparison takes O(1) time. A sequence
of such statements takes as much time as its longest operation. A loop
iterating over such statements takes the time of the operations take,
multiplied by the time that iterating over the loop takes."
This statement is not perfect - there may be loopholes.

--
/-- Joona Palaste (palaste@cc.helsinki.fi) ------------- Finland --------\
\-- http://www.helsinki.fi/~palaste --------------------- rules! --------/
"Show me a good mouser and I'll show you a cat with bad breath."
- Garfield

Derk Gwen 02-20-2004 09:01 AM

Re: complexity of an algorithm
 
junky_fellow@yahoo.co.in (junky_fellow) wrote:
# How do we calculate the complexity of an algorithm?
#
# Am i right if i say the complexity of an algorithm
# is the number of comparisons done in that algorithm?

Peruse a copy of Knuth's Art of Programming. Volume 1 introduces the
topic, and he does space and time complexities throughout. It's too
complex a topic to try to teach in one post.

--
Derk Gwen http://derkgwen.250free.com/html/index.html
I have no respect for people with no shopping agenda.

Malcolm 02-21-2004 06:25 PM

Re: complexity of an algorithm
 
"junky_fellow" <junky_fellow@yahoo.co.in> wrote in message
>
> How do we calculate the complexity of an algorithm?
>
> Am i right if i say the complexity of an algorithm
> is the number of comparisons done in that algorithm?
>

This is probably as good a measure as any - count the for, while and ifs in
the code. switch() presents you with a bit of a problem, as do function
pointers.

The problem is that what you really want to know is, psychologically, how
hard is the algorithm to implement? There isn't really a good way of
defining this.



shlinlin 11-20-2010 05:50 AM

max flow
 
in book "introduction of Algorithm" 3rd Ed. chapter 26-Maximum Flow, exercises 26.2-10, Show how to find a maximum flow in a network G=(V,E) by a sequence of at most |E| augmenting paths. (Hint: Determine the paths after finding the maximum flow),
except repeat copy Ford-Fulkerson and Edmonds-Karp algorithm, I do not know what else I should reply. Am I right? looking to hear advancer's advice,
Eric, shlinlin at 37 dot com


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