From:

=?ISO-8859-1?Q?Erik_Wikstr=F6m?= <Erik-wikstrom@telia.com>

Newsgroups:

comp.lang.c++

Date:

Tue, 26 Jun 2007 07:19:19 GMT

Message-ID:

<X53gi.2954$ZA.1451@newsb.telia.net>

Pete Becker wrote:

I am not interested in the asymptotic difference but a measurement of

the difference in time for a single operation - this way its possible to

give an idea of how many elements you need to operate with before it

makes sense to use a more complicated structure with a better asymptotic

complexity.

desktop wrote:

Yes, but that's not what asymptotic complexity is about. Asymptotic

complexity measures how well an algorithm scales when you increase the

amount of data. It answers questions like: it takes twenty seconds to

find all the records matching X in my database; if I double the number

of data elements, how long will it take?

Erik Wikstr?m wrote:

Is it possible to make an exact measurement in the difference in time

for 1 operation for a set and a list?

On 2007-06-25 22:21, desktop wrote:

In operations yes, not necessarily in time. If the operations on the

list takes 1 time and the operations on the set takes 50,000 then

they'll be equally fast. This will of course not be true in any

implementation (the set will be significantly faster than the list)

but it shows that just because one container/algorithm has a better

asymptotic running time it will in fact perform better. All it says

is that for a sufficiently large set of input, the algorithm will

perform better.

In practice you'll often find that using a vector for small sets will

be faster than most other containers, even if you need to traverse

the whole vector.

If I have a sorted std::list with 1.000.000 elements it takes

1.000.000 operations to find element with value = 1.000.000 (need to

iterator through the whole list).

In comparison, if I have a std::set with 1.000.000 element it will

only take approx lg 1.000.000 = 20 operations! Can it really be true

that the difference is a factor of 1.000.000/20 = 50.000 in this case?

1.000.000 operations to find element with value = 1.000.000 (need to

iterator through the whole list).

In comparison, if I have a std::set with 1.000.000 element it will

only take approx lg 1.000.000 = 20 operations! Can it really be true

that the difference is a factor of 1.000.000/20 = 50.000 in this case?

In operations yes, not necessarily in time. If the operations on the

list takes 1 time and the operations on the set takes 50,000 then

they'll be equally fast. This will of course not be true in any

implementation (the set will be significantly faster than the list)

but it shows that just because one container/algorithm has a better

asymptotic running time it will in fact perform better. All it says

is that for a sufficiently large set of input, the algorithm will

perform better.

In practice you'll often find that using a vector for small sets will

be faster than most other containers, even if you need to traverse

the whole vector.

Is it possible to make an exact measurement in the difference in time

for 1 operation for a set and a list?

Yes, but that's not what asymptotic complexity is about. Asymptotic

complexity measures how well an algorithm scales when you increase the

amount of data. It answers questions like: it takes twenty seconds to

find all the records matching X in my database; if I double the number

of data elements, how long will it take?

I am not interested in the asymptotic difference but a measurement of

the difference in time for a single operation - this way its possible to

give an idea of how many elements you need to operate with before it

makes sense to use a more complicated structure with a better asymptotic

complexity.

The time one operation needs is usually not interesting since you rarely

us only one operation, instead you use a mix of a few. So what's

interesting is how long time your mix performs. Consider an application

where you perform a number of operations on a collection, let's say you

perform 10 operations of type A, 1 of type B and 100 of type C. Given

that mix it's quite uninteresting if the B operation is fast or not,

what matters is, probably, how well C performs, then A.

--

Erik Wikstr?m

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