Velocity Reviews > C++ > Filling 2d array in less than O(n^2) time

# Filling 2d array in less than O(n^2) time

pjhyett@gmail.com
Guest
Posts: n/a

 11-18-2005
standard 2d array filling with increasing numbers for rows and columns:

for(int i=0;i<n;i++)
for(int j=0;j<n;j++)
a[i][j] = i + j;

problem is it's O(n^2). I'm looking for a method to decrease the time,
any suggestions? I'm googling for dynamic programming solutions, but
not coming up with much.

red floyd
Guest
Posts: n/a

 11-18-2005
wrote:
> standard 2d array filling with increasing numbers for rows and columns:
>
> for(int i=0;i<n;i++)
> for(int j=0;j<n;j++)
> a[i][j] = i + j;
>
> problem is it's O(n^2). I'm looking for a method to decrease the time,
> any suggestions? I'm googling for dynamic programming solutions, but
> not coming up with much.
>

I don't think it's possible, since you *must* assign n^2 elements.

rwf_20
Guest
Posts: n/a

 11-18-2005

red floyd wrote:
> wrote:
> > standard 2d array filling with increasing numbers for rows and columns:
> >
> > for(int i=0;i<n;i++)
> > for(int j=0;j<n;j++)
> > a[i][j] = i + j;
> >
> > problem is it's O(n^2). I'm looking for a method to decrease the time,
> > any suggestions? I'm googling for dynamic programming solutions, but
> > not coming up with much.
> >

>
> I don't think it's possible, since you *must* assign n^2 elements.

Yes, this algorithm is not O(n^2). It is O(n), and as efficient
(theoretically) as can be.

Ryan

Markus Moll
Guest
Posts: n/a

 11-18-2005
Hi

rwf_20 wrote:

>
> red floyd wrote:
>> I don't think it's possible, since you *must* assign n^2 elements.

>
> Yes, this algorithm is not O(n^2). It is O(n), and as efficient
> (theoretically) as can be.

Huh? Linear in what? If, as given in the example, n is to denote the number
of columns and rows and you count the number of assignments, then of course
there are exactly n^2 \in O(n^2) of them.

Nevertheless it is obviously true that this is optimal.

Markus

red floyd
Guest
Posts: n/a

 11-18-2005
rwf_20 wrote:
> red floyd wrote:
>
>> wrote:
>>
>>>standard 2d array filling with increasing numbers for rows and columns:
>>>
>>>for(int i=0;i<n;i++)
>>> for(int j=0;j<n;j++)
>>> a[i][j] = i + j;
>>>
>>>problem is it's O(n^2). I'm looking for a method to decrease the time,
>>>any suggestions? I'm googling for dynamic programming solutions, but
>>>not coming up with much.
>>>

>>
>>I don't think it's possible, since you *must* assign n^2 elements.

>
>
> Yes, this algorithm is not O(n^2). It is O(n), and as efficient
> (theoretically) as can be.

Would you care to explain how it's O(n), and not O(n^2)?

E. Mark Ping
Guest
Posts: n/a

 11-18-2005
In article <_7sff.15956$> , red floyd <> wrote: >rwf_20 wrote: >> >> >> Yes, this algorithm is not O(n^2). It is O(n), and as efficient >> (theoretically) as can be. > >Would you care to explain how it's O(n), and not O(n^2)? Because 'n' typically represents the number of elements. There are are rows*columns elements. One operation per element. Hence O(n) where n is the number of elements in the array. -- Mark Ping mlimber Guest Posts: n/a  11-18-2005 wrote: > standard 2d array filling with increasing numbers for rows and columns: > > for(int i=0;i<n;i++) > for(int j=0;j<n;j++) > a[i][j] = i + j; > > problem is it's O(n^2). I'm looking for a method to decrease the time, > any suggestions? I'm googling for dynamic programming solutions, but > not coming up with much. Initialize it statically, and then it will be filled at load-time rather than run-time. At file/namespace scope, do this: int a[][] = { { 0, 1, 2, 3 }, { 4, 5, 6, 7 } }; Of course this limits your flexibility. Cheers! --M Howard Guest Posts: n/a  11-18-2005 "E. Mark Ping" <> wrote in message news:dlljok$1isk$... > In article <_7sff.15956$> ,
> red floyd <> wrote:
>>rwf_20 wrote:
>>>
>>>
>>> Yes, this algorithm is not O(n^2). It is O(n), and as efficient
>>> (theoretically) as can be.

>>
>>Would you care to explain how it's O(n), and not O(n^2)?

>
> Because 'n' typically represents the number of elements. There are
> are rows*columns elements. One operation per element. Hence O(n)
> where n is the number of elements in the array.
> --

There are not neccessarily any "elements" to speak of in the general case.

And in this case, he's speaking of n as the size of both the rows and the
columns, as you can see by the code. There are rows*columns operations, so
that means n*n operations, which makes it O(n^2). The cost grows by the
square of the value n.

-Howard

Pete Becker
Guest
Posts: n/a

 11-19-2005
Howard wrote:

> "E. Mark Ping" <> wrote in message
> news:dlljok$1isk$...
>
>>In article <_7sff.15956\$> ,
>>red floyd <> wrote:
>>
>>>rwf_20 wrote:
>>>
>>>>
>>>>Yes, this algorithm is not O(n^2). It is O(n), and as efficient
>>>>(theoretically) as can be.
>>>
>>>Would you care to explain how it's O(n), and not O(n^2)?

>>
>>Because 'n' typically represents the number of elements. There are
>>are rows*columns elements. One operation per element. Hence O(n)
>>where n is the number of elements in the array.
>>--

>
>
> There are not neccessarily any "elements" to speak of in the general case.
>

Big-Oh notation refers to the depenency of the time complexity of an
algorithm on the number of elements that it's applied to.

> And in this case, he's speaking of n as the size of both the rows and the
> columns, as you can see by the code. There are rows*columns operations, so
> that means n*n operations, which makes it O(n^2). The cost grows by the
> square of the value n.
>

The cost grows by the square of the value of n, but that's not the
meaning of big-Oh notation.

--

Pete Becker
Dinkumware, Ltd. (http://www.dinkumware.com)

Greg Comeau
Guest
Posts: n/a

 11-19-2005
In article < .com>,
mlimber <> wrote:
> int a[][] = { { 0, 1, 2, 3 }, { 4, 5, 6, 7 } };

You can't have [][] like that even on a definition.
Only the first dimension can be []'d
--
Greg Comeau / Celebrating 20 years of Comeauity!
Comeau C/C++ ONLINE ==> http://www.comeaucomputing.com/tryitout
World Class Compilers: Breathtaking C++, Amazing C99, Fabulous C90.
Comeau C/C++ with Dinkumware's Libraries... Have you tried it?

 Thread Tools

 Posting Rules You may not post new threads You may not post replies You may not post attachments You may not edit your posts BB code is On Smilies are On [IMG] code is On HTML code is OffTrackbacks are On Pingbacks are On Refbacks are Off Forum Rules

 Similar Threads Thread Thread Starter Forum Replies Last Post bbawa1@yahoo.com ASP .Net 4 06-21-2007 08:03 PM RayC NZ Computing 12 06-21-2006 09:32 AM Don Hills NZ Computing 4 05-15-2006 07:39 AM falcon Java 10 02-24-2006 01:23 PM Ray Wood ASP .Net Web Services 0 07-17-2003 02:06 PM

Advertisments