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Ranking an array (with ties and tollerances)

 
 
Michael Angelo Ravera
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      08-17-2011
I WILL be writing this myself (unless someone posts a solution that I particularly like), but does anyone have any tricks for efficient method of ranking the values in an unsorted array.
The result that I would like to achieve is that we have an unsorted array "score" (for the first case we will assume that it is a 32-bit signed integer) of size "size" and two arrays of unsigned integers "rank" and "ties" large enough to hold a number at least as large as "size". Upon completion, I want each element of "rank" to be one larger than the number of items in score that are greater than the corresponding element of "score" and each element of "ties" to equal the number of other elements in "score" that are equal to the corresponding element in "score".

For the second case, "fscore" is a floating point number of appropriate precision and "size" "rank" and "ties" are as before, but we have a multiplicative tollerance within which scores are to be considered as equal.

What I have done in the past is to iniialize all of the elements of rank to1 and all of the elements of ties to 0 and for each element of score ade the comparision and incremented rank and ties as necessary while skipping the current element.

Something like this for the integer case.

#define size appropriately
int this_el, comp_el;
INT32 score [size];
unsigned rank [size], ties [size];

for (this_el = 0; this_el < size; this_el ++)
{
rank [this_el] = 1;
ties [this_el] = 0;
}

for (this_el = 0; this_el < size; this_el ++)
{
for (comp_el = 0; comp_el < this_el; comp_el ++)
{
if (score [this_el] < score [comp_el])
rank [this_el] ++;
else if (score [this_el] == score [comp_el])
ties [this_el] ++;
}
for (comp_el = this_el + 1; comp_el < size; comp_el ++)
{
if (score [this_el] < score [comp_el])
rank [this_el] ++;
else if (score [this_el] == score [comp_el])
ties [this_el] ++;
}
}

Yeah, you can just have one internal loop and test for and skip over the (this_el == comp_el) but I think that the way that I have shown here is the better first cut.

For the floating point case it looks like this:
#define size appropriately
/* tol should be between 0 and 1 */
#define tol 0.001
int this_el, comp_el;
float score [size];
unsigned rank [size], ties [size];

for (this_el = 0; this_el < size; this_el ++)
{
rank [this_el] = 1;
ties [this_el] = 0;
}

for (this_el = 0; this_el < size; this_el ++)
{
for (comp_el = 0; comp_el < this_el; comp_el ++)
{
if (score [this_el] < (score [comp_el] / (1 + tol)))
rank [this_el] ++;
else if (score [this_el] < ((1 + tol) * score [comp_el]))
ties [this_el] ++;
}
for (comp_el = this_el + 1; comp_el < size; comp_el ++)
{
if (score [this_el] < (score [comp_el] / (1 + tol)))
rank [this_el] ++;
else if (score [this_el] < ((1 + tol) * score [comp_el]))
ties [this_el] ++;
}
}

Is there some trick to doing a lot better than this given the assumptions? The reason that sorting is undesirable is that I need to be able to presentranks for several different scores for the same contestant. If someone wants to make a credible argument that I can sort, compute ranks and ties and present the results more efficiently than just computing each as above, I am willing to listen.
 
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Ben Pfaff
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Posts: n/a
 
      08-17-2011
Michael Angelo Ravera <(E-Mail Removed)> writes:

> Is there some trick to doing a lot better than this given the
> assumptions? The reason that sorting is undesirable is that I
> need to be able to present ranks for several different scores
> for the same contestant. If someone wants to make a credible
> argument that I can sort, compute ranks and ties and present
> the results more efficiently than just computing each as above,
> I am willing to listen.


You are using nested loops to do ranking, with cost O(n**2).
A competently implemented sort-based rank would cost O(n lg n).
If n is small, your loops are probably just as fast, or at any
rate fast enough that the difference doesn't signify. But as
n grows, you should find that the sort-based solution passes
nested loops in performance.
--
char a[]="\n .CJacehknorstu";int putchar(int);int main(void){unsigned long b[]
={0x67dffdff,0x9aa9aa6a,0xa77ffda9,0x7da6aa6a,0xa6 7f6aaa,0xaa9aa9f6,0x11f6},*p
=b,i=24;for(;p+=!*p;*p/=4)switch(0[p]&3)case 0:{return 0;for(p--;i--;i--)case+
2:{i++;if(i)break;else default:continue;if(0)case 1utchar(a[i&15]);break;}}}
 
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Gene
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Posts: n/a
 
      08-17-2011
On Aug 17, 2:49*pm, Michael Angelo Ravera <(E-Mail Removed)>
wrote:
> I WILL be writing this myself (unless someone posts a solution that I particularly like), but does anyone have any tricks for efficient method of ranking the values in an unsorted array.
> The result that I would like to achieve is that we have an unsorted array"score" (for the first case we will assume that it is a 32-bit signed integer) of size "size" and two arrays of unsigned integers "rank" and "ties" large enough to hold a number at least as large as "size". Upon completion, I want each element of "rank" to be one larger than the number of items in score that are greater than the corresponding element of "score" and each element of "ties" to equal the number of other elements in "score" that are equal to the corresponding element in "score".
>
> For the second case, "fscore" is a floating point number of appropriate precision and "size" "rank" and "ties" are as before, but we have a multiplicative tollerance within which scores are to be considered as equal.
>
> What I have done in the past is to iniialize all of the elements of rank to 1 and all of the elements of ties to 0 and for each element of score adethe comparision and incremented rank and ties as necessary while skipping the current element.
>
> Something like this for the integer case.
>
> #define size appropriately
> int this_el, comp_el;
> INT32 score [size];
> unsigned rank [size], ties [size];
>
> for (this_el = 0; this_el < size; this_el ++)
> * {
> * rank [this_el] = 1;
> * ties [this_el] = 0;
> * }
>
> for (this_el = 0; this_el < size; this_el ++)
> * {
> * for (comp_el = 0; comp_el < this_el; comp_el ++)
> * * {
> * * if (score [this_el] < score [comp_el])
> * * * rank [this_el] ++;
> * * else if (score [this_el] == score [comp_el])
> * * * ties [this_el] ++;
> * * }
> * for (comp_el = this_el + 1; comp_el < size; comp_el ++)
> * * {
> * * if (score [this_el] < score [comp_el])
> * * * rank [this_el] ++;
> * * else if (score [this_el] == score [comp_el])
> * * * ties [this_el] ++;
> * * }
> * }
>
> Yeah, you can just have one internal loop and test for and skip over the (this_el == comp_el) but I think that the way that I have shown here isthe better first cut.
>
> For the floating point case it looks like this:
> #define size appropriately
> /* tol should be between 0 and 1 */
> #define tol 0.001
> int this_el, comp_el;
> float score [size];
> unsigned rank [size], ties [size];
>
> for (this_el = 0; this_el < size; this_el ++)
> * {
> * rank [this_el] = 1;
> * ties [this_el] = 0;
> * }
>
> for (this_el = 0; this_el < size; this_el ++)
> * {
> * for (comp_el = 0; comp_el < this_el; comp_el ++)
> * * {
> * * if (score [this_el] < (score [comp_el] / (1 + tol)))
> * * * rank [this_el] ++;
> * * else if (score [this_el] < ((1 + tol) * score [comp_el]))
> * * * ties [this_el] ++;
> * * }
> * for (comp_el = this_el + 1; comp_el < size; comp_el ++)
> * * {
> * * if (score [this_el] < (score [comp_el] / (1 + tol)))
> * * * rank [this_el] ++;
> * * else if (score [this_el] < ((1 + tol) * score [comp_el]))
> * * * ties [this_el] ++;
> * * }
> * }
>
> Is there some trick to doing a lot better than this given the assumptions? The reason that sorting is undesirable is that I need to be able to present ranks for several different scores for the same contestant. If someone wants to make a credible argument that I can sort, compute ranks and ties and present the results more efficiently than just computing each as above, Iam willing to listen.


First, prepare to be told this isn't a C question. Comp.programming
used to be great for this sort of thing, but lo it has fallen...

How about an indirect sort in a temporary array of indices, then
compute the ranks and ties in one pass and throw the array away? If
size is over a couple of hundred or so, there ought to be a
performance improvement. Of course this is relative. If you're doing
the computation once an hour, it won't make much difference perhaps
until roughly 10K to 100K.

A more interesting question is how to maintain a data structure "on
line" so that you can always get the rank and number of ties of any
team on the fly as scores change. One way is an order statistics
tree, which is at heart a specialized search tree (BST, B-Tree, etc.).
 
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Michael Angelo Ravera
Guest
Posts: n/a
 
      08-17-2011
On Wednesday, August 17, 2011 12:38:59 PM UTC-7, Gene wrote:
> On Aug 17, 2:49*pm, Michael Angelo Ravera <(E-Mail Removed)>
> wrote:
> > I WILL be writing this myself (unless someone posts a solution that I particularly like), but does anyone have any tricks for efficient method of ranking the values in an unsorted array.
> > The result that I would like to achieve is that we have an unsorted array "score" (for the first case we will assume that it is a 32-bit signed integer) of size "size" and two arrays of unsigned integers "rank" and "ties"large enough to hold a number at least as large as "size". Upon completion, I want each element of "rank" to be one larger than the number of items in score that are greater than the corresponding element of "score" and eachelement of "ties" to equal the number of other elements in "score" that are equal to the corresponding element in "score".
> >
> > For the second case, "fscore" is a floating point number of appropriateprecision and "size" "rank" and "ties" are as before, but we have a multiplicative tollerance within which scores are to be considered as equal.
> >
> > What I have done in the past is to iniialize all of the elements of rank to 1 and all of the elements of ties to 0 and for each element of score ade the comparision and incremented rank and ties as necessary while skipping the current element.
> >
> > Something like this for the integer case.
> >
> > #define size appropriately
> > int this_el, comp_el;
> > INT32 score [size];
> > unsigned rank [size], ties [size];
> >
> > for (this_el = 0; this_el < size; this_el ++)
> > * {
> > * rank [this_el] = 1;
> > * ties [this_el] = 0;
> > * }
> >
> > for (this_el = 0; this_el < size; this_el ++)
> > * {
> > * for (comp_el = 0; comp_el < this_el; comp_el ++)
> > * * {
> > * * if (score [this_el] < score [comp_el])
> > * * * rank [this_el] ++;
> > * * else if (score [this_el] == score [comp_el])
> > * * * ties [this_el] ++;
> > * * }
> > * for (comp_el = this_el + 1; comp_el < size; comp_el ++)
> > * * {
> > * * if (score [this_el] < score [comp_el])
> > * * * rank [this_el] ++;
> > * * else if (score [this_el] == score [comp_el])
> > * * * ties [this_el] ++;
> > * * }
> > * }
> >
> > Yeah, you can just have one internal loop and test for and skip over the (this_el == comp_el) but I think that the way that I have shown here is the better first cut.
> >
> > For the floating point case it looks like this:
> > #define size appropriately
> > /* tol should be between 0 and 1 */
> > #define tol 0.001
> > int this_el, comp_el;
> > float score [size];
> > unsigned rank [size], ties [size];
> >
> > for (this_el = 0; this_el < size; this_el ++)
> > * {
> > * rank [this_el] = 1;
> > * ties [this_el] = 0;
> > * }
> >
> > for (this_el = 0; this_el < size; this_el ++)
> > * {
> > * for (comp_el = 0; comp_el < this_el; comp_el ++)
> > * * {
> > * * if (score [this_el] < (score [comp_el] / (1 + tol)))
> > * * * rank [this_el] ++;
> > * * else if (score [this_el] < ((1 + tol) * score [comp_el]))
> > * * * ties [this_el] ++;
> > * * }
> > * for (comp_el = this_el + 1; comp_el < size; comp_el ++)
> > * * {
> > * * if (score [this_el] < (score [comp_el] / (1 + tol)))
> > * * * rank [this_el] ++;
> > * * else if (score [this_el] < ((1 + tol) * score [comp_el]))
> > * * * ties [this_el] ++;
> > * * }
> > * }
> >
> > Is there some trick to doing a lot better than this given the assumptions? The reason that sorting is undesirable is that I need to be able to present ranks for several different scores for the same contestant. If someonewants to make a credible argument that I can sort, compute ranks and ties and present the results more efficiently than just computing each as above,I am willing to listen.

>
> First, prepare to be told this isn't a C question. Comp.programming
> used to be great for this sort of thing, but lo it has fallen...


I agree. This is actually an algorithms question. However, I was looking for a C "trick". So, it is actually topical.

> How about an indirect sort in a temporary array of indices, then
> compute the ranks and ties in one pass and throw the array away? If
> size is over a couple of hundred or so, there ought to be a
> performance improvement. Of course this is relative. If you're doing
> the computation once an hour, it won't make much difference perhaps
> until roughly 10K to 100K.


Once sorted, the common case *looks* linear, but I think that the *worst* case is still O(N**2). Maybe you can compare forward testing for equality (or tollerance) and never do any retracing.

> A more interesting question is how to maintain a data structure "on
> line" so that you can always get the rank and number of ties of any
> team on the fly as scores change. One way is an order statistics
> tree, which is at heart a specialized search tree (BST, B-Tree, etc.).


I agree that the problem that you proposed is a more interesting case. In fact, in the online case, you might be interested in absolute tollerances aswell as multiplicative ones, as well as fuzzy ranking of contestants who scores can't be strictly compared at present because of competitions that are in progress while others are complete.
 
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Keith Thompson
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      08-17-2011
Michael Angelo Ravera <(E-Mail Removed)> writes:
> I WILL be writing this myself (unless someone posts a solution that I particularly like), but does anyone have any tricks for efficient method of ranking the values in an unsorted array.

[...]

Michael, it would be helpful if you'd format your text in lines no
longer than 72 columns (or 80 at the most). Thanks.

--
Keith Thompson (The_Other_Keith) http://www.velocityreviews.com/forums/(E-Mail Removed) <http://www.ghoti.net/~kst>
Nokia
"We must do something. This is something. Therefore, we must do this."
-- Antony Jay and Jonathan Lynn, "Yes Minister"
 
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Eric Sosman
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      08-18-2011
On 8/17/2011 4:21 PM, Michael Angelo Ravera wrote:
> On Wednesday, August 17, 2011 12:38:59 PM UTC-7, Gene wrote:
>> On Aug 17, 2:49 pm, Michael Angelo Ravera<(E-Mail Removed)>
>> wrote:
>>> ]...]

>> First, prepare to be told this isn't a C question. Comp.programming
>> used to be great for this sort of thing, but lo it has fallen...

>
> I agree. This is actually an algorithms question. However, I was looking for a C "trick". So, it is actually topical.


There are very few tricks to C. Lots of tricksters, but they're
just playing a shell game. There is less to it than meets the eye.

>> How about an indirect sort in a temporary array of indices, then
>> compute the ranks and ties in one pass and throw the array away? If
>> size is over a couple of hundred or so, there ought to be a
>> performance improvement. Of course this is relative. If you're doing
>> the computation once an hour, it won't make much difference perhaps
>> until roughly 10K to 100K.

>
> Once sorted, the common case *looks* linear, but I think that the *worst* case is still O(N**2). Maybe you can compare forward testing for equality (or tollerance) and never do any retracing.


Linear.

for (int bgn = 0, end; bgn < size; bgn = end) {
for (end = bgn; ++end < size; ) {
... suitable tests and `break' ...
}
}

Visits each array element once and once only, hence linear.

--
Eric Sosman
(E-Mail Removed)d
 
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Michael Angelo Ravera
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Posts: n/a
 
      08-18-2011
Until about a week ago, GoogleGroups did that for me. I guess the new version
stopped.
 
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Kenny McCormack
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      08-18-2011
In article <(E-Mail Removed)>,
Keith Thompson <(E-Mail Removed)> wrote:
>Michael Angelo Ravera <(E-Mail Removed)> writes:
>> Until about a week ago, GoogleGroups did that for me. I guess the new version
>> stopped.

>
>Google Groups also used to properly quote previous articles. I think
>you can get the correct behavior back by going back to the old
>interface.
>
>Or, better yet, get a real newsreader and sign up with a free NNTP
>server (I use eternal-september.org). Google Groups is useful for
>searching, and find for its own non-Usenet groups, but horrible for
>reading and posting to Usenet.


If it is (so) horrible, then why do so many people use it?

I.e., isn't it fair to say that your complaint is about as effective as
telling us that "Dancing With The Stars" is horrible? No one who likes DWTS
(or GG) is going to listen to your complaint.

--
Is God willing to prevent evil, but not able? Then he is not omnipotent.
Is he able, but not willing? Then he is malevolent.
Is he both able and willing? Then whence cometh evil?
Is he neither able nor willing? Then why call him God?
~ Epicurus

 
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John Gordon
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      08-18-2011
In <j2jrdq$ibr$(E-Mail Removed)> (E-Mail Removed) (Kenny McCormack) writes:

> >server (I use eternal-september.org). Google Groups is useful for
> >searching, and find for its own non-Usenet groups, but horrible for
> >reading and posting to Usenet.


> If it is (so) horrible, then why do so many people use it?


Perhaps because many people don't want to go to the effort of getting
and using a real newsreader, or are simply unaware that better options
exist.

Surely you do not mean to imply that popularity equals worth.

--
John Gordon A is for Amy, who fell down the stairs
(E-Mail Removed) B is for Basil, assaulted by bears
-- Edward Gorey, "The Gashlycrumb Tinies"

 
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Seebs
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Posts: n/a
 
      08-18-2011
On 2011-08-18, John Gordon <(E-Mail Removed)> wrote:
> In <j2jrdq$ibr$(E-Mail Removed)> (E-Mail Removed) (Kenny McCormack) writes:
>> If it is (so) horrible, then why do so many people use it?


> Perhaps because many people don't want to go to the effort of getting
> and using a real newsreader, or are simply unaware that better options
> exist.


> Surely you do not mean to imply that popularity equals worth.


I think he rather does, given that he's said so in the past in so many
words. He does not believe there is value other than status; popularity
is a kind of status.

-s
--
Copyright 2011, all wrongs reversed. Peter Seebach / (E-Mail Removed)
http://www.seebs.net/log/ <-- lawsuits, religion, and funny pictures
http://en.wikipedia.org/wiki/Fair_Game_(Scientology) <-- get educated!
I am not speaking for my employer, although they do rent some of my opinions.
 
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