Home » Other » General » Puzzle n°09 - Finding a query for sine function distribution **
Puzzle n°09 - Finding a query for sine function distribution ** [message #186198] Sun, 06 August 2006 23:35 Go to next message
zozogirl
Messages: 77
Registered: November 2005
Location: Seoul, Korea
Member

Let me tell you something about distribution function.
Here, i use the term, 'distribution function' differently from what we use in general mathematics.

See the following query which generates self-counting sequence.

SELECT     TRUNC (1 / 2 + SQRT (2 * LEVEL)) level#
      FROM DUAL
CONNECT BY LEVEL <= 1000



LEVEL#
------
1
2
2
3
3
3
4
4
4
4
5
5
5
5
5
...
...
...


and, if we add some group by and counting to the above query...

SELECT   level#
       , LPAD ('*', COUNT (*), '*')
    FROM (SELECT     TRUNC (1 / 2 + SQRT (2 * LEVEL)) level#
                FROM DUAL
          CONNECT BY LEVEL <= 1000)
GROUP BY level#


we can see a graph like below

LEVEL# LPAD('*',COUNT(*),'*')
------ ----------------------
1      *
2      **
3      ***
4      ****
5      *****
6      ******
7      *******
8      ********
9      *********
10     **********
11     ***********
12     ************
13     *************
14     **************
15     ***************
16     ****************
17     *****************
18     ******************
19     *******************
20     ********************
...
...
...


As we all know, this is like a function f(x) = x.

i use the term, 'distribution function' as this meaning!
Distribution of numbers of data values.




Now, my question is this.
Find a query that generates distribution function f(x) = sin(x)
(Here, any amplitude and any period of sine function is allowed except zero.
And only the form of sine function is important.
No subquery factoring or user-defined function or procedure is allowed.
Use simple select statement only.)

And now, have a good challenge!



SELECT   level#
       , LPAD ('*', COUNT (*), '*')
    FROM (
   -------- some query -------------------
       )
GROUP BY level#


LEVEL# LPAD('*',COUNT(*),'*')
------ ----------------------------------------------------
0      *
1      **
2      *******
3      *************
4      *****************
5      **********************
6      **************************
7      ******************************
8      **********************************
9      **************************************
10     ****************************************
11     ********************************************
12     *********************************************
13     ************************************************
14     *************************************************
15     *************************************************
16     **************************************************
17     **************************************************
18     *************************************************
19     ************************************************
20     ***********************************************
21     ********************************************
22     ******************************************
23     ***************************************
24     ***********************************
25     ********************************
26     ****************************
27     ************************
28     *******************
29     **************
30     *********
31     *****



Query Your Dream & Future at
http://www.soqool.com

[Updated on: Thu, 14 February 2008 03:26] by Moderator

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Re: query quiz> find a query for sine function distribution [message #223740 is a reply to message #186198] Sat, 10 March 2007 19:32 Go to previous messageGo to next message
zozogirl
Messages: 77
Registered: November 2005
Location: Seoul, Korea
Member

Is my quiz mathematically incorrect?
Or is it weird?
Or is my english not goot?
Re: query quiz> find a query for sine function distribution [message #223747 is a reply to message #223740] Sat, 10 March 2007 21:26 Go to previous messageGo to next message
rleishman
Messages: 3724
Registered: October 2005
Location: Melbourne, Australia
Senior Member
No, its just that the interest level is not there for such a difficult question.

I had a go at this when you posted it, but I ended up with what looked like a Tan distribution.

Your level of mathematics education (or least your ability) is probably a lot greater than most programmers. Since I.T. is a dedicated degree these days, most programmers have not done any mathematics since high school.

Personally, I did two years of mathematics and statistics at university, but that was 20 years ago. I suspect that the problem requires integral calculus plus some other discipline. After doing my best and coming up with something counter to my expectations, I realised very quickly that I did not know enough, and without further research I was wasting my time.

It was an interesting question though.

Ross Leishman
Re: Puzzle n°09 - Finding a query for sine function distribution * [message #300056 is a reply to message #186198] Thu, 14 February 2008 02:12 Go to previous messageGo to next message
rajavu1
Messages: 1574
Registered: May 2005
Location: Bangalore , India
Senior Member

One more interesting puzzle.

Enjoy.

Thumbs Up
Rajuvan.

[Updated on: Thu, 14 February 2008 02:42] by Moderator

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Re: Puzzle n°09 - Finding a query for sine function distribution * [message #300065 is a reply to message #300056] Thu, 14 February 2008 02:42 Go to previous messageGo to next message
Michel Cadot
Messages: 64151
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Location: Nanterre, France, http://...
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Account Moderator
It's just a row generator and applying the function you want.
SQL> col val format a80
SQL> col line format 990
SQL> with lines as (select level-1 line from dual connect by level <= 100)
  2  select line, rpad('*',40*(1+sin(5*line*3.14159265359/180)),'*') val
  3  from lines
  4  order by line
  5  /
LINE VAL
---- --------------------------------------------------------------------------------
   0 ****************************************
   1 *******************************************
   2 **********************************************
   3 **************************************************
   4 *****************************************************
   5 ********************************************************
   6 ************************************************************
   7 **************************************************************
   8 *****************************************************************
   9 ********************************************************************
  10 **********************************************************************
  11 ************************************************************************
  12 **************************************************************************
  13 ****************************************************************************
  14 *****************************************************************************
  15 ******************************************************************************
  16 *******************************************************************************
  17 *******************************************************************************
  18 *******************************************************************************
  19 *******************************************************************************
  20 *******************************************************************************
  21 ******************************************************************************
  22 *****************************************************************************
  23 ****************************************************************************
  24 **************************************************************************
  25 ************************************************************************
  26 **********************************************************************
  27 ********************************************************************
  28 *****************************************************************
  29 **************************************************************
  30 ***********************************************************
  31 ********************************************************
  32 *****************************************************
  33 **************************************************
  34 **********************************************
  35 *******************************************
  36 ***************************************
  37 ************************************
  38 *********************************
  39 *****************************
  40 **************************
  41 ***********************
  42 *******************
  43 *****************
  44 **************
  45 ***********
  46 *********
  47 *******
  48 *****
  49 ***
  50 **
  51 *
  52
  53
  54
  55
  56
  57 *
  58 **
  59 ***
  60 *****
  61 *******
  62 *********
  63 ***********
  64 **************
  65 *****************
  66 ********************
  67 ***********************
  68 **************************
  69 *****************************
  70 *********************************
  71 ************************************
  72 ****************************************
  73 *******************************************
  74 **********************************************
  75 **************************************************
  76 *****************************************************
  77 ********************************************************
  78 ************************************************************
  79 **************************************************************
  80 *****************************************************************
  81 ********************************************************************
  82 **********************************************************************
  83 ************************************************************************
  84 **************************************************************************
  85 ****************************************************************************
  86 *****************************************************************************
  87 ******************************************************************************
  88 *******************************************************************************
  89 *******************************************************************************
  90 *******************************************************************************
  91 *******************************************************************************
  92 *******************************************************************************
  93 ******************************************************************************
  94 *****************************************************************************
  95 ****************************************************************************
  96 **************************************************************************
  97 ************************************************************************
  98 **********************************************************************
  99 ********************************************************************

100 rows selected.

Regards
Michel

Re: Puzzle n°09 - Finding a query for sine function distribution * [message #300069 is a reply to message #300065] Thu, 14 February 2008 02:57 Go to previous messageGo to next message
zozogirl
Messages: 77
Registered: November 2005
Location: Seoul, Korea
Member

sorry for my bad explanation.
but i don't want just a sine function.
i want a 'distribution function' of column values.
thanks.

Re: Puzzle n°09 - Finding a query for sine function distribution * [message #300076 is a reply to message #300069] Thu, 14 February 2008 03:19 Go to previous messageGo to next message
Frank
Messages: 7880
Registered: March 2000
Senior Member
Nice solution (once again!)
by the way: pi is 2 * acos(0)
Re: Puzzle n°09 - Finding a query for sine function distribution * [message #300077 is a reply to message #300076] Thu, 14 February 2008 03:21 Go to previous messageGo to next message
zozogirl
Messages: 77
Registered: November 2005
Location: Seoul, Korea
Member

Frank, this is not what i want.

Re: Puzzle n°09 - Finding a query for sine function distribution * [message #300079 is a reply to message #186198] Thu, 14 February 2008 03:25 Go to previous messageGo to next message
rajavu1
Messages: 1574
Registered: May 2005
Location: Bangalore , India
Senior Member

Ie, OP wants Something like Wrapper Function with some input , and display like Full single curve structure.

ie, If input is 50 . OP wants the Full curve structure with 50 lines. and so on ..

So Let me update the star level Smile

Thumbs Up
Rajuvan

[Updated on: Thu, 14 February 2008 03:32]

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Re: Puzzle n°09 - Finding a query for sine function distribution * [message #300082 is a reply to message #300069] Thu, 14 February 2008 03:29 Go to previous messageGo to next message
Michel Cadot
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I don't understand what you want.
Could you post a full test case.

Regards
Michel
Re: Puzzle n°09 - Finding a query for sine function distribution * [message #300105 is a reply to message #300082] Thu, 14 February 2008 04:30 Go to previous messageGo to next message
zozogirl
Messages: 77
Registered: November 2005
Location: Seoul, Korea
Member

for example,
if a test table 'T' with a column name 'COL' has data like this:


col
---
1
2
2
3
3
3
4
4
4
4
...
...
...


and you make a query like this:


select col, LPAD ('*', COUNT (*), '*') a
from t
group by col
order by col



then, you can make a distribution f(x)=x


       COL A                                                 
---------- -------------------
         1 *                                                 
         2 **                                                
         3 ***                                               
         4 ****  



so, likewise if you make some select statement in from clause below,
you can make a 'sine function distribution' of 'column data' with a half period in my first post.


select col, LPAD ('*', COUNT (*), '*') a
from  ( ... some select statement ... )
group by col
order by col





if you make some select statement, you can see a sine function distribution with a half period,




SELECT   level#
       , LPAD ('*', COUNT (*), '*')
    FROM ( ... some select statement ... )
GROUP BY level#



LEVEL# LPAD('*',COUNT(*),'*')
------ ----------------------------------------------------
0      *
1      **
2      *******
3      *************
4      *****************
5      **********************
6      **************************
7      ******************************
8      **********************************
9      **************************************
10     ****************************************
11     ********************************************
12     *********************************************
13     ************************************************
14     *************************************************
15     *************************************************
16     **************************************************
17     **************************************************
18     *************************************************
19     ************************************************
20     ***********************************************
21     ********************************************
22     ******************************************
23     ***************************************
24     ***********************************
25     ********************************
26     ****************************
27     ************************
28     *******************
29     **************
30     *********
31     *****




or if you make some select statement, you can see a tangent function distribution with a 1/4 period



0  *
2  *
3  *
4  **
5  ***
6  ***
7  ***
8  *****
9  *****
10 ******
11 ******
12 *******
13 ********
14 **********
15 **********
16 ***********
17 ************
18 **************
19 ****************
20 *****************
21 ********************
22 **********************
23 **************************
24 ******************************
25 *************************************
26 *********************************************
27 ************************************************************
28 **************************************************************************************




can you find that query above?
i hope you understand me exactly.
thanks.


[Updated on: Thu, 14 February 2008 05:40] by Moderator

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Re: Puzzle n°09 - Finding a query for sine function distribution * [message #300108 is a reply to message #300105] Thu, 14 February 2008 04:44 Go to previous messageGo to next message
Michel Cadot
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Location: Nanterre, France, http://...
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Sorry, but I still don't understand.
I don't understand what you have and what you want.
Assume you work with scott.emp table and sal column, what do you want from it?

Regards
Michel
Re: Puzzle n°09 - Finding a query for sine function distribution * [message #300112 is a reply to message #300108] Thu, 14 February 2008 04:54 Go to previous messageGo to next message
zozogirl
Messages: 77
Registered: November 2005
Location: Seoul, Korea
Member

if you have a query like this:


SELECT  TRUNC (1 / 2 + SQRT (2 * LEVEL)) col
FROM    DUAL
CONNECT BY LEVEL <= 1000



data of column 'col' have a 'sine function distribution'.
you can under stand me?

[Updated on: Thu, 14 February 2008 05:41] by Moderator

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Re: Puzzle n°09 - Finding a query for sine function distribution ** [message #300129 is a reply to message #186198] Thu, 14 February 2008 05:37 Go to previous messageGo to next message
rajavu1
Messages: 1574
Registered: May 2005
Location: Bangalore , India
Senior Member

Hi Micheal,

Posting looks difficult to understand .

What I understood as per zozo's description is

1. She wants the output from One Outer and Inner query .

2. Inner query should be different for Sine distribution for 1/2 period and Tan distribution of 1/4 period .

3. Outer query (used to display Graphic distribution) should be same

4. Sine function distribution with a half period is

0 *
1 **
2 *******
3 *************
4 *****************
5 **********************
6 **************************
7 ******************************
8 **********************************
9 **************************************
10 ****************************************
11 ********************************************
12 *********************************************
13 ************************************************
14 *************************************************
15 *************************************************
16 **************************************************
17 **************************************************
18 *************************************************
19 ************************************************
20 ***********************************************
21 ********************************************
22 ******************************************
23 ***************************************
24 ***********************************
25 ********************************
26 ****************************
27 ************************
28 *******************
29 **************
30 *********
31 *****


5. Tan function distribution with a 1/4 period is

0 *
2 *
3 *
4 **
5 ***
6 ***
7 ***
8 *****
9 *****
10 ******
11 ******
12 *******
13 ********
14 **********
15 **********
16 ***********
17 ************
18 **************
19 ****************
20 *****************
21 ********************
22 **********************
23 **************************
24 ******************************
25 *************************************
26 *********************************************
27 ************************************************************
28 **************************************************************************************



6. Inner select query should be from some Row generator . it is nothing to do with Scott.Emp.

Thumbs Up
Rajuvan.
Re: Puzzle n°09 - Finding a query for sine function distribution ** [message #300131 is a reply to message #300129] Thu, 14 February 2008 05:41 Go to previous messageGo to next message
zozogirl
Messages: 77
Registered: November 2005
Location: Seoul, Korea
Member

yes, what rajavu1 says is exactly what i want!
thank you again, rajavu1

Re: Puzzle n°09 - Finding a query for sine function distribution ** [message #300137 is a reply to message #300131] Thu, 14 February 2008 06:11 Go to previous messageGo to next message
Michel Cadot
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I hope you will find the solution as I still don't understand.
For a SQL query has:
- one or more row source
- an output

I understand neither the first part nor the last one in your post.
But don't care, it is not mandatory I understand, better spend your time to find the solution.

Regards
Michel
Re: Puzzle n°09 - Finding a query for sine function distribution ** [message #300163 is a reply to message #300137] Thu, 14 February 2008 08:11 Go to previous messageGo to next message
zozogirl
Messages: 77
Registered: November 2005
Location: Seoul, Korea
Member

- one or more row source
this row source(row generator) itself is what we should find.
ex. (select ... from dual connect by level ...)

- an output
and this row source(row generator) has sine function distribution.




if you find a row source(row generator) like below,


SELECT TRUNC (1 / 2 + SQRT (2 * LEVEL)) col
FROM DUAL
CONNECT BY LEVEL <= 1000 -- 1000 or whatever number


this row source(row generator) has f(x)=x function distribution.




if you find a row source(row generator) of some kind,


SELECT ...
FROM DUAL
CONNECT BY LEVEL <= 100 -- 100 or whatever number


this row source(row generator) maybe has f(x)=sin(x) function distribution.




so, we should just find that kind of row source(row generator).
this is all.

Re: Puzzle n°09 - Finding a query for sine function distribution ** [message #300177 is a reply to message #300163] Thu, 14 February 2008 08:52 Go to previous messageGo to next message
Michel Cadot
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If the question is:
- row source whatever you want
- output sin "distribution"

Then my query generates that, doesn't it?

Ah! but it must generates that without SIN function, is this the question?

Regards
Michel
Re: Puzzle n°09 - Finding a query for sine function distribution ** [message #300191 is a reply to message #300177] Thu, 14 February 2008 09:27 Go to previous messageGo to next message
zozogirl
Messages: 77
Registered: November 2005
Location: Seoul, Korea
Member

if you find a row source like below,



SELECT TRUNC (1 / 2 + SQRT (2 * LEVEL)) col
FROM DUAL
CONNECT BY LEVEL <= 100


it generates:


col
---
1
2
2
3
3
3
4
4
4
4
5
5
5
5
5
...
...
...


ie,
1 record with col=1
2 records with col=2
3 records with col=3
4 records with col=4
5 records with col=5
...
...
...


this show a distribution,

col (count of records with asterisks)
--- ---------------------------------
1 *
2 **
3 ***
4 ****
5 *****
6 ******
...
...
...

and THIS MEANS the above row source(row generator) has f(x)=x DISTRIBUTION.




if you find some sort of row source(row generator),
it will generates,


col
---
0
1
1
2
2
2
2
2
2
2
...
...
...


this will show a distribution,

col (count of records with asterisks)
--- ---------------------------------
0 *
1 **
2 *******
3 *************
4 *****************
5 **********************
6 **************************
...
...
...
...


this will have a SIN DISTRIBUTION.


to make a matters more simple,
we can find a combination of built-in functions
(incluing sin function or not is not so important)
in below query.


select /* ..a combination of built-in functions here.. */
from dual
connect by level<=1000 -- 1000 or whatever number


and the above query has a SIN DISTRIBUTION.

Re: Puzzle n°09 - Finding a query for sine function distribution ** [message #300205 is a reply to message #300191] Thu, 14 February 2008 10:41 Go to previous messageGo to next message
Michel Cadot
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But is this not what my query gives?

Regards
Michel
Re: Puzzle n°09 - Finding a query for sine function distribution ** [message #300208 is a reply to message #300205] Thu, 14 February 2008 10:47 Go to previous messageGo to next message
Michel Cadot
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Ah OK! I understand (finally) but what is the meaning of a sin distribution?
The number of rows having value x is sin(x).
But sin(x) is between -1 and 1.

Regards
Michel

Re: Puzzle n°09 - Finding a query for sine function distribution ** [message #300629 is a reply to message #300208] Sat, 16 February 2008 22:36 Go to previous messageGo to next message
zozogirl
Messages: 77
Registered: November 2005
Location: Seoul, Korea
Member

if you can clearly show the characteristics of sine distribution,
any amplitude will be ok.
but it can only have 1/2 period.



the following is ok:

    0 *                                                                                         
    1 **                                                                                        
    2 *******                                                                                   
    3 *************                                                                             
    4 *****************                                                                         
    5 **********************                                                                    
    6 **************************                                                                
    7 ******************************                                                            
    8 **********************************                                                        
    9 **************************************                                                    
   10 ****************************************                                                  
   11 ********************************************                                              
   12 *********************************************                                             
   13 ************************************************                                          
   14 *************************************************                                         
   15 *************************************************                                         
   16 **************************************************                                        
   17 **************************************************                                        
   18 *************************************************                                         
   19 ************************************************                                          
   20 ***********************************************                                           
   21 ********************************************                                              
   22 ******************************************                                                
   23 ***************************************                                                   
   24 ***********************************                                                       
   25 ********************************                                                          
   26 ****************************                                                              
   27 ************************                                                                  
   28 *******************                                                                       
   29 **************                                                                            
   30 *********                                                                                 
   31 *****   



and the following is also ok!

    0 *                                                                                         
    1 ***                                                                                       
    2 *********                                                                                 
    3 **************                                                                            
    4 *******************                                                                       
    5 ***********************                                                                   
    6 ************************                                                                  
    7 *************************                                                                 
    8 ************************                                                                  
    9 *********************                                                                     
   10 ******************                                                                        
   11 ************                                                                              
   12 ******                                                                                    
   13 *  
Re: Puzzle n°09 - Finding a query for sine function distribution ** [message #302098 is a reply to message #300629] Sat, 23 February 2008 08:05 Go to previous messageGo to next message
zozogirl
Messages: 77
Registered: November 2005
Location: Seoul, Korea
Member

can anybody understand and solve this quiz?

Re: Puzzle n°09 - Finding a query for sine function distribution ** [message #302102 is a reply to message #302098] Sat, 23 February 2008 09:33 Go to previous message
Michel Cadot
Messages: 64151
Registered: March 2007
Location: Nanterre, France, http://...
Senior Member
Account Moderator
After several days I understood the problem. Embarassed
But it is more a mathematical/arithmetical problem than a SQL one.
If you are seriously seeking for an answer, you should better post it in a mathematic forum.
Currently I have no time to search on this but I keep it in mind.
If you explain how you came from f(x)=x to v=trunc(1/2+sqrt(2*level)) in your example, maybe this will help us to find a solution for f(x)=K*sin(x).

Regards
Michel
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