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Puzzle n°10 - All possible solution for Fibonacci Series * [message #354373] Sat, 18 October 2008 04:03 Go to next message
rajavu1
Messages: 1574
Registered: May 2005
Location: Bangalore , India
Senior Member

Let me invite all the possible solution for generating Fibonacci Series in SQL or PL/SQL.

Quote:
In mathematics, the Fibonacci numbers are a sequence of numbers named after Leonardo of Pisa, known as Fibonacci.The first number of the sequence is 0, the second number is 1, and each subsequent number is equal to the sum of the previous two numbers of the sequence itself, yielding the sequence 0, 1, 1, 2, 3, 5, 8, etc.


The output should be as follows .

Code:
             0
             1
             1
             2
             3
             5
             8
            13
            21
            34
            55
            89


Thumbs Up
Rajuvan.

[Updated on: Sun, 19 October 2008 08:00]

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Re: Puzzle n°10 - All possible solution for Fibonacci Series [message #354407 is a reply to message #354373] Sat, 18 October 2008 09:17 Go to previous messageGo to next message
Michel Cadot
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Here are 2 solutions (I choosed the easiest way Wink ):
SQL> DEFINE N=12
SQL> SELECT ' F('||num||') = '||fibo "Fibonacci" 
  2  FROM ( SELECT 1 rn FROM DUAL )
  3  MODEL
  4    DIMENSION BY (rn)
  5    MEASURES (0 num, 1 fibo)
  6    RULES
  7      ITERATE (&N)
  8      ( num[ITERATION_NUMBER] = ITERATION_NUMBER,
  9        fibo[ITERATION_NUMBER] = 
 10          CASE 
 11          WHEN ITERATION_NUMBER IN (0,1) THEN ITERATION_NUMBER
 12          ELSE fibo[CV()-1] + fibo[CV()-2] 
 13          END
 14      )
 15  ORDER BY num
 16  /
Fibonacci
------------------------------------------------------------------
 F(0) = 0
 F(1) = 1
 F(2) = 1
 F(3) = 2
 F(4) = 3
 F(5) = 5
 F(6) = 8
 F(7) = 13
 F(8) = 21
 F(9) = 34
 F(10) = 55
 F(11) = 89

12 rows selected.

SQL> SELECT ' F('||rn||') = '||fibo "Fibonacci" 
  2  FROM ( SELECT rownum-1 rn FROM DUAL CONNECT BY LEVEL <= &N )
  3  MODEL
  4    DIMENSION BY (rn)
  5    MEASURES (1 fibo)
  6    RULES 
  7      ( fibo[ANY] = 
  8          CASE 
  9          WHEN CV(rn) IN (0,1) THEN CV(rn)
 10          ELSE fibo[CV()-1] + fibo[CV()-2] 
 11          END 
 12      )
 13  ORDER BY rn
 14  /
Fibonacci
------------------------------------------------------------------
 F(0) = 0
 F(1) = 1
 F(2) = 1
 F(3) = 2
 F(4) = 3
 F(5) = 5
 F(6) = 8
 F(7) = 13
 F(8) = 21
 F(9) = 34
 F(10) = 55
 F(11) = 89

12 rows selected.

Regards
Michel

[Updated on: Sun, 19 October 2008 00:23]

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Re: Puzzle n°10 - All possible solution for Fibonacci Series [message #354421 is a reply to message #354373] Sat, 18 October 2008 14:59 Go to previous messageGo to next message
ebrian
Messages: 2794
Registered: April 2006
Senior Member
SQL> select level - 1 "LEVEL"
  2     , (1 / sqrt(5)) *
  3     (power(((1 + sqrt(5))/2), level - 1) - power(((1 - sqrt(5))/2), level - 1)) fibonacci
  4  from dual
  5  connect by level < 13;

     LEVEL  FIBONACCI
---------- ----------
         0          0
         1          1
         2          1
         3          2
         4          3
         5          5
         6          8
         7         13
         8         21
         9         34
        10         55
        11         89

12 rows selected.

[Updated on: Sat, 18 October 2008 15:04]

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Re: Puzzle n°10 - All possible solution for Fibonacci Series [message #354441 is a reply to message #354421] Sun, 19 October 2008 00:27 Go to previous messageGo to next message
Michel Cadot
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Binet's formula. Neat. Wink

Regards
Michel

[Updated on: Sun, 19 October 2008 00:30]

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Re: Puzzle n°10 - All possible solution for Fibonacci Series [message #354463 is a reply to message #354373] Sun, 19 October 2008 07:59 Go to previous messageGo to next message
rajavu1
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Registered: May 2005
Location: Bangalore , India
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Good ..

Anyway my favorite method is Table function . PL/SQL way of doing it.

SQL> CREATE OR REPLACE TYPE FIBONACCI as table OF NUMBER(10);
  2  /

Type created.

SQL> CREATE OR REPLACE FUNCTION gen_fibonacci (series_length IN NUMBER)
  2  RETURN FIBONACCI PIPELINED
  3  AS
  4  n0 NUMBER :=0;
  5  n1 NUMBER :=1;
  6  n2 NUMBER :=0;
  7  BEGIN
  8      PIPE ROW(n0);
  9      PIPE ROW(n1);
 10    FOR i IN n0..series_length-3
 11    LOOP
 12      n2 := n0 + n1 ;
 13      PIPE ROW(n2);
 14      n0 := n1;
 15      n1 := n2;
 16    END LOOP;
 17    RETURN;
 18  END gen_fibonacci;
 19  /

Function created.

SQL> select COLUMN_VALUE FIBONACCI
  2  from TABLE(gen_fibonacci(10));

 FIBONACCI
----------
         0
         1
         1
         2
         3
         5
         8
        13
        21
        34

10 rows selected.

SQL>


Thumbs Up
Rajuvan.
Re: Puzzle n°10 - All possible solution for Fibonacci Series [message #354477 is a reply to message #354441] Sun, 19 October 2008 10:39 Go to previous messageGo to next message
ebrian
Messages: 2794
Registered: April 2006
Senior Member
Michel Cadot wrote on Sun, 19 October 2008 01:27
Binet's formula. Neat. Wink

Yeah, but the MODEL looks cooler !!

Rajuvan...nice use of PIPELINED.
Re: Puzzle n°10 - All possible solution for Fibonacci Series * [message #539497 is a reply to message #354373] Mon, 16 January 2012 10:11 Go to previous messageGo to next message
Barbara Boehmer
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Registered: November 2002
Location: California, USA
Senior Member
rajavu1 wrote on Sat, 18 October 2008 02:03


Let me invite all the possible solution for generating Fibonacci Series in SQL or PL/SQL.


Here is an 11g recursive sub-query factoring method that was not available yet when this thread was started.

SCOTT@orcl_11gR2> with
  2    numbers (lvl, fibonacci, next) as
  3  	 (select 0, 0, 1
  4  	  from	 dual
  5  	  union  all
  6  	  select lvl + 1, next, fibonacci + next
  7  	  from	 numbers
  8  	  where  lvl <= 10)
  9  select lvl "LEVEL", fibonacci
 10  from   numbers
 11  order  by lvl
 12  /

     LEVEL  FIBONACCI
---------- ----------
         0          0
         1          1
         2          1
         3          2
         4          3
         5          5
         6          8
         7         13
         8         21
         9         34
        10         55
        11         89

12 rows selected.

Re: Puzzle n°10 - All possible solution for Fibonacci Series * [message #539512 is a reply to message #539497] Mon, 16 January 2012 11:20 Go to previous message
Michel Cadot
Messages: 57613
Registered: March 2007
Location: Nanterre, France, http://...
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Account Moderator
Yeap! When I saw you answered on this topic I knew you had added this solution before reading it. Wink

Regards
Michel

[Updated on: Mon, 16 January 2012 11:20]

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