Want to protect your cyber security and still get fast solutions? Ask a secure question today.Go Premium

x
  • Status: Solved
  • Priority: Medium
  • Security: Public
  • Views: 544
  • Last Modified:

Fibonacci Numbers With a SQL query

Is it possible to generate a fibonacci sequence with a single SQL query?
0
dignified
Asked:
dignified
  • 2
  • 2
  • 2
  • +2
1 Solution
 
jdlambert1Commented:
Yes, in any database that supports Stored Procedures or User-Defined Functions.

Which database are you using, and do you need one number per row, or in a comma delimited list?
0
 
AaronAbendCommented:
This works in SQL Server.  


drop table a
create table a(a int, b int)
insert a values (1, 1)
insert a values (2, 1)
-- repeat this next statement as many times as you want...
insert a select max(a)+1, sum(b) from a where a>(select max(a) from a)-2  
-- get your results with this statement
select * from a

A few syntax changes might be needed for oracle ("insert into a" instead of "insert a" - I do not have Oracle on my machine so I cannot test it right now)
0
 
Gustav BrockCIOCommented:
I guess it would be fastest to generate a fixed lookup table from an external function:

I brushed up some VB(A) code in the archive. It don't use recursion as often seen (which is _extremely_ slow for anything more than a handful of elements); instead it fills a simple array (very fast):

Public Function FibonacciElementDec( _
  ByVal lngElements As Long) _
  As Variant

' Returns the value of element lngElements in the
' Fibonacci sequence of numbers.
' Max. number returned:
'   50095301248058391139327916261
'
' 2004-10-03. Gustav Brock, Cactus Data, CPH.

  Const clngIndexMin  As Long = 0
  Const clngIndexMax  As Long = 139
 
  Dim decValue        As Variant
 
  If lngElements < clngIndexMin Or lngElements > clngIndexMax Then
    ' Not a valid input. Return error.
    decValue = CDec(-1)
  Else
    ' Return last number in sequence in array.
    decValue = FibonacciSequenceDec(lngElements)(lngElements)
  End If
 
  FibonacciElementDec = decValue

End Function

Public Function FibonacciSequenceDec( _
  ByVal lngElements As Long) _
  As Variant()

' Build and return array with Fibonacci sequence of numbers.
' Count of elements is determined by lngElements.
' Max. number returned in array:
'   50095301248058391139327916261
'
' 2004-10-03. Gustav Brock, Cactus Data, CPH.

  ' Min. index of sequence per definition.
  Const clngIndexMin  As Long = 0
  ' Max. possible index of sequence for datatype Decimal.
  Const clngIndexMax  As Long = 139
 
  Dim adecSeq()       As Variant
  Dim lngIndex        As Long
 
  If lngElements < clngIndexMin Or lngElements > clngIndexMax Then
    ' Not a valid input.
  Else
    ' Build and fill array with the Fibonacci sequence of numbers.
    ReDim adecSeq(clngIndexMin To lngElements)
    For lngIndex = clngIndexMin To lngElements
      If lngIndex < 2 Then
        ' Values of the first two elements are 0 and 1 per definition.
        adecSeq(lngIndex) = CDec(lngIndex)
      Else
        ' Value is the sum of the two preceding numbers.
        adecSeq(lngIndex) = CDec(adecSeq(lngIndex - 2)) + CDec(adecSeq(lngIndex - 1))
      End If
''      Debug.Print adecSeq(lngIndex);
    Next
  End If
 
  FibonacciSequenceDec = adecSeq()

End Function

You can create a simple loop - using either the array from the last function or just repetitive calls of the first function, speed is so fast that you hardly can tell the difference - to insert the index and the value in two fields of the table.
Note that the first element (index zero) is zero.

If you need more than 139 elements I have the equivalent functions for datatype Double but note that you will loose absolute accuracy for element index 76 and beyond.

/gustav
0
Concerto Cloud for Software Providers & ISVs

Can Concerto Cloud Services help you focus on evolving your application offerings, while delivering the best cloud experience to your customers? From DevOps to revenue models and customer support, the answer is yes!

Learn how Concerto can help you.

 
AaronAbendCommented:
I reread the question - to be accurate - as far as I know, unless you use a SQL Programming language like TSQL or PL/SQL, it is not possible to create a query that recurses and generates rows without some underlying data. As a result, it is technically impossible to generate the sequence with a SINGLE SQL (pure) statement without using some kind of driver table (a table that has enough rows to drive the creation of new records).  Of couse any table with a couple of hundred or so rows will do for this - including data dictionary tables like sysobjects.  Once you get into the programming languages, you could program it as easily as you would with VB, just using variables (why bother with a table if you are going to generate a few hundred rows based on a simple algorithm?)

A nice weekend challenge though...

0
 
Ken SelviaRetiredCommented:
Binets formula. http://mathworld.wolfram.com/BinetsFibonacciNumberFormula.html

A single statement using a derived table - but it's limited to the first 72 digits before rounding errors cause errors.

select cast (
            floor((power((cast(1 as decimal(30,0))+sqrt(cast(5 as decimal(30,0)))),id)-
         power((cast(1 as decimal(30,0))-sqrt(cast(5 as decimal(30,0)))),id))/
         (power(cast(2 as decimal(30,0)),id)*sqrt(cast(5 as decimal(30,0)))))
                  as decimal(30,0)) fn
FROM
(
 select top 72 cast((a0.id + a1.id) as decimal(30,0)) id FROM
(select 0 id union select 1 union select 2 union select 3 union select 4 union
 select 5 union select 6 union select 7 union select 8 union select 9) a0,  
(select 0 id union select 10 union select 20 union select 30 union select 40 union
 select 50 union select 60 union select 70 union select 80 union  select 90) a1
) Numbers
0
 
dignifiedAuthor Commented:
Wow, that's very cool. I don't mind using derived tables. I'm already using one. Actually, I just used the term fibonacci numbers because everyone knows what it is. My aplication doesn't actually use fibonacci numbers, but the idea is almost identical. Basically I have a stack and I want add the numbers up so that it follows a similar fibonacci recurrance relation. So the ith index in the stack equals the sum of the digits from zeroth to (i-1)th indices.
0
 
Ken SelviaRetiredCommented:
In that case it's probably better just to create a permanent table of integers to join against for you nth index lookups

Select top 1000000 id = identity(int,1,1) Into Numbers from sysobjects s1, sysobjects s1, sysobjects s1, sysobjects s1

In general, an actual table as opposed to a derived table will perform better once you get above a few thousand rows because statistics are kept for a real table and derived tables will be converted to unindexed work tables at some point.

What exactly is your algorithm? We may be able to optimize it.
0
 
dignifiedAuthor Commented:
This goes beyond the scope of the question. If you'd like to email me, drop me a line at rcdetert at nospam ucdavis edu and I'll tell you exactly what I'm doing.
0

Featured Post

Concerto's Cloud Advisory Services

Want to avoid the missteps to gaining all the benefits of the cloud? Learn more about the different assessment options from our Cloud Advisory team.

  • 2
  • 2
  • 2
  • +2
Tackle projects and never again get stuck behind a technical roadblock.
Join Now