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Re: Recursion or iteration (was Fibonacci series recursion error)

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From Ian Kelly <ian.g.kelly@gmail.com>
Date Fri, 13 May 2011 07:55:51 -0600
Subject Re: Recursion or iteration (was Fibonacci series recursion error)
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On Fri, May 13, 2011 at 5:11 AM, rusi <rustompmody@gmail.com> wrote:
> The tightest way I knew so far was this:
> The 2x2 matrix
> 0 1
> 1 1
> raised to the nth power gives the nth fibonacci number. [And then use
> a logarithmic matrix mult]
> Your version is probably tighter than this.

Oh, nice!  I did it this way once:

V = [0 1]

M =
[0 1]
[1 1]

fib(n) = (V * M ** n)[0]

Since I viewed M as operating on V, it never occurred to me that
multiplying by V is actually unnecessary, but it is obvious in
retrospect.  I think it's just a fortuitous coincidence that it works,
since V sets up the base case and M describes the recursive case.  For
a FIbonacci sequence starting with any other pair of numbers, V would
change, but M would not, and so V would no longer happen to be
identical to the top row of M.

Ian

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Thread

Fibonacci series recursion error lalit <opposite800@gmail.com> - 2011-04-29 20:22 -0700
  Re: Fibonacci series recursion error Gary Herron <gherron@islandtraining.com> - 2011-04-29 20:41 -0700
  Re: Fibonacci series recursion error Jason Friedman <jason@powerpull.net> - 2011-04-30 03:57 +0000
  Re: Fibonacci series recursion error harrismh777 <harrismh777@charter.net> - 2011-04-29 23:45 -0500
    Re: Fibonacci series recursion error harrismh777 <harrismh777@charter.net> - 2011-04-29 23:51 -0500
      Re: Fibonacci series recursion error harrismh777 <harrismh777@charter.net> - 2011-04-30 00:31 -0500
        Re: Fibonacci series recursion error Peter Otten <__peter__@web.de> - 2011-04-30 08:14 +0200
          Re: Fibonacci series recursion error rusi <rustompmody@gmail.com> - 2011-05-02 00:08 -0700
    Re: Fibonacci series recursion error Hans Georg Schaathun <hg@schaathun.net> - 2011-04-30 06:50 +0100
    Re: Fibonacci series recursion error Paul Rudin <paul.nospam@rudin.co.uk> - 2011-04-30 06:43 +0100
  Re: Fibonacci series recursion error Ian Kelly <ian.g.kelly@gmail.com> - 2011-04-29 23:27 -0600
    Re: Fibonacci series recursion error harrismh777 <harrismh777@charter.net> - 2011-04-30 00:35 -0500
      Re: Fibonacci series recursion error Peter Otten <__peter__@web.de> - 2011-04-30 08:32 +0200
        Re: Fibonacci series recursion error Chris Angelico <rosuav@gmail.com> - 2011-04-30 16:37 +1000
      Re: Fibonacci series recursion error Thomas Rachel <nutznetz-0c1b6768-bfa9-48d5-a470-7603bd3aa915@spamschutz.glglgl.de> - 2011-04-30 11:37 +0200
        Re: Fibonacci series recursion error harrismh777 <harrismh777@charter.net> - 2011-05-02 16:50 -0500
          Re: Fibonacci series recursion error Chris Angelico <rosuav@gmail.com> - 2011-05-03 08:17 +1000
            Re: Fibonacci series recursion error harrismh777 <harrismh777@charter.net> - 2011-05-03 12:10 -0500
              Re: Fibonacci series recursion error Chris Angelico <rosuav@gmail.com> - 2011-05-04 07:41 +1000
              Re: Fibonacci series recursion error Ian Kelly <ian.g.kelly@gmail.com> - 2011-05-03 16:31 -0600
              Re: Fibonacci series recursion error Chris Angelico <rosuav@gmail.com> - 2011-05-04 09:09 +1000
          Re: Fibonacci series recursion error Ian Kelly <ian.g.kelly@gmail.com> - 2011-05-02 16:22 -0600
          Re: Fibonacci series recursion error Chris Angelico <rosuav@gmail.com> - 2011-05-03 08:42 +1000
          Recursion or iteration (was Fibonacci series recursion error) rusi <rustompmody@gmail.com> - 2011-05-02 18:48 -0700
            Re: Recursion or iteration (was Fibonacci series recursion error) Chris Angelico <rosuav@gmail.com> - 2011-05-03 12:13 +1000
            Re: Recursion or iteration (was Fibonacci series recursion error) Chris Angelico <rosuav@gmail.com> - 2011-05-03 15:29 +1000
              Re: Recursion or iteration (was Fibonacci series recursion error) rusi <rustompmody@gmail.com> - 2011-05-03 00:52 -0700
                Re: Recursion or iteration (was Fibonacci series recursion error) Dave Angel <davea@ieee.org> - 2011-05-03 06:32 -0400
                Re: Recursion or iteration (was Fibonacci series recursion error) rusi <rustompmody@gmail.com> - 2011-05-03 03:51 -0700
                Re: Recursion or iteration (was Fibonacci series recursion error) Chris Angelico <rosuav@gmail.com> - 2011-05-03 21:04 +1000
                Re: Recursion or iteration (was Fibonacci series recursion error) Steven D'Aprano <steve+comp.lang.python@pearwood.info> - 2011-05-03 12:49 +0000
                Re: Recursion or iteration (was Fibonacci series recursion error) Chris Angelico <rosuav@gmail.com> - 2011-05-03 23:02 +1000
                Re: Recursion or iteration (was Fibonacci series recursion error) Hans Mulder <hansmu@xs4all.nl> - 2011-05-12 00:06 +0200
                Re: Recursion or iteration (was Fibonacci series recursion error) rusi <rustompmody@gmail.com> - 2011-05-13 04:11 -0700
                Re: Recursion or iteration (was Fibonacci series recursion error) Ian Kelly <ian.g.kelly@gmail.com> - 2011-05-13 07:55 -0600
                Re: Recursion or iteration (was Fibonacci series recursion error) Hans Mulder <hansmu@xs4all.nl> - 2011-05-13 21:46 +0200
                Re: Recursion or iteration (was Fibonacci series recursion error) Mark Dickinson <dickinsm@gmail.com> - 2011-05-13 14:48 -0700
                Re: Recursion or iteration (was Fibonacci series recursion error) rusi <rustompmody@gmail.com> - 2011-05-14 10:24 -0700
                Re: Recursion or iteration (was Fibonacci series recursion error) Ian Kelly <ian.g.kelly@gmail.com> - 2011-05-14 15:19 -0600
                Re: Recursion or iteration (was Fibonacci series recursion error) rusi <rustompmody@gmail.com> - 2011-05-14 20:32 -0700
                Re: Recursion or iteration (was Fibonacci series recursion error) Mark Dickinson <dickinsm@gmail.com> - 2011-05-15 12:20 -0700
                Re: Recursion or iteration (was Fibonacci series recursion error) Mark Dickinson <dickinsm@gmail.com> - 2011-05-15 12:29 -0700
            Re: Recursion or iteration (was Fibonacci series recursion error) Ian Kelly <ian.g.kelly@gmail.com> - 2011-05-02 23:46 -0600

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