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

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From	Ian Kelly <ian.g.kelly@gmail.com>
Date	Sat, 14 May 2011 15:19:55 -0600
Subject	Re: Recursion or iteration (was Fibonacci series recursion error)
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On Sat, May 14, 2011 at 11:24 AM, rusi <rustompmody@gmail.com> wrote:
> def fib(n):
>    if n==1 or n==2:
>        return 1
>    elif even(n):
>        return sq(fib (n//2)) + 2 * fib(n//2) * fib(n//2 - 1)
>    else:
>        return sq(fib (n//2 + 1)) + sq(fib(n // 2))
>
> This is a strange algo  -- logarithmic because it halves the n,
> exponential because of the double (triple) calls.  [I cannot say I
> know how to work out its exact complexity but I would guess its about
> linear]

Yup, linear.  Assuming you optimize the even case so that it doesn't
actually call fib(n//2) twice, the call tree can be approximated as a
balanced binary tree with height log(n).  The total number of nodes in
the tree is thus O(2 ** log(n)) = O(n).

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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