Re: Fibonacci series recursion error

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From	Terry Reedy <tjreedy@udel.edu>
Subject	Re: Fibonacci series recursion error
Date	Sun, 01 May 2011 22:30:02 -0400
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On 5/1/2011 7:16 PM, BartC wrote:

> Yes, it generates lots of calls.
>
> About 22000 for fib(20), and 330 million for fib(40).

Using the standard double recursion implementation of fib, ncf(n) 
(number of calls to fib() for fib(n)) requires ncf(n-2) + ncf(n+1) + 1 
calls. The +1 is for the call to fib(n) itself). So it grows a bit 
faster than fib(n).

Fib(n) is actually calculated as the sum of fib(n) 1s: 1+1+1....+1 
fib(n) times as 1 is the only non-0 base case and there is nothing else 
added or multiplied in non-base cases. To put it another way, there are 
fib(n) leaf nodes labeled 1 in the unbalanced tree generated by the 
recursion.

-- 
Terry Jan Reedy

Thread

Re: Fibonacci series recursion error Steven D'Aprano <steve+comp.lang.python@pearwood.info> - 2011-04-30 07:18 +0000
  Re: Fibonacci series recursion error "BartC" <bc@freeuk.com> - 2011-05-02 00:16 +0100
    Re: Fibonacci series recursion error Terry Reedy <tjreedy@udel.edu> - 2011-05-01 22:30 -0400
  Re: Fibonacci series recursion error rusi <rustompmody@gmail.com> - 2011-05-02 01:27 -0700
    Re: Fibonacci series recursion error Steven D'Aprano <steve+comp.lang.python@pearwood.info> - 2011-05-02 08:56 +0000
      Re: Fibonacci series recursion error Hans Georg Schaathun <hg@schaathun.net> - 2011-05-02 10:53 +0100
        Re: Fibonacci series recursion error rusi <rustompmody@gmail.com> - 2011-05-02 03:40 -0700
        Re: Fibonacci series recursion error Steven D'Aprano <steve+comp.lang.python@pearwood.info> - 2011-05-02 16:24 +0000
          Re: Fibonacci series recursion error Mark Dickinson <dickinsm@gmail.com> - 2011-05-02 14:18 -0700
      Re: Fibonacci series recursion error Chris Angelico <rosuav@gmail.com> - 2011-05-02 19:03 +1000
        Re: Fibonacci series recursion error Gregory Ewing <greg.ewing@canterbury.ac.nz> - 2011-05-05 14:35 +1200

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