From: already5chosen@yahoo.com   
      
   On Fri, 24 Oct 2025 15:36:58 +0200   
   Janis Papanagnou  wrote:   
      
   > On 24.10.2025 09:53, Rosario19 wrote:   
   > >   
   > >   
   > >> into the above pair of functions, or anything similar.   
   > >>   
   > >> That's not ordinary optimization of the type which improves the   
   > >> code generated for the user's algorithm; that's recognizing and   
   > >> redesigning the algorithm.   
   > >>   
   > >> The line between those is blurred, but not /that/ blurred.   
   > >   
   > > int fib1(int n){return fib_tail(0, 1, n);}   
   > >   
   > > is different from   
   > >   
   > > int fib(int n){if(n<2) return 1;return fib(n - 1) + fib(n - 2);   
   > >   
   > >   
   > > both these function calculate from the 0 1  the number result, but   
   > > fib() start to calculate from n goes dowwn until n=0, than goes up   
   > > until n=input, instead fib1() go only down for n. It seen the calls   
   > > (fib has 2 call each call... instead fib_tail() just 1), I think   
   > > fib() is O(n^2) instead fib1 is O(n).   
   >   
   > It's worse; it's O(2^N).   
   >   
   > Janis   
   >   
      
   Actually, the number of calls in naive recursive variant = 2*FIB(N)-1.   
   So, O(1.618**n) - a little less bad than your suggestion.   
      
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