On Sat, Jul 20, 2019 at 7:30 AM 'Jon Hough' via Programming
wrote:
> > Am I making any sense here?"
>
> Sorry, I am struggling to understand your point. Converting to ASCII
> is just to pack the bytes. It seems more purposeful than leaving as
> an array of 0s and 1s. It isn't a necessary step, but
FWIW, here’s my code for changing back to decimal representation.
z2d =: 3 : 0
if. _1 < <./ y do.
+/ #/ y join Fb
else.
+/ */ y join Fb
end.
)
join =: 3 : 0
join/ y
:
l =. - ({:@$x) >. {:@$y
r =. (l{."1 x),: l{."1 y
if. 2<#$r do.
(l{."1 x), l{."1 y
end.
)
eg
d2z 100
1 0 0 0 0 1
"In other words, it's not the fibonacci part that's the problem for me,
it's whatever you are using to convert to ascii that's the problem.
(Note also that there's no need to add any 1s into the represented
result - you just terminate the sequence by eliminating what would be
trailing ascii nul c
"You mention the possibility of 1 1 1 appearing in an encode result and that
making decode awkward without a loop. My guess is that that can happen if
you encode multiple numbers into a single result where two adjacent
encodings produce the 1 1 1. Is that right?"
This is correct. Simplest exampl
Since the Fibonacci numbers grow exponentially (powers of phi, -:1+%:5),
the representation is logarithmic and therefore efficient. (For example,
"Arabic notation" is logarithmic. Roman numerals are not.)
On Thu, Jul 18, 2019 at 9:49 PM Devon McCormick wrote:
> So you're decomposing a given
;
> >f2=:13 :'{."1([:+/\|.)^:(i.y)1 1'
> >
> >Fibs2=: 13 :'}.f2 y'
> >
> >Fibs2 10
> > 1 2 3 5 8 13 21 34 55
> >
> >(genfibs 1400)-:Fibs2 1400
> > 1
> >1
> > 1
> > On to underst
7;}.f2 y'
>
>Fibs2 10
> 1 2 3 5 8 13 21 34 55
>
>(genfibs 1400)-:Fibs2 1400
> 1
>1
> 1
> On to understand encode and decode.
>
> -Original Message-
> From: Programming On Behalf Of
> 'Jon Hough' via Programming
> Sent: T
I understand the fibonacci aspect.
Using Roger Hui's code:
,.fsum 449239438124834384923493383837734733747181x
280571172992510140037611932413038677189525
107168651819712326877926895128666735145224
40934782466626840596168752972961528246147
15635695580168194910579363790217849593217
3691087032
The Fibonacci Number System is treated on page 296 in the great book Concrete
Mathematics. https://en.wikipedia.org/wiki/Concrete_MathematicsDen fredag
den 19. juli 2019 12.23.43 CEST skrev 'Mike Day' via Programming
:
Just time to list d2z, dec to Zeckendorf...
_8{.Fb NB. Revers
Just time to list d2z, dec to Zeckendorf...
_8{.Fb NB. Reverse list of fibs...
34 21 13 8 5 3 2 1
d2z. NB. Dec to z
3 : 0
f =. Fb, 0
if. y = 0 do. ,0 return. end.
if. y e. f do. (#~>./\ ) Fb = y return.end.
reduce =. | }. +/\ inv f&(( (] - I.{[)^:a:)) n =. y NB. 12 ==> 12 4 1
}: (#~>.
I did a quick compare - on the hoof, so briefly- my d2z and z2d, ie
decimal-Zeckendorf switches appear faster than decode/encode - no time to say
how or why!
More later,
Mike
Sent from my iPad
> On 19 Jul 2019, at 01:26, 'Jon Hough' via Programming
> wrote:
>
> The encoding follows the
e.
-Original Message-
From: Programming On Behalf Of 'Jon
Hough' via Programming
Sent: Thursday, July 18, 2019 10:46 AM
To: Programming Forum
Subject: [Jprogramming] Fibonacci Encoding
Positive integers can be encoded using Fibonacci numbers.
For the sake of easer, assume Fibo
You mention the possibility of 1 1 1 appearing in an encode result and that
making decode awkward without a loop. My guess is that that can happen if
you encode multiple numbers into a single result where two adjacent
encodings produce the 1 1 1. Is that right?
Anyhow, could you produce a workarou
So you're decomposing a given number into a unique(?) sum of F=.Fibonaccis
represented by a Boolean with a 1 for each F? That is, the Boolean does
not waste space by representing non-F numbers: the positions 0 1 2 3 4..
represent 1 2 3 5 8...?
It looks potentially efficient if you have very large
The encoding follows the following algorithm:
"To encode an integer N:
Find the largest Fibonacci number equal to or less than N; subtract this number
from N, keeping track of the remainder.
If the number subtracted was the ith Fibonacci number F(i), put a 1 in place
i−2 in the code word (coun
I'm not quite sure I understand your encoding scheme.
Specifically, you're encoding into a sequence of characters, but when
decoding, you're not using (8#2)#:a.i.y and it looks like you've
cooked up some mechanism to compensate for how |."1#: behaves ...
In other words, I think that the fibonacci
See also http://code.jsoftware.com/wiki/Essays/Fibonacci_Sums
On Thu, Jul 18, 2019 at 7:57 AM 'Mike Day' via Programming <
[email protected]> wrote:
> FWIW, I spent some time on Zeckendorf representation a year or so ago.
> There’s some Rossetti Code stuff on it. I didn’t get round to sh
FWIW, I spent some time on Zeckendorf representation a year or so ago. There’s
some Rossetti Code stuff on it. I didn’t get round to sharing my results, but
could do so privately or on the forum if there’s interest. I worked up
functions for various arithmetic compositions, including harder o
Positive integers can be encoded using Fibonacci numbers.
For the sake of easer, assume Fibonacci numbers are 1,2,3,5,... (only one 1).
We can encode a positive integer uniquely using non-consecutive Fibonacci
numbers. For example
4 = 1 + 3 (note: 1 and 3 a re non-consecutive)
5 = 5 (already a Fi
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