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Ingy döt Net 2023-07-01 11:58:00 -04:00
parent 7387c8f97b
commit cb5bb5e222
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2
Task/Zeckendorf-number-representation/00-META.yaml Normal file
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---
from: http://rosettacode.org/wiki/Zeckendorf_number_representation

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Task/Zeckendorf-number-representation/00-TASK.txt Normal file
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Just as numbers can be represented in a positional notation as sums of multiples of the powers of ten (decimal) or two (binary); all the positive integers can be represented as the sum of one or zero times the distinct members of the Fibonacci series.
Recall that the first six distinct Fibonacci numbers are: 1, 2, 3, 5, 8, 13.
The decimal number eleven can be written as 0*13 + 1*8 + 0*5 + 1*3 + 0*2 + 0*1 or 010100 in positional notation where the columns represent multiplication by a particular member of the sequence. Leading zeroes are dropped so that 11 decimal becomes 10100.
10100 is not the only way to make 11 from the Fibonacci numbers however; 0*13 + 1*8 + 0*5 + 0*3 + 1*2 + 1*1 or 010011 would also represent decimal 11. For a true Zeckendorf number there is the added restriction that ''no two consecutive Fibonacci numbers can be used'' which leads to the former unique solution.
;Task:
Generate and show here a table of the Zeckendorf number representations of the decimal numbers zero to twenty, in order.
The intention in this task to find the Zeckendorf form of an arbitrary integer. The Zeckendorf form can be iterated by some bit twiddling rather than calculating each value separately but leave that to another separate task.
;Also see:
*   [http://oeis.org/A014417 OEIS A014417]   for the the sequence of required results.
*   [http://www.youtube.com/watch?v=kQZmZRE0cQY&list=UUoxcjq-8xIDTYp3uz647V5A&index=3&feature=plcp Brown's Criterion - Numberphile]
;Related task:
*   [[Fibonacci sequence]]
<br><br>

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Task/Zeckendorf-number-representation/11l/zeckendorf-number-representation.11l Normal file
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V n = 20
F z(=n)
I n == 0
R [0]
V fib = [2, 1]
L fib[0] < n
fib = [sum(fib[0.<2])] [+] fib
[Int] dig
L(f) fib
I f <= n
dig [+]= 1
n -= f
E
dig [+]= 0
R I dig[0] {dig} E dig[1..]
L(i) 0..n
print(‘#3: #8’.format(i, z(i).map(d -> String(d)).join(‘’)))

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Task/Zeckendorf-number-representation/360-Assembly/zeckendorf-number-representation.360 Normal file
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* Zeckendorf number representation 04/04/2017
ZECKEN CSECT
USING ZECKEN,R13 base register
B 72(R15) skip savearea
DC 17F'0' savearea
STM R14,R12,12(R13) save previous context
ST R13,4(R15) link backward
ST R15,8(R13) link forward
LR R13,R15 set addressability
LA R6,0 i=0
DO WHILE=(C,R6,LE,=A(20)) do i=0 to 20
MVC PG,=CL80'xx : ' init buffer
LA R10,PG pgi=0
XDECO R6,XDEC i
MVC 0(2,R10),XDEC+10 output i
LA R10,5(R10) pgi+=5
MVC FIB,=A(1) fib(1)=1
MVC FIB+4,=A(2) fib(2)=2
LA R7,2 j=2
LR R1,R7 j
SLA R1,2 @fib(j)
DO WHILE=(C,R6,GT,FIB-4(R1) do while fib(j)<i
LA R7,1(R7) j++
LR R1,R7 j
SLA R1,2 ~
L R2,FIB-8(R1) fib(j-1)
A R2,FIB-12(R1) fib(j-2)
ST R2,FIB-4(R1) fib(j)=fib(j-1)+fib(j-2)
LR R1,R7 j
SLA R1,2 @fib(j)
ENDDO , enddo j
LR R8,R6 k=i
MVI BB,X'00' bb=false
DO WHILE=(C,R7,GE,=A(1)) do j=j to 1 by -1
LR R1,R7 j
SLA R1,2 ~
IF C,R8,GE,FIB-4(R1) THEN if fib(j)<=k then
MVI BB,X'01' bb=true
MVC 0(1,R10),=C'1' output '1'
LA R10,1(R10) pgi+=1
LR R1,R7 j
SLA R1,2 ~
S R8,FIB-4(R1) k=k-fib(j)
ELSE , else
IF CLI,BB,EQ,X'01' THEN if bb then
MVC 0(1,R10),=C'0' output '0'
LA R10,1(R10) pgi+=1
ENDIF , endif
ENDIF , endif
BCTR R7,0 j--
ENDDO , enddo j
IF CLI,BB,NE,X'01' THEN if not bb then
MVC 0(1,R10),=C'0' output '0'
ENDIF , endif
XPRNT PG,L'PG print buffer
LA R6,1(R6) i++
ENDDO , enddo i
L R13,4(0,R13) restore previous savearea pointer
LM R14,R12,12(R13) restore previous context
XR R15,R15 rc=0
BR R14 exit
FIB DS 32F Fibonnacci table
BB DS X flag
PG DS CL80 buffer
XDEC DS CL12 temp
YREGS
END ZECKEN

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Task/Zeckendorf-number-representation/ALGOL-68/zeckendorf-number-representation.alg Normal file
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# print some Zeckendorf number representations #
# We handle 32-bit numbers, the maximum fibonacci number that can fit in a #
# 32 bit number is F(45) #
# build a table of 32-bit fibonacci numbers #
[ 45 ]INT fibonacci;
fibonacci[ 1 ] := 1;
fibonacci[ 2 ] := 2;
FOR i FROM 3 TO UPB fibonacci DO fibonacci[ i ] := fibonacci[ i - 1 ] + fibonacci[ i - 2 ] OD;
# returns the Zeckendorf representation of n or "?" if one cannot be found #
PROC to zeckendorf = ( INT n )STRING:
IF n = 0 THEN
"0"
ELSE
STRING result := "";
INT f pos := UPB fibonacci;
INT rest := ABS n;
# find the first non-zero Zeckendorf digit #
WHILE f pos > LWB fibonacci AND rest < fibonacci[ f pos ] DO
f pos -:= 1
OD;
# if we found a digit, build the representation #
IF f pos >= LWB fibonacci THEN
# have a digit #
BOOL skip digit := FALSE;
WHILE f pos >= LWB fibonacci DO
IF rest <= 0 THEN
result +:= "0"
ELIF skip digit THEN
# we used the previous digit #
skip digit := FALSE;
result +:= "0"
ELIF rest < fibonacci[ f pos ] THEN
# can't use the digit at f pos #
skip digit := FALSE;
result +:= "0"
ELSE
# can use this digit #
skip digit := TRUE;
result +:= "1";
rest -:= fibonacci[ f pos ]
FI;
f pos -:= 1
OD
FI;
IF rest = 0 THEN
# found a representation #
result
ELSE
# can't find a representation #
"?"
FI
FI; # to zeckendorf #
FOR i FROM 0 TO 20 DO
print( ( whole( i, -3 ), " ", to zeckendorf( i ), newline ) )
OD

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Task/Zeckendorf-number-representation/Action-/zeckendorf-number-representation.action Normal file
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PROC Encode(INT x CHAR ARRAY s)
INT ARRAY fib(22)=
[1 2 3 5 8 13 21 34 55 89 144 233 377 610
987 1597 2584 4181 6765 10946 17711 28657]
INT i
BYTE append
IF x=0 THEN
s(0)=1
s(1)='0
RETURN
FI
i=21 append=0
s(0)=0
WHILE i>=0
DO
IF x>=fib(i) THEN
x==-fib(i)
s(0)==+1
s(s(0))='1
append=1
ELSEIF append THEN
s(0)==+1
s(s(0))='0
FI
i==-1
OD
RETURN
PROC Main()
INT i
CHAR ARRAY s(10)
FOR i=0 TO 20
DO
Encode(i,s)
PrintF("%I -> %S%E",i,s)
OD
RETURN

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Task/Zeckendorf-number-representation/Ada/zeckendorf-number-representation.ada Normal file
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with Ada.Text_IO, Ada.Strings.Unbounded;
procedure Print_Zeck is
function Zeck_Increment(Z: String) return String is
begin
if Z="" then
return "1";
elsif Z(Z'Last) = '1' then
return Zeck_Increment(Z(Z'First .. Z'Last-1)) & '0';
elsif Z(Z'Last-1) = '0' then
return Z(Z'First .. Z'Last-1) & '1';
else -- Z has at least two digits and ends with "10"
return Zeck_Increment(Z(Z'First .. Z'Last-2)) & "00";
end if;
end Zeck_Increment;
use Ada.Strings.Unbounded;
Current: Unbounded_String := Null_Unbounded_String;
begin
for I in 1 .. 20 loop
Current := To_Unbounded_String(Zeck_Increment(To_String(Current)));
Ada.Text_IO.Put(To_String(Current) & " ");
end loop;
end Print_Zeck;

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Task/Zeckendorf-number-representation/AppleScript/zeckendorf-number-representation.applescript Normal file
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--------------------- ZECKENDORF NUMBERS -------------------
-- zeckendorf :: Int -> String
on zeckendorf(n)
script f
on |λ|(n, x)
if n < x then
[n, 0]
else
[n - x, 1]
end if
end |λ|
end script
if n = 0 then
{0} as string
else
item 2 of mapAccumL(f, n, |reverse|(just of tailMay(fibUntil(n)))) as string
end if
end zeckendorf
-- fibUntil :: Int -> [Int]
on fibUntil(n)
set xs to {}
set limit to n
script atLimit
property ceiling : limit
on |λ|(x)
(item 2 of x) > (atLimit's ceiling)
end |λ|
end script
script nextPair
property series : xs
on |λ|([a, b])
set nextPair's series to nextPair's series & b
[b, a + b]
end |λ|
end script
|until|(atLimit, nextPair, {0, 1})
return nextPair's series
end fibUntil
---------------------------- TEST --------------------------
on run
intercalate(linefeed, ¬
map(zeckendorf, enumFromTo(0, 20)))
end run
--------------------- GENERIC FUNCTIONS --------------------
-- enumFromTo :: Int -> Int -> [Int]
on enumFromTo(m, n)
if m > n then
set d to -1
else
set d to 1
end if
set lst to {}
repeat with i from m to n by d
set end of lst to i
end repeat
return lst
end enumFromTo
-- foldl :: (a -> b -> a) -> a -> [b] -> a
on foldl(f, startValue, xs)
tell mReturn(f)
set v to startValue
set lng to length of xs
repeat with i from 1 to lng
set v to |λ|(v, item i of xs, i, xs)
end repeat
return v
end tell
end foldl
-- 'The mapAccumL function behaves like a combination of map and foldl;
-- it applies a function to each element of a list, passing an
-- accumulating parameter from left to right, and returning a final
-- value of this accumulator together with the new list.' (see Hoogle)
-- mapAccumL :: (acc -> x -> (acc, y)) -> acc -> [x] -> (acc, [y])
on mapAccumL(f, acc, xs)
script
on |λ|(a, x)
tell mReturn(f) to set pair to |λ|(item 1 of a, x)
[item 1 of pair, (item 2 of a) & item 2 of pair]
end |λ|
end script
foldl(result, [acc, []], xs)
end mapAccumL
-- map :: (a -> b) -> [a] -> [b]
on map(f, xs)
tell mReturn(f)
set lng to length of xs
set lst to {}
repeat with i from 1 to lng
set end of lst to |λ|(item i of xs, i, xs)
end repeat
return lst
end tell
end map
-- Lift 2nd class handler function into 1st class script wrapper
-- mReturn :: Handler -> Script
on mReturn(f)
if class of f is script then
f
else
script
property |λ| : f
end script
end if
end mReturn
-- intercalate :: Text -> [Text] -> Text
on intercalate(strText, lstText)
set {dlm, my text item delimiters} to {my text item delimiters, strText}
set strJoined to lstText as text
set my text item delimiters to dlm
return strJoined
end intercalate
-- reverse :: [a] -> [a]
on |reverse|(xs)
if class of xs is text then
(reverse of characters of xs) as text
else
reverse of xs
end if
end |reverse|
-- tailMay :: [a] -> Maybe [a]
on tailMay(xs)
if length of xs > 1 then
{nothing:false, just:items 2 thru -1 of xs}
else
{nothing:true}
end if
end tailMay
-- until :: (a -> Bool) -> (a -> a) -> a -> a
on |until|(p, f, x)
set mp to mReturn(p)
set v to x
tell mReturn(f)
repeat until mp's |λ|(v)
set v to |λ|(v)
end repeat
end tell
return v
end |until|

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Task/Zeckendorf-number-representation/Arturo/zeckendorf-number-representation.arturo Normal file
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Z: function [x][
if x=0 -> return "0"
fib: new [2 1]
n: new x
while -> n > first fib
-> insert 'fib 0 fib\0 + fib\1
result: new ""
loop fib 'f [
if? f =< n [
'result ++ "1"
'n - f
]
else -> 'result ++ "0"
]
if result\0 = `0` ->
result: slice result 1 (size result)-1
return result
]
loop 0..20 'i ->
print [pad to :string i 3 pad Z i 8]

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Task/Zeckendorf-number-representation/AutoHotkey/zeckendorf-number-representation.ahk Normal file
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Fib := NStepSequence(1, 2, 2, 20)
Loop, 21 {
i := A_Index - 1
, Out .= i ":`t", n := ""
Loop, % Fib.MaxIndex() {
x := Fib.MaxIndex() + 1 - A_Index
if (Fib[x] <= i)
n .= 1, i -= Fib[x]
else
n .= 0
}
Out .= (n ? LTrim(n, "0") : 0) "`n"
}
MsgBox, % Out
NStepSequence(v1, v2, n, k) {
a := [v1, v2]
Loop, % k - 2 {
a[j := A_Index + 2] := 0
Loop, % j < n + 2 ? j - 1 : n
a[j] += a[j - A_Index]
}
return, a
}

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Task/Zeckendorf-number-representation/AutoIt/zeckendorf-number-representation.autoit Normal file
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For $i = 0 To 20
ConsoleWrite($i &": "& Zeckendorf($i)&@CRLF)
Next
Func Zeckendorf($int, $Fibarray = "")
If Not IsArray($Fibarray) Then $Fibarray = Fibonacci($int)
Local $ret = ""
For $i = UBound($Fibarray) - 1 To 1 Step -1
If $Fibarray[$i] > $int And $ret = "" Then ContinueLoop ; dont use Leading Zeros
If $Fibarray[$i] > $int Then
$ret &= "0"
Else
If StringRight($ret, 1) <> "1" Then
$ret &= "1"
$int -= $Fibarray[$i]
Else
$ret &= "0"
EndIf
EndIf
Next
If $ret = "" Then $ret = "0"
Return $ret
EndFunc ;==>Zeckendorf
Func Fibonacci($max)
$AList = ObjCreate("System.Collections.ArrayList")
$AList.add("0")
$current = 0
While True
If $current > 1 Then
$count = $AList.Count
$current = $AList.Item($count - 1)
$current = $current + $AList.Item($count - 2)
Else
$current += 1
EndIf
$AList.add($current)
If $current > $max Then ExitLoop
WEnd
$Array = $AList.ToArray
Return $Array
EndFunc ;==>Fibonacci

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Task/Zeckendorf-number-representation/BBC-BASIC/zeckendorf-number-representation.basic Normal file
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FOR n% = 0 TO 20
PRINT n% RIGHT$(" " + FNzeckendorf(n%), 8)
NEXT
PRINT '"Checking numbers up to 10000..."
FOR n% = 21 TO 10000
IF INSTR(FNzeckendorf(n%), "11") STOP
NEXT
PRINT "No Zeckendorf numbers contain consecutive 1's"
END
DEF FNzeckendorf(n%)
LOCAL i%, o$, fib%() : DIM fib%(45)
fib%(0) = 1 : fib%(1) = 1 : i% = 1
REPEAT
i% += 1
fib%(i%) = fib%(i%-1) + fib%(i%-2)
UNTIL fib%(i%) > n%
REPEAT
i% -= 1
IF n% >= fib%(i%) THEN
o$ += "1"
n% -= fib%(i%)
ELSE
o$ += "0"
ENDIF
UNTIL i% = 1
= o$

7
Task/Zeckendorf-number-representation/Befunge/zeckendorf-number-representation.bf Normal file
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45*83p0>:::.0`"0"v
v53210p 39+!:,,9+<
>858+37 *66g"7Y":v
>3g`#@_^ v\g39$<
^8:+1,+5_5<>-:0\`|
v:-\g39_^#:<*:p39<
>0\`:!"0"+#^ ,#$_^

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Task/Zeckendorf-number-representation/C++/zeckendorf-number-representation-1.cpp Normal file
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// For a class N which implements Zeckendorf numbers:
// I define an increment operation ++()
// I define a comparison operation <=(other N)
// Nigel Galloway October 22nd., 2012
#include <iostream>
class N {
private:
int dVal = 0, dLen;
public:
N(char const* x = "0"){
int i = 0, q = 1;
for (; x[i] > 0; i++);
for (dLen = --i/2; i >= 0; i--) {
dVal+=(x[i]-48)*q;
q*=2;
}}
const N& operator++() {
for (int i = 0;;i++) {
if (dLen < i) dLen = i;
switch ((dVal >> (i*2)) & 3) {
case 0: dVal += (1 << (i*2)); return *this;
case 1: dVal += (1 << (i*2)); if (((dVal >> ((i+1)*2)) & 1) != 1) return *this;
case 2: dVal &= ~(3 << (i*2));
}}}
const bool operator<=(const N& other) const {return dVal <= other.dVal;}
friend std::ostream& operator<<(std::ostream&, const N&);
};
N operator "" N(char const* x) {return N(x);}
std::ostream &operator<<(std::ostream &os, const N &G) {
const static std::string dig[] {"00","01","10"}, dig1[] {"","1","10"};
if (G.dVal == 0) return os << "0";
os << dig1[(G.dVal >> (G.dLen*2)) & 3];
for (int i = G.dLen-1; i >= 0; i--) os << dig[(G.dVal >> (i*2)) & 3];
return os;
}

5
Task/Zeckendorf-number-representation/C++/zeckendorf-number-representation-2.cpp Normal file
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int main(void) {
//for (N G; G <= 101010N; ++G) std::cout << G << std::endl; // from zero to 101010M
for (N G(101N); G <= 101010N; ++G) std::cout << G << std::endl; // from 101N to 101010N
return 0;
}

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Task/Zeckendorf-number-representation/C-sharp/zeckendorf-number-representation.cs Normal file
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using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
namespace Zeckendorf
{
class Program
{
private static uint Fibonacci(uint n)
{
if (n < 2)
{
return n;
}
else
{
return Fibonacci(n - 1) + Fibonacci(n - 2);
}
}
private static string Zeckendorf(uint num)
{
IList<uint> fibonacciNumbers = new List<uint>();
uint fibPosition = 2;
uint currentFibonaciNum = Fibonacci(fibPosition);
do
{
fibonacciNumbers.Add(currentFibonaciNum);
currentFibonaciNum = Fibonacci(++fibPosition);
} while (currentFibonaciNum <= num);
uint temp = num;
StringBuilder output = new StringBuilder();
foreach (uint item in fibonacciNumbers.Reverse())
{
if (item <= temp)
{
output.Append("1");
temp -= item;
}
else
{
output.Append("0");
}
}
return output.ToString();
}
static void Main(string[] args)
{
for (uint i = 1; i <= 20; i++)
{
string zeckendorfRepresentation = Zeckendorf(i);
Console.WriteLine(string.Format("{0} : {1}", i, zeckendorfRepresentation));
}
Console.ReadKey();
}
}
}

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Task/Zeckendorf-number-representation/C/zeckendorf-number-representation.c Normal file
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#include <stdio.h>
typedef unsigned long long u64;
#define FIB_INVALID (~(u64)0)
u64 fib[] = {
1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597,
2584, 4181, 6765, 10946, 17711, 28657, 46368, 75025, 121393, 196418,
317811, 514229, 832040, 1346269, 2178309, 3524578, 5702887, 9227465,
14930352, 24157817, 39088169, 63245986, 102334155, 165580141,
267914296, 433494437, 701408733, 1134903170, 1836311903,
2971215073ULL, 4807526976ULL, 7778742049ULL, 12586269025ULL,
20365011074ULL, 32951280099ULL, 53316291173ULL, 86267571272ULL,
139583862445ULL, 225851433717ULL, 365435296162ULL, 591286729879ULL,
956722026041ULL, 1548008755920ULL, 2504730781961ULL, 4052739537881ULL,
6557470319842ULL, 10610209857723ULL, 17167680177565ULL,
27777890035288ULL // this 65-th one is for range check
};
u64 fibbinary(u64 n)
{
if (n >= fib[64]) return FIB_INVALID;
u64 ret = 0;
int i;
for (i = 64; i--; )
if (n >= fib[i]) {
ret |= 1ULL << i;
n -= fib[i];
}
return ret;
}
void bprint(u64 n, int width)
{
if (width > 64) width = 64;
u64 b;
for (b = 1ULL << (width - 1); b; b >>= 1)
putchar(b == 1 && !n
? '0'
: b > n ? ' '
: b & n ? '1' : '0');
putchar('\n');
}
int main(void)
{
int i;
for (i = 0; i <= 20; i++)
printf("%2d:", i), bprint(fibbinary(i), 8);
return 0;
}

41
Task/Zeckendorf-number-representation/CLU/zeckendorf-number-representation.clu Normal file
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% Get list of distinct Fibonacci numbers up to N
fibonacci = proc (n: int) returns (array[int])
list: array[int] := array[int]$[]
a: int := 1
b: int := 2
while a <= n do
array[int]$addh(list,a)
a, b := b, a+b
end
return(list)
end fibonacci
% Find the Zeckendorf representation of N
zeckendorf = proc (n: int) returns (string) signals (negative)
if n<0 then signal negative end
if n=0 then return("0") end
fibs: array[int] := fibonacci(n)
result: array[char] := array[char]$[]
while ~array[int]$empty(fibs) do
fib: int := array[int]$remh(fibs)
if fib <= n then
n := n - fib
array[char]$addh(result,'1')
else
array[char]$addh(result,'0')
end
end
return(string$ac2s(result))
end zeckendorf
% Print the Zeckendorf representations of 0 to 20
start_up = proc ()
po: stream := stream$primary_output()
for i: int in int$from_to(0,20) do
stream$putright(po, int$unparse(i), 2)
stream$puts(po, ": ")
stream$putl(po, zeckendorf(i))
end
end start_up

13
Task/Zeckendorf-number-representation/Clojure/zeckendorf-number-representation.clj Normal file
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(def fibs (lazy-cat [1 1] (map + fibs (rest fibs))))
(defn z [n]
(if (zero? n)
"0"
(let [ps (->> fibs (take-while #(<= % n)) rest reverse)
fz (fn [[s n] p]
(if (>= n p)
[(conj s 1) (- n p)]
[(conj s 0) n]))]
(->> ps (reduce fz [[] n]) first (apply str)))))
(doseq [n (range 0 21)] (println n (z n)))

15
Task/Zeckendorf-number-representation/Common-Lisp/zeckendorf-number-representation-1.lisp Normal file
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(defun zeckendorf (n)
"returns zeckendorf integer of n (see OEIS A003714)"
(let ((fib '(2 1)))
;; extend Fibonacci sequence long enough
(loop while (<= (car fib) n) do
(push (+ (car fib) (cadr fib)) fib))
(loop with r = 0 for f in fib do
(setf r (* 2 r))
(when (>= n f) (setf n (- n f))
(incf r))
finally (return r))))
;;; task requirement
(loop for i from 0 to 20 do
(format t "~2D: ~2R~%" i (zeckendorf i)))

10
Task/Zeckendorf-number-representation/Common-Lisp/zeckendorf-number-representation-2.lisp Normal file
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;; Print Zeckendorf numbers upto 20.
;; I have implemented this as a state machine.
;; Nigel Galloway - October 13th., 2012
;;
(let ((fibz '(13 8 5 3 2 1))) (dotimes (G 21) (progn (format t "~S is " G)
(let ((z 0) (ng G)) (dolist (N fibz)
(if (> z 1) (progn (setq z 1) (format t "~S" 0))
(if (>= ng N) (progn (setq z 2) (setq ng (- ng N)) (format t "~S" 1))
(if (= z 1) (format t "~S" 0)))))
(if (= z 0) (format t "~S~%" 0) (format t "~%"))))))

45
Task/Zeckendorf-number-representation/Cowgol/zeckendorf-number-representation.cowgol Normal file
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include "cowgol.coh";
sub zeckendorf(n: uint32, buf: [uint8]): (r: [uint8]) is
var fibs: uint32[] := {
0,1,2,3,5,8,13,21,34,55,89,144,233,377,610,987,1597,
2584,4181,6765,10946,17711,28657,46368,75025,121393,
196418,317811,514229,832040,1346269,2178309,3524578,
5702887,9227465,14930352,24157817,39088169,63245986,
102334155,165580141,267914296,433494437,701408733,
1134903170,1836311903,2971215073
};
r := buf;
if n == 0 then
[r] := '0';
[@next r] := 0;
return;
end if;
var fib: [uint32] := &fibs[1];
while n >= [fib] loop
fib := @next fib;
end loop;
fib := @prev fib;
while [fib] != 0 loop
if [fib] <= n then
n := n - [fib];
[buf] := '1';
else
[buf] := '0';
end if;
fib := @prev fib;
buf := @next buf;
end loop;
[buf] := 0;
end sub;
var i: uint32 := 0;
while i <= 20 loop
print_i32(i);
print(": ");
print(zeckendorf(i, LOMEM));
print_nl();
i := i + 1;
end loop;

16
Task/Zeckendorf-number-representation/Crystal/zeckendorf-number-representation-1.crystal Normal file
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def zeckendorf(n)
return 0 if n.zero?
fib = [1, 2]
while fib[-1] < n; fib << fib[-2] + fib[-1] end
digit = ""
fib.reverse_each do |f|
if f <= n
digit, n = digit + "1", n - f
else
digit += "0"
end
end
digit.to_i
end
(0..20).each { |i| puts "%3d: %8d" % [i, zeckendorf(i)] }

23
Task/Zeckendorf-number-representation/Crystal/zeckendorf-number-representation-2.crystal Normal file
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class ZeckendorfIterator
include Iterator(String)
def initialize
@x = 0
end
def next
bin = @x.to_s(2)
@x += 1
while bin.includes?("11")
bin = @x.to_s(2)
@x += 1
end
bin
end
end
def zeckendorf(n)
ZeckendorfIterator.new.first(n)
end
zeckendorf(21).each_with_index{ |x,i| puts "%3d: %8s"% [i, x] }

11
Task/Zeckendorf-number-representation/Crystal/zeckendorf-number-representation-3.crystal Normal file
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def zeckendorf(n)
0.step.map(&.to_s(2)).reject(&.includes?("11")).first(n)
end
# or a little faster
def zeckendorf(n)
0.step.compact_map{ |x| bin = x.to_s(2); bin unless bin.includes?("11") }.first(n)
end
zeckendorf(21).each_with_index{ |x,i| puts "%3d: %8s"% [i, x] }

10
Task/Zeckendorf-number-representation/D/zeckendorf-number-representation-1.d Normal file
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import std.stdio, std.range, std.algorithm, std.functional;
void main() {
size_t
.max
.iota
.filter!q{ !(a & (a >> 1)) }
.take(21)
.binaryReverseArgs!writefln("%(%b\n%)");
}

22
Task/Zeckendorf-number-representation/D/zeckendorf-number-representation-2.d Normal file
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import std.stdio, std.typecons;
int zeckendorf(in int n) pure nothrow {
Tuple!(int,"remaining", int,"set")
zr(in int fib0, in int fib1, in int n, in uint bit) pure nothrow {
if (fib1 > n)
return typeof(return)(n, 0);
auto rs = zr(fib1, fib0 + fib1, n, bit + 1);
if (fib1 <= rs.remaining) {
rs.set |= 1 << bit;
rs.remaining -= fib1;
}
return rs;
}
return zr(1, 1, n, 0)[1];
}
void main() {
foreach (i; 0 .. 21)
writefln("%2d: %6b", i, zeckendorf(i));
}

21
Task/Zeckendorf-number-representation/D/zeckendorf-number-representation-3.d Normal file
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import std.stdio, std.algorithm, std.range;
string zeckendorf(size_t n) {
if (n == 0)
return "0";
auto fibs = recurrence!q{a[n - 1] + a[n - 2]}(1, 2);
string result;
foreach_reverse (immutable f; fibs.until!(x => x > n).array) {
result ~= (f <= n) ? '1' : '0';
if (f <= n)
n -= f;
}
return result;
}
void main() {
foreach (immutable i; 0 .. 21)
writefln("%2d: %6s", i, i.zeckendorf);
}

33
Task/Zeckendorf-number-representation/Delphi/zeckendorf-number-representation.delphi Normal file
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const FibNums: array [0..21] of integer =
(1, 2, 3, 5, 8, 13, 21, 34, 55, 89,
144, 233, 377, 610, 987, 1597, 2584,
4181, 6765, 10946, 17711, 28657);
function GetZeckNumber(N: integer): string;
{Returns Zeckendorf number for N as string}
var I: integer;
begin
Result:='';
{Subtract Fibonacci numbers from N}
for I:=High(FibNums) downto 0 do
if (N-FibNums[I])>=0 then
begin
Result:=Result+'1';
N:=N-FibNums[I];
end
else if Length(Result)>0 then Result:=Result+'0';
if Result='' then Result:='0';
end;
procedure ShowZeckendorfNumbers(Memo: TMemo);
var I: integer;
var S: string;
begin
S:='';
for I:=0 to 20 do
begin
Memo.Lines.Add(IntToStr(I)+': '+GetZeckNumber(I));
end;
end;

27
Task/Zeckendorf-number-representation/EchoLisp/zeckendorf-number-representation.l Normal file
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;; special fib's starting with 1 2 3 5 ...
(define (fibonacci n)
(+ (fibonacci (1- n)) (fibonacci (- n 2))))
(remember 'fibonacci #(1 2))
(define-constant Φ (// (1+ (sqrt 5)) 2))
(define-constant logΦ (log Φ))
;; find i : fib(i) >= n
(define (iFib n)
(floor (// (log (+ (* n Φ) 0.5)) logΦ)))
;; left trim zeroes
(string-delimiter "")
(define (zeck->string digits)
(if (!= 0 (first digits))
(string-join digits "")
(zeck->string (rest digits))))
(define (Zeck n)
(cond
(( < n 0) "no negative zeck")
((inexact? n) "no floating zeck")
((zero? n) "0")
(else (zeck->string
(for/list ((s (reverse (take fibonacci (iFib n)))))
(if ( > s n) 0
(begin (-= n s) 1 )))))))

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Task/Zeckendorf-number-representation/Elena/zeckendorf-number-representation.elena Normal file
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import system'routines;
import system'collections;
import system'text;
import extensions;
extension op
{
fibonacci()
{
if (self < 2)
{
^ self
}
else
{
^ (self - 1).fibonacci() + (self - 2).fibonacci()
};
}
zeckendorf()
{
var fibonacciNumbers := new List<int>();
int num := self;
int fibPosition := 2;
int currentFibonaciNum := fibPosition.fibonacci();
while (currentFibonaciNum <= num)
{
fibonacciNumbers.append:currentFibonaciNum;
fibPosition := fibPosition + 1;
currentFibonaciNum := fibPosition.fibonacci()
};
auto output := new TextBuilder();
int temp := num;
fibonacciNumbers.sequenceReverse().forEach:(item)
{
if (item <= temp)
{
output.write("1");
temp := temp - item
}
else
{
output.write("0")
}
};
^ output.Value
}
}
public program()
{
for(int i := 1, i <= 20, i += 1)
{
console.printFormatted("{0} : {1}",i,i.zeckendorf()).writeLine()
};
console.readChar()
}

13
Task/Zeckendorf-number-representation/Elixir/zeckendorf-number-representation-1.elixir Normal file
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defmodule Zeckendorf do
def number do
Stream.unfold(0, fn n -> zn_loop(n) end)
end
defp zn_loop(n) do
bin = Integer.to_string(n, 2)
if String.match?(bin, ~r/11/), do: zn_loop(n+1), else: {bin, n+1}
end
end
Zeckendorf.number |> Enum.take(21) |> Enum.with_index
|> Enum.each(fn {zn, i} -> IO.puts "#{i}: #{zn}" end)

14
Task/Zeckendorf-number-representation/Elixir/zeckendorf-number-representation-2.elixir Normal file
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defmodule Zeckendorf do
def number(n) do
fib_loop(n, [2,1])
|> Enum.reduce({"",n}, fn f,{dig,i} ->
if f <= i, do: {dig<>"1", i-f}, else: {dig<>"0", i}
end)
|> elem(0) |> String.to_integer
end
defp fib_loop(n, fib) when n < hd(fib), do: fib
defp fib_loop(n, [a,b|_]=fib), do: fib_loop(n, [a+b | fib])
end
for i <- 0..20, do: IO.puts "#{i}: #{Zeckendorf.number(i)}"

14
Task/Zeckendorf-number-representation/F-Sharp/zeckendorf-number-representation.fs Normal file
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let fib = Seq.unfold (fun (x, y) -> Some(x, (y, x + y))) (1,2)
let zeckendorf n =
if n = 0 then ["0"]
else
let folder k state =
let (n, z) = (fst state), (snd state)
if n >= k then (n - k, "1" :: z)
else (n, "0" :: z)
let fb = fib |> Seq.takeWhile (fun i -> i<=n) |> Seq.toList
snd (List.foldBack folder fb (n, []))
|> List.rev
for i in 0 .. 20 do printfn "%2d: %8s" i (String.concat "" (zeckendorf i))

11
Task/Zeckendorf-number-representation/Factor/zeckendorf-number-representation.factor Normal file
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USING: formatting kernel locals make math sequences ;
:: fib<= ( n -- seq )
1 2 [ [ dup n <= ] [ 2dup + [ , ] 2dip ] while drop , ]
{ } make ;
:: zeck ( n -- str )
0 :> s! n fib<= <reversed>
[ dup s + n <= [ s + s! 49 ] [ drop 48 ] if ] "" map-as ;
21 <iota> [ dup zeck "%2d: %6s\n" printf ] each

15
Task/Zeckendorf-number-representation/Forth/zeckendorf-number-representation.fth Normal file
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: fib<= ( n -- n )
>r 0 1 BEGIN dup r@ <= WHILE tuck + REPEAT drop rdrop ;
: z. ( n -- )
dup fib<= dup . -
BEGIN ?dup WHILE
dup fib<= dup [char] + emit space . -
REPEAT ;
: tab 9 emit ;
: zeckendorf ( -- )
21 0 DO
cr i 2 .r tab i z.
LOOP ;

1
Task/Zeckendorf-number-representation/Fortran/zeckendorf-number-representation-1.f Normal file
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F(N) = ((1 + SQRT(5))**N - (1 - SQRT(5))**N)/(SQRT(5)*2**N)

86
Task/Zeckendorf-number-representation/Fortran/zeckendorf-number-representation-2.f Normal file
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MODULE ZECKENDORF ARITHMETIC !Using the Fibonacci series, rather than powers of some base.
INTEGER ZLAST !The standard 32-bit two's complement integers
PARAMETER (ZLAST = 45) !only get so far, just as there's a limit to the highest power.
INTEGER F1B(ZLAST) !I want the Fibonacci series, and, starting with its second one.
c PARAMETER (F1B = (/1,2, !But alas, the compiler doesn't allow
c 3 F1B(1) + F1B(2), !for this sort of carpet-unrolling
c 4 F1B(2) + F1B(3), !initialisation sequence.
INTEGER,PRIVATE:: F01,F02,F03,F04,F05,F06,F07,F08,F09,F10, !So, not bothering with F00,
1 F11,F12,F13,F14,F15,F16,F17,F18,F19,F20, !Prepare a horde of simple names,
2 F21,F22,F23,F24,F25,F26,F27,F28,F29,F30, !which can be initialised
3 F31,F32,F33,F34,F35,F36,F37,F38,F39,F40, !in a certain way,
4 F41,F42,F43,F44,F45 !without scaring the compiler.
PARAMETER (F01 = 1, F02 = 2, F03 = F02 + F01, F04 = F03 + F02, !Thusly.
1 F05=F04+F03,F06=F05+F04,F07=F06+F05,F08=F07+F06,F09=F08+F07, !Typing all this
2 F10=F09+F08,F11=F10+F09,F12=F11+F10,F13=F12+F11,F14=F13+F12, !is an invitation
3 F15=F14+F13,F16=F15+F14,F17=F16+F15,F18=F17+F16,F19=F18+F17, !for mistypes.
4 F20=F19+F18,F21=F20+F19,F22=F21+F20,F23=F22+F21,F24=F23+F22, !So a regular layout
5 F25=F24+F23,F26=F25+F24,F27=F26+F25,F28=F27+F26,F29=F28+F27, !helps a little.
6 F30=F29+F28,F31=F30+F29,F32=F31+F30,F33=F32+F31,F34=F33+F32, !Otherwise,
7 F35=F34+F33,F36=F35+F34,F37=F36+F35,F38=F37+F36,F39=F38+F37, !devise a prog.
8 F40=F39+F38,F41=F40+F39,F42=F41+F40,F43=F42+F41,F44=F43+F42, !to generate these texts...
9 F45=F44+F43) !The next is 2971215073. Too big for 32-bit two's complement integers.
PARAMETER (F1B = (/F01,F02,F03,F04,F05,F06,F07,F08,F09,F10, !And now,
1 F11, F12, F13, F14, F15, F16, F17, F18, F19, F20, !Here is the desired
2 F21, F22, F23, F24, F25, F26, F27, F28, F29, F30, !array of constants.
3 F31, F32, F33, F34, F35, F36, F37, F38, F39, F40, !And as such, possibly
4 F41, F42, F43, F44, F45/)) !protected from alteration.
CONTAINS !After all that, here we go.
SUBROUTINE ZECK(N,D) !Convert N to a "Zeckendorf" digit sequence.
Counts upwards from digit one. D(i) ~ F1B(i). D(0) fingers the high-order digit.
INTEGER N !The normal number, in the computer's base.
INTEGER D(0:) !The digits, to be determined.
INTEGER R !The remnant.
INTEGER L !A finger, similar to the power of the base.
IF (N.LT.0) STOP "ZECK! No negative numbers!" !I'm not thinking about them.
R = N !Grab a copy that I can mess with.
D = 0 !Scrub the lot in one go.
L = ZLAST !As if starting with BASE**MAX, rather than BASE**0.
10 IF (R.GE.F1B(L)) THEN !Has the remnant sufficient for this digit?
R = R - F1B(L) !Yes! Remove that amount.
IF (D(0).EQ.0) THEN !Is this the first non-zero digit?
IF (L.GT.UBOUND(D,DIM=1)) STOP "ZECK! Not enough digits!" !Yes.
D(0) = L !Remember the location of the high-order digit.
END IF !Two loops instead, to avoid repeated testing?
D(L) = 1 !Place the digit, knowing a place awaits.
L = L - 1 !Never need a ...11... sequence because F1B(i) + F1B(i+1) = F1B(i+2).
END IF !So much for that digit "power".
L = L - 1 !Down a digit.
IF (L.GT.0 .AND. R.GT.0) GO TO 10 !Are we there yet?
IF (N.EQ.0) D(0) = 1 !Zero has one digit.
END SUBROUTINE ZECK !That was fun.
INTEGER FUNCTION ZECKN(D) !Converts a "Zeckendorf" digit sequence to a number.
INTEGER D(0:) !The digits. D(0) fingers the high-order digit.
IF (D(0).LE.0) STOP "ZECKN! Empty number!" !General paranoia.
IF (D(0).GT.ZLAST) STOP "ZECKN! Oversize number!" !I hate array bound hiccoughs.
ZECKN = SUM(D(1:D(0))*F1B(1:D(0))) !This is what positional notation means.
IF (ZECKN.LT.0) STOP "ZECKN! Integer overflow!" !Oh for IF OVERFLOW as in First Fortran.
END FUNCTION ZECKN !Overflows by a small amount will produce a negative number.
END MODULE ZECKENDORF ARITHMETIC !Odd stuff.
PROGRAM POKE
USE ZECKENDORF ARITHMETIC !Please.
INTEGER ZD(0:ZLAST) !A scratchpad.
INTEGER I,J,W
CHARACTER*1 DIGIT(0:1) !Assistance for the output.
PARAMETER (DIGIT = (/"0","1"/), W = 6) !This field width suffices.
c WRITE (6,*) F1B
c WRITE (6,*) INT8(F1B(44)) + INT8(F1B(45))
WRITE (6,1) F1B(1:4),ZLAST,ZLAST,F1B(ZLAST),HUGE(I) !Show some provenance.
1 FORMAT ("Converts integers to their Zeckendorf digit string "
1 "using the Fib1nacci sequence (",4(I0,","),
2 " ...) as the equivalent of powers."/
3 "At most, ",I0," digits because Fib1nacci(",I0,") = ",I0,
4 " and the integer limit is ",I0,".",//," N ZN") !Ends with a heading.
DO I = 0,20 !Step through the specified range.
CALL ZECK(I,ZD) !Convert I to ZD.
c WRITE (6,2) I,ZD(ZD(0):1:-1) !Show digits from high-order to low.
c 2 FORMAT (I3,1X,66I1) !Or, WRITE (6,2) I,(ZD(J), J = ZD(0),1,-1)
WRITE (6,3) I,(" ",J = ZD(0) + 1,W),DIGIT(ZD(ZD(0):1:-1)) !Right-aligned in field width W.
3 FORMAT (I3,1X,66A1) !The digits appear as characters.
IF (I.NE.ZECKN(ZD)) STOP "Huh?" !Should never happen...
END DO !On to the next.
END

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Task/Zeckendorf-number-representation/FreeBASIC/zeckendorf-number-representation.basic Normal file
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' version 17-10-2016
' compile with: fbc -s console
#Define max 92 ' max for Fibonacci number
Dim Shared As ULongInt fib(max)
fib(0) = 1
fib(1) = 1
For x As Integer = 2 To max
fib(x) = fib(x-1) + fib(x-2)
Next
Function num2zeck(n As Integer) As String
If n < 0 Then
Print "Error: no negative numbers allowed"
Beep : Sleep 5000,1 : End
End If
If n < 2 Then Return Str(n)
Dim As String zeckendorf
For x As Integer = max To 1 Step -1
If fib(x) <= n Then
zeckendorf = zeckendorf + "1"
n = n - fib(x)
Else
zeckendorf = zeckendorf + "0"
End If
Next
return LTrim(zeckendorf, "0") ' get rid of leading zeroes
End Function
' ------=< MAIN >=------
Dim As Integer x, e
Dim As String zeckendorf
Print "number zeckendorf"
For x = 0 To 200000
zeckendorf = num2zeck(x)
If x <= 20 Then Print x, zeckendorf
' check for two consecutive Fibonacci numbers
If InStr(zeckendorf, "11") <> 0 Then
Print " Error: two consecutive Fibonacci numbers "; x, zeckendorf
e = e +1
End If
Next
Print
If e = 0 Then
Print " No Zeckendorf numbers with two consecutive Fibonacci numbers found"
Else
Print e; " error(s) found"
End If
' empty keyboard buffer
While Inkey <> "" : Wend
Print : Print "hit any key to end program"
Sleep
End

31
Task/Zeckendorf-number-representation/Go/zeckendorf-number-representation.go Normal file
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package main
import "fmt"
func main() {
for i := 0; i <= 20; i++ {
fmt.Printf("%2d %7b\n", i, zeckendorf(i))
}
}
func zeckendorf(n int) int {
// initial arguments of fib0 = 1 and fib1 = 1 will produce
// the Fibonacci sequence {1, 2, 3,..} on the stack as successive
// values of fib1.
_, set := zr(1, 1, n, 0)
return set
}
func zr(fib0, fib1, n int, bit uint) (remaining, set int) {
if fib1 > n {
return n, 0
}
// recurse.
// construct sequence on the way in, construct ZR on the way out.
remaining, set = zr(fib1, fib0+fib1, n, bit+1)
if fib1 <= remaining {
set |= 1 << bit
remaining -= fib1
}
return
}

9
Task/Zeckendorf-number-representation/Haskell/zeckendorf-number-representation-1.hs Normal file
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import Data.Bits
import Numeric
zeckendorf = map b $ filter ones [0..] where
ones :: Int -> Bool
ones x = 0 == x .&. (x `shiftR` 1)
b x = showIntAtBase 2 ("01"!!) x ""
main = mapM_ putStrLn $ take 21 zeckendorf

4
Task/Zeckendorf-number-representation/Haskell/zeckendorf-number-representation-2.hs Normal file
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zeckendorf = "0":"1":[s++[d] | s <- tail zeckendorf, d <- "01",
last s /= '1' || d /= '1']
main = mapM putStrLn $ take 21 zeckendorf

11
Task/Zeckendorf-number-representation/Haskell/zeckendorf-number-representation-3.hs Normal file
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import Numeric
fib = 1 : 1 : zipWith (+) fib (tail fib)
pow2 = iterate (2*) 1
zeckendorf = map b z where
z = 0:concat (zipWith f fib pow2)
f x y = map (y+) (take x z)
b x = showIntAtBase 2 ("01"!!) x ""
main = mapM_ putStrLn $ take 21 zeckendorf

15
Task/Zeckendorf-number-representation/Haskell/zeckendorf-number-representation-4.hs Normal file
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import Data.List (mapAccumL)
fib :: [Int]
fib = 1 : 2 : zipWith (+) fib (tail fib)
zeckendorf :: Int -> String
zeckendorf 0 = "0"
zeckendorf n = snd $ mapAccumL f n $ reverse $ takeWhile (<= n) fib
where
f n x
| n < x = (n, '0')
| otherwise = (n - x, '1')
main :: IO ()
main = (putStrLn . unlines) $ zeckendorf <$> [0 .. 20]

29
Task/Zeckendorf-number-representation/J/zeckendorf-number-representation.j Normal file
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fib=: 3 : 0 " 0
mp=. +/ .*
{.{: mp/ mp~^:(I.|.#:y) 2 2$0 1 1 1x
)
phi=: -:1+%:5
fi =: 3 : 'n - y<fib n=. 0>.(1=y)-~>.(phi^.%:5)+phi^.y'
fsum=: 3 : 0
z=. 0$r=. y
while. 3<r do.
m=. fib fi r
z=. z,m
r=. r-m
end.
z,r$~(*r)+.0=y
)
Filter=: (#~`)(`:6)
' '&~:Filter@:":@:#:@:#.@:((|. fib 2+i.8) e. fsum)&.>i.3 7
┌──────┬──────┬──────┬──────┬──────┬──────┬──────┐
│0 │1 │10 │100 │101 │1000 │1001 │
├──────┼──────┼──────┼──────┼──────┼──────┼──────┤
│1010 │10000 │10001 │10010 │10100 │10101 │100000│
├──────┼──────┼──────┼──────┼──────┼──────┼──────┤
│100001│100010│100100│100101│101000│101001│101010│
└──────┴──────┴──────┴──────┴──────┴──────┴──────┘

33
Task/Zeckendorf-number-representation/Java/zeckendorf-number-representation-1.java Normal file
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import java.util.*;
class Zeckendorf
{
public static String getZeckendorf(int n)
{
if (n == 0)
return "0";
List<Integer> fibNumbers = new ArrayList<Integer>();
fibNumbers.add(1);
int nextFib = 2;
while (nextFib <= n)
{
fibNumbers.add(nextFib);
nextFib += fibNumbers.get(fibNumbers.size() - 2);
}
StringBuilder sb = new StringBuilder();
for (int i = fibNumbers.size() - 1; i >= 0; i--)
{
int fibNumber = fibNumbers.get(i);
sb.append((fibNumber <= n) ? "1" : "0");
if (fibNumber <= n)
n -= fibNumber;
}
return sb.toString();
}
public static void main(String[] args)
{
for (int i = 0; i <= 20; i++)
System.out.println("Z(" + i + ")=" + getZeckendorf(i));
}
}

41
Task/Zeckendorf-number-representation/Java/zeckendorf-number-representation-2.java Normal file
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import java.util.ArrayList;
import java.util.List;
public class Zeckendorf {
private List<Integer> getFibList(final int maxNum, final int n1, final int n2, final List<Integer> fibs){
if(n2 > maxNum) return fibs;
fibs.add(n2);
return getFibList(maxNum, n2, n1 + n2, fibs);
}
public String getZeckendorf(final int num) {
if (num <= 0) return "0";
final List<Integer> fibs = getFibList(num, 1, 2, new ArrayList<Integer>(){{ add(1); }});
return getZeckString("", num, fibs.size() - 1, fibs);
}
private String getZeckString(final String zeck, final int num, final int index, final List<Integer> fibs){
final int curFib = fibs.get(index);
final boolean placeZeck = num >= curFib;
final String outString = placeZeck ? zeck + "1" : zeck + "0";
final int outNum = placeZeck ? num - curFib : num;
if(index == 0) return outString;
return getZeckString(outString, outNum, index - 1, fibs);
}
public static void main(final String[] args) {
final Zeckendorf zeckendorf = new Zeckendorf();
for(int i =0; i <= 20; i++){
System.out.println("Z("+ i +"):\t" + zeckendorf.getZeckendorf(i));
}
}
}

135
Task/Zeckendorf-number-representation/JavaScript/zeckendorf-number-representation.js Normal file
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(() => {
'use strict';
const main = () =>
unlines(
map(n => concat(zeckendorf(n)),
enumFromTo(0, 20)
)
);
// zeckendorf :: Int -> String
const zeckendorf = n => {
const go = (n, x) =>
n < x ? (
Tuple(n, '0')
) : Tuple(n - x, '1')
return 0 < n ? (
snd(mapAccumL(
go, n,
reverse(fibUntil(n))
))
) : ['0'];
};
// fibUntil :: Int -> [Int]
const fibUntil = n =>
cons(1, takeWhile(x => n >= x,
map(snd, iterateUntil(
tpl => n <= fst(tpl),
tpl => {
const x = snd(tpl);
return Tuple(x, x + fst(tpl));
},
Tuple(1, 2)
))));
// GENERIC FUNCTIONS ----------------------------
// Tuple (,) :: a -> b -> (a, b)
const Tuple = (a, b) => ({
type: 'Tuple',
'0': a,
'1': b,
length: 2
});
// concat :: [[a]] -> [a]
// concat :: [String] -> String
const concat = xs =>
0 < xs.length ? (() => {
const unit = 'string' !== typeof xs[0] ? (
[]
) : '';
return unit.concat.apply(unit, xs);
})() : [];
// cons :: a -> [a] -> [a]
const cons = (x, xs) =>
Array.isArray(xs) ? (
[x].concat(xs)
) : (x + xs);
// enumFromTo :: Int -> Int -> [Int]
const enumFromTo = (m, n) =>
m <= n ? iterateUntil(
x => n <= x,
x => 1 + x,
m
) : [];
// fst :: (a, b) -> a
const fst = tpl => tpl[0];
// iterateUntil :: (a -> Bool) -> (a -> a) -> a -> [a]
const iterateUntil = (p, f, x) => {
const vs = [x];
let h = x;
while (!p(h))(h = f(h), vs.push(h));
return vs;
};
// map :: (a -> b) -> [a] -> [b]
const map = (f, xs) => xs.map(f);
// 'The mapAccumL function behaves like a combination of map and foldl;
// it applies a function to each element of a list, passing an accumulating
// parameter from left to right, and returning a final value of this
// accumulator together with the new list.' (See Hoogle)
// mapAccumL :: (acc -> x -> (acc, y)) -> acc -> [x] -> (acc, [y])
const mapAccumL = (f, acc, xs) =>
xs.reduce((a, x, i) => {
const pair = f(a[0], x, i);
return Tuple(pair[0], a[1].concat(pair[1]));
}, Tuple(acc, []));
// reverse :: [a] -> [a]
const reverse = xs =>
'string' !== typeof xs ? (
xs.slice(0).reverse()
) : xs.split('').reverse().join('');
// snd :: (a, b) -> b
const snd = tpl => tpl[1];
// tail :: [a] -> [a]
const tail = xs => 0 < xs.length ? xs.slice(1) : [];
// takeWhile :: (a -> Bool) -> [a] -> [a]
// takeWhile :: (Char -> Bool) -> String -> String
const takeWhile = (p, xs) => {
const lng = xs.length;
return 0 < lng ? xs.slice(
0,
until(
i => i === lng || !p(xs[i]),
i => 1 + i,
0
)
) : [];
};
// unlines :: [String] -> String
const unlines = xs => xs.join('\n');
// until :: (a -> Bool) -> (a -> a) -> a -> a
const until = (p, f, x) => {
let v = x;
while (!p(v)) v = f(v);
return v;
};
// MAIN ---
return main();
})();

25
Task/Zeckendorf-number-representation/Jq/zeckendorf-number-representation-1.jq Normal file
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def zeckendorf:
def fibs($n):
# input: [f(i-2), f(i-1)]
[1,1] | [recurse(select(.[1] < $n) | [.[1], add]) | .[1]] ;
# Emit an array of 0s and 1s corresponding to the Zeckendorf encoding
# $f should be the relevant Fibonacci numbers in increasing order.
def loop($f):
[ recurse(. as [$n, $ix]
| select( $ix > -1 )
| $f[$ix] as $next
| if $n >= $next
then [$n - $next, $ix-1, 1]
else [$n, $ix-1, 0]
end )
| .[2] // empty ]
# remove any superfluous leading 0:
# remove leading 0 if any unless length==1
| if length>1 and .[0] == 0 then .[1:] else . end ;
# state: [$n, index_in_fibs, digit ]
fibs(.) as $f
| [., ($f|length)-1]
| loop($f)
| join("") ;

1
Task/Zeckendorf-number-representation/Jq/zeckendorf-number-representation-2.jq Normal file
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range(0;21) | "\(.): \(zeckendorf)"

22
Task/Zeckendorf-number-representation/Jq/zeckendorf-number-representation-3.jq Normal file
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$ jq -n -r -f zeckendorf.jq
0: 0
1: 1
2: 10
3: 100
4: 101
5: 1000
6: 1001
7: 1010
8: 10000
9: 10001
10: 10010
11: 10100
12: 10101
13: 100000
14: 100001
15: 100010
16: 100100
17: 100101
18: 101000
19: 101001
20: 101010

6
Task/Zeckendorf-number-representation/Julia/zeckendorf-number-representation.julia Normal file
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function zeck(n)
n <= 0 && return 0
fib = [2,1]; while fib[1] < n unshift!(fib,sum(fib[1:2])) end
dig = Int[]; for f in fib f <= n ? (push!(dig,1); n = n-f;) : push!(dig,0) end
return dig[1] == 0 ? dig[2:end] : dig
end

27
Task/Zeckendorf-number-representation/Klingphix/zeckendorf-number-representation.klingphix Normal file
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include ..\Utilitys.tlhy
:listos
%i$ "" !i$
len [ get tostr $i$ chain !i$ ] for drop
$i$
;
:Zeckendorf %n !n
%i 0 !i %c 0 !c
[
$i 8 itob listos
"11" find not (
[ ( $c ":" 9 tochar ) lprint tonum ? $c 1 + !c ]
[drop]
) if
$i 1 + !i
]
[$c $n >] until
;
20 Zeckendorf
nl "End " input

39
Task/Zeckendorf-number-representation/Kotlin/zeckendorf-number-representation.kotlin Normal file
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// version 1.0.6
const val LIMIT = 46 // to stay within range of signed 32 bit integer
val fibs = fibonacci(LIMIT)
fun fibonacci(n: Int): IntArray {
if (n !in 2..LIMIT) throw IllegalArgumentException("n must be between 2 and $LIMIT")
val fibs = IntArray(n)
fibs[0] = 1
fibs[1] = 1
for (i in 2 until n) fibs[i] = fibs[i - 1] + fibs[i - 2]
return fibs
}
fun zeckendorf(n: Int): String {
if (n < 0) throw IllegalArgumentException("n must be non-negative")
if (n < 2) return n.toString()
var lastFibIndex = 1
for (i in 2..LIMIT)
if (fibs[i] > n) {
lastFibIndex = i - 1
break
}
var nn = n - fibs[lastFibIndex--]
val zr = StringBuilder("1")
for (i in lastFibIndex downTo 1)
if (fibs[i] <= nn) {
zr.append('1')
nn -= fibs[i]
} else {
zr.append('0')
}
return zr.toString()
}
fun main(args: Array<String>) {
println(" n z")
for (i in 0..20) println("${"%2d".format(i)} : ${zeckendorf(i)}")
}

27
Task/Zeckendorf-number-representation/Liberty-BASIC/zeckendorf-number-representation.basic Normal file
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samples = 20
call zecklist samples
print "Decimal","Zeckendorf"
for n = 0 to samples
print n, zecklist$(n)
next n
Sub zecklist inDEC
dim zecklist$(inDEC)
do
bin$ = dec2bin$(count)
if instr(bin$,"11") = 0 then
zecklist$(found) = bin$
found = found + 1
end if
count = count+1
loop until found = inDEC + 1
End sub
function dec2bin$(inDEC)
do
bin$ = str$(inDEC mod 2) + bin$
inDEC = int(inDEC/2)
loop until inDEC = 0
dec2bin$ = bin$
end function

29
Task/Zeckendorf-number-representation/Lingo/zeckendorf-number-representation-1.lingo Normal file
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-- Return the distinct Fibonacci numbers not greater than 'n'
on fibsUpTo (n)
fibList = []
last = 1
current = 1
repeat while current <= n
fibList.add(current)
nxt = last + current
last = current
current = nxt
end repeat
return fibList
end
-- Return the Zeckendorf representation of 'n'
on zeckendorf (n)
fib = fibsUpTo(n)
zeck = ""
repeat with pos = fib.count down to 1
if n >= fib[pos] then
zeck = zeck & "1"
n = n - fib[pos]
else
zeck = zeck & "0"
end if
end repeat
if zeck = "" then return "0"
return zeck
end

3
Task/Zeckendorf-number-representation/Lingo/zeckendorf-number-representation-2.lingo Normal file
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repeat with n = 0 to 20
put n & ": " & zeckendorf(n)
end repeat

79
Task/Zeckendorf-number-representation/Little-Man-Computer/zeckendorf-number-representation.lmc Normal file
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// Little Man Computer, for Rosetta Code.
// Writes Zeckendorf representations of numbers 0..20.
// Works with Peter Higginson's LMC simulator, except that
// user must intervene manually to capture all the output.
LDA c0 // initialize to N = 0
loop STA N
OUT // write N
LDA equals // then equals sign
OTC
BRA wr_zeck // then Zeckendorf rep
return LDA space // then space
OTC
LDA N // done maximum N?
SUB N_max
BRZ halt // yes, halt
LDA N // no, inc N and loop back
ADD c1
BRA loop
halt HLT
c0 DAT 0
N_max DAT 20
equals DAT 61
space DAT 32
// Routine to write Zeckendorf representation of number stored in N.
// Since LMC doesn't support subroutines, returns with "BRA return".
wr_zeck LDA N
SUB c1
BRP phase_1
// N = 0, special case
LDA ascii_0
OTC
BRA done
// N > 0. Phase 1: find largest Fibonacci number <= N
phase_1 STA res // res := N - 1
LDA c1 // initialize Fibonacci terms
STA a
STA b
loop_1 LDA res // here res = N - a (easy proof)
SUB b // is next Fibonacci a + b > N?
BRP next_fib // no, continue Fibonacci
BRA phase_2 // yes, on to phase 2
next_fib STA res // res := res - b
LDA a // (a, b) := (a + b, a)
ADD b
STA a
SUB b
STA b
BRA loop_1 // loop to test new (a, b)
// Phase 2: get Zeckendorf digits by winding Fibonacci back
phase_2 LDA ascii_1 // first digit must be 1
OTC
loop_2 LDA a // done when wound back to a = 1
SUB c1
BRZ done
LDA res // decide next Zeckendorf digit
SUB b // 0 if res < b, 1 if res >= b
BRP dig_is_1
LDA ascii_0
BRA wr_dig
dig_is_1 STA res // res := res - b
LDA ascii_1
wr_dig OTC // write Zeckendorf digit 0 or 1
LDA a // (a, b) := (b, a - b)
SUB b
STA b
LDA a
SUB b
STA a
BRA loop_2 // loop to test new (a, b)
done BRA return
N DAT
res DAT
a DAT
b DAT
c1 DAT 1
ascii_0 DAT 48
ascii_1 DAT 49
// end

51
Task/Zeckendorf-number-representation/Logo/zeckendorf-number-representation.logo Normal file
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; return the (N+1)th Fibonacci number (1,2,3,5,8,13,...)
to fib m
local "n
make "n sum :m 1
if [lessequal? :n 0] [output difference fib sum :n 2 fib sum :n 1]
global "_fib
if [not name? "_fib] [
make "_fib [1 1]
]
local "length
make "length count :_fib
while [greater? :n :length] [
make "_fib (lput (sum (last :_fib) (last (butlast :_fib))) :_fib)
make "length sum :length 1
]
output item :n :_fib
end
; return the binary Zeckendorf representation of a nonnegative number
to zeckendorf n
if [less? :n 0] [(throw "error [Number must be nonnegative.])]
(local "i "f "result)
make "i :n
make "f fib :i
while [less? :f :n] [make "i sum :i 1 make "f fib :i]
make "result "||
while [greater? :i 0] [
ifelse [greaterequal? :n :f] [
make "result lput 1 :result
make "n difference :n :f
] [
if [not empty? :result] [
make "result lput 0 :result
]
]
make "i difference :i 1
make "f fib :i
]
if [equal? :result "||] [
make "result 0
]
output :result
end
type zeckendorf 0
repeat 20 [
type word "| | zeckendorf repcount
]
print []
bye

33
Task/Zeckendorf-number-representation/Lua/zeckendorf-number-representation.lua Normal file
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-- Return the distinct Fibonacci numbers not greater than 'n'
function fibsUpTo (n)
local fibList, last, current, nxt = {}, 1, 1
while current <= n do
table.insert(fibList, current)
nxt = last + current
last = current
current = nxt
end
return fibList
end
-- Return the Zeckendorf representation of 'n'
function zeckendorf (n)
local fib, zeck = fibsUpTo(n), ""
for pos = #fib, 1, -1 do
if n >= fib[pos] then
zeck = zeck .. "1"
n = n - fib[pos]
else
zeck = zeck .. "0"
end
end
if zeck == "" then return "0" end
return zeck
end
-- Main procedure
print(" n\t| Zeckendorf(n)")
print(string.rep("-", 23))
for n = 0, 20 do
print(" " .. n, "| " .. zeckendorf(n))
end

6
Task/Zeckendorf-number-representation/Mathematica/zeckendorf-number-representation.math Normal file
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ZeckendorfRepresentation[0] = 0;
ZeckendorfRepresentation[n_Integer?Positive]:=
NumberDecompose[n, Reverse@Fibonacci@Range[2,1000]] // FromDigits
ZeckendorfRepresentation /@ Range[0, 20]

18
Task/Zeckendorf-number-representation/Nim/zeckendorf-number-representation.nim Normal file
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import strformat, strutils
proc z(n: Natural): string =
if n == 0: return "0"
var fib = @[2,1]
var n = n
while fib[0] < n: fib.insert(fib[0] + fib[1])
for f in fib:
if f <= n:
result.add '1'
dec n, f
else:
result.add '0'
if result[0] == '0':
result = result[1..result.high]
for i in 0 .. 20:
echo &"{i:>3} {z(i):>8}"

14
Task/Zeckendorf-number-representation/OCaml/zeckendorf-number-representation.ocaml Normal file
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let zeck n =
let rec enc x s = function
| h :: t when h <= x -> enc (x - h) (s ^ "1") t
| _ :: t -> enc x (s ^ "0") t
| _ -> s
and fib b a l =
if b > n
then enc (n - a) "1" l
else fib (b + a) b (a :: l)
in
if n = 0 then "0" else fib 2 1 []
let () =
for i = 0 to 20 do Printf.printf "%3u:%8s\n" i (zeck i) done

2
Task/Zeckendorf-number-representation/PARI-GP/zeckendorf-number-representation.parigp Normal file
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Z(n)=if(!n,print1(0));my(k=2);while(fibonacci(k)<=n,k++); forstep(i=k-1,2,-1,print1(if(fibonacci(i)<=n,n-=fibonacci(i);1,0)));print
for(n=0,20,Z(n))

22
Task/Zeckendorf-number-representation/PHP/zeckendorf-number-representation.php Normal file
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<?php
$m = 20;
$F = array(1,1);
while ($F[count($F)-1] <= $m)
$F[] = $F[count($F)-1] + $F[count($F)-2];
while ($n = $m--) {
while ($F[count($F)-1] > $n) array_pop($F);
$l = count($F)-1;
print "$n: ";
while ($n) {
if ($n >= $F[$l]) {
$n = $n - $F[$l];
print '1';
} else print '0';
--$l;
}
print str_repeat('0',$l);
print "\n";
}
?>

51
Task/Zeckendorf-number-representation/Pascal/zeckendorf-number-representation.pas Normal file
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program ZeckendorfRep_RC;
{$mode objfpc}{$H+}
uses SysUtils;
// Return Zeckendorf representation of the passed-in cardinal.
function ZeckRep( C : cardinal) : string;
var
a, b, rem : cardinal;
j, nrDigits: integer;
begin
// Case C = 0 has to be treated specially
if (C = 0) then begin
result := '0';
exit;
end;
// Find largest Fibonacci number not exceeding C
a := 1;
b := 1;
nrDigits := 1;
rem := C - 1;
while (rem >= b) do begin
dec( rem, b);
inc( a, b);
b := a - b;
inc( nrDigits);
end;
// Fill in digits by reversing Fibonacci back to start
SetLength( result, nrDigits);
j := 1;
result[j] := '1';
for j := 2 to nrDigits do begin
if (rem >= b) then begin
dec( rem, b);
result[j] := '1';
end
else result[j] := '0';
b := a - b;
dec( a, b);
end;
// Assert((a = 1) and (b = 1)); // optional check
end;
// Main routine
var
C : cardinal;
begin
for C := 1 to 20 do
WriteLn( SysUtils.Format( '%2d: %s', [C, ZeckRep(C)]));
end.

23
Task/Zeckendorf-number-representation/Perl/zeckendorf-number-representation.pl Normal file
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my @fib;
sub fib {
my $n = shift;
return 1 if $n < 2;
return $fib[$n] //= fib($n-1)+fib($n-2);
}
sub zeckendorf {
my $n = shift;
return "0" unless $n;
my $i = 1;
$i++ while fib($i) <= $n;
my $z = '';
while( --$i ) {
$z .= "0", next if fib( $i ) > $n;
$z .= "1";
$n -= fib( $i );
}
return $z;
}
printf "%4d: %8s\n", $_, zeckendorf($_) for 0..20;

19
Task/Zeckendorf-number-representation/Phix/zeckendorf-number-representation.phix Normal file
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(phixonline)-->
<span style="color: #008080;">function</span> <span style="color: #000000;">zeckendorf</span><span style="color: #0000FF;">(</span><span style="color: #004080;">integer</span> <span style="color: #000000;">n</span><span style="color: #0000FF;">)</span>
<span style="color: #004080;">integer</span> <span style="color: #000000;">r</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">c</span>
<span style="color: #004080;">sequence</span> <span style="color: #000000;">fib</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1</span><span style="color: #0000FF;">}</span>
<span style="color: #008080;">while</span> <span style="color: #000000;">fib</span><span style="color: #0000FF;">[$]<</span><span style="color: #000000;">n</span> <span style="color: #008080;">do</span>
<span style="color: #000000;">fib</span> <span style="color: #0000FF;">&=</span> <span style="color: #000000;">fib</span><span style="color: #0000FF;">[$]</span> <span style="color: #0000FF;">+</span> <span style="color: #000000;">fib</span><span style="color: #0000FF;">[$-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">while</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">fib</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">to</span> <span style="color: #000000;">2</span> <span style="color: #008080;">by</span> <span style="color: #0000FF;">-</span><span style="color: #000000;">1</span> <span style="color: #008080;">do</span>
<span style="color: #000000;">c</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">n</span><span style="color: #0000FF;">>=</span><span style="color: #000000;">fib</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]</span>
<span style="color: #000000;">r</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">r</span><span style="color: #0000FF;">+</span><span style="color: #000000;">c</span>
<span style="color: #000000;">n</span> <span style="color: #0000FF;">-=</span> <span style="color: #000000;">c</span><span style="color: #0000FF;">*</span><span style="color: #000000;">fib</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #008080;">return</span> <span style="color: #000000;">r</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">0</span> <span style="color: #008080;">to</span> <span style="color: #000000;">20</span> <span style="color: #008080;">do</span>
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"%2d: %7b\n"</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">i</span><span style="color: #0000FF;">,</span><span style="color: #000000;">zeckendorf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">i</span><span style="color: #0000FF;">)})</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<!--

21
Task/Zeckendorf-number-representation/Phixmonti/zeckendorf-number-representation.phixmonti Normal file
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def Zeckendorf /# n -- #/
0 var i 0 var c 1 1 2 tolist var pattern
true
while
i 8 int>bit reverse
pattern find
not if
c print ":\t" print print nl
dup c == if
false
else
c 1 + var c
true
endif
endif
i 1 + var i
endwhile
drop
enddef
20 Zeckendorf

61
Task/Zeckendorf-number-representation/Picat/zeckendorf-number-representation-1.picat Normal file
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go =>
foreach(Num in 0..20)
zeckendorf_cp(Num,X,F),
Nums = [F[I] : I in 1..X.length, X[I] = 1],
printf("%2d %6s %w\n",Num, rep(X),Nums),
end,
nl.
zeckendorf_cp(Num, X,F) =>
F = get_fibs(Num).reverse(),
N = F.length,
X = new_list(N),
X :: 0..1,
% From the task description:
% """
% For a true Zeckendorf number there is the added restriction that
% no two consecutive Fibonacci numbers can be used which leads to
% the former unique solution.
% """
foreach(I in 2..N)
X[I-1] #= 1 #=> X[I] #= 0
end,
scalar_product(F,X,Num),
solve([ff,split],X).
%
% Fibonacci numbers
%
table
fib(0) = 0.
fib(1) = 1.
fib(N) = fib(N-1) + fib(N-2).
%
% Remove leading 0's and stringify it
%
rep(X) = Str =>
First = 1,
if X.length > 1, X[First] = 0 then
while (X[First] == 0)
First := First + 1
end
end,
Str = [X[I].to_string() : I in First..X.length].join('').
%
% Return a list of fibs <= N
%
get_fibs(N) = Fibs =>
I = 2,
Fib = fib(I),
Fibs1 = [Fib],
while (Fib < N)
I := I + 1,
Fib := fib(I),
Fibs1 := Fibs1 ++ [Fib]
end,
Fibs = Fibs1.

24
Task/Zeckendorf-number-representation/Picat/zeckendorf-number-representation-2.picat Normal file
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go2 =>
foreach(Num in 0..20)
zeckendorf2(Num,X,F),
Nums = [F[I] : I in 1..X.length, X[I]= 1],
printf("%2d %6s %w\n",Num, rep(X),Nums)
end,
nl.
zeckendorf2(0, [0],[0]).
zeckendorf2(Num, X,F) :-
Fibs = get_fibs(Num),
I = Fibs.length,
N = Num,
X1 = [],
while (I > 0)
Fib := Fibs[I],
X1 := X1 ++ [cond(Fib > N,0,1)],
if Fib <= N then
N := N - Fib
end,
I := I - 1
end,
X = X1,
F = Fibs.reverse().

31
Task/Zeckendorf-number-representation/PicoLisp/zeckendorf-number-representation.l Normal file
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(de fib (N)
(let Fibs (1 1)
(while (>= N (+ (car Fibs) (cadr Fibs)))
(push 'Fibs (+ (car Fibs) (cadr Fibs))) )
(uniq Fibs) ) )
(de zecken1 (N)
(make
(for I (fib N)
(if (> I N)
(link 0)
(link 1)
(dec 'N I) ) ) ) )
(de zecken2 (N)
(make
(when (=0 N) (link 0))
(for I (fib N)
(when (<= I N)
(link I)
(dec 'N I) ) ) ) )
(for (N 0 (> 21 N) (inc N))
(tab (2 4 6 2 -10)
N
" -> "
(zecken1 N)
" "
(glue " + " (zecken2 N)) ) )
(bye)

37
Task/Zeckendorf-number-representation/PlainTeX/zeckendorf-number-representation.tex Normal file
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\def\genfibolist#1{% #creates the fibo list which sum>=#1
\let\fibolist\empty\def\targetsum{#1}\def\fibosum{0}%
\genfibolistaux1,1\relax
}
\def\genfibolistaux#1,#2\relax{%
\ifnum\fibosum<\targetsum\relax
\edef\fibosum{\number\numexpr\fibosum+#2}%
\edef\fibolist{#2,\fibolist}%
\edef\tempfibo{\noexpand\genfibolistaux#2,\number\numexpr#1+#2\relax\relax}%
\expandafter\tempfibo
\fi
}
\def\zeckendorf#1{\expandafter\zeckendorfaux\fibolist,\relax#1\relax\relax0}
\def\zeckendorfaux#1,#2\relax#3\relax#4\relax#5{%
\ifx\relax#2\relax
#4%
\else
\ifnum#3<#1
\edef\temp{#2\relax#3\relax#4\ifnum#5=1 0\fi\relax#5}%
\else
\edef\temp{#2\relax\number\numexpr#3-#1\relax\relax#41\relax1}%
\fi
\expandafter\expandafter\expandafter\zeckendorfaux\expandafter\temp
\fi
}
\newcount\ii
\def\listzeckendorf#1{%
\genfibolist{#1}%
\ii=0
\loop
\ifnum\ii<#1
\advance\ii1
\number\ii: \zeckendorf\ii\endgraf
\repeat
}
\listzeckendorf{20}% any integer accepted
\bye

26
Task/Zeckendorf-number-representation/PowerShell/zeckendorf-number-representation-1.psh Normal file
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function Get-ZeckendorfNumber ( $N )
{
# Calculate relevant portation of Fibonacci series
$Fib = @( 1, 1 )
While ( $Fib[-1] -lt $N ) { $Fib += $Fib[-1] + $Fib[-2] }
# Start with 0
$ZeckendorfNumber = 0
# For each number in the relevant portion of Fibonacci series
For ( $i = $Fib.Count - 1; $i -gt 0; $i-- )
{
# If Fibonacci number is less than or equal to remainder of N
If ( $Fib[$i] -le $N )
{
# Double Z number and add 1 (equivalent to adding a '1' to the end of a binary number)
$ZeckendorfNumber = $ZeckendorfNumber * 2 + 1
# Reduce N by Fibonacci number, skip next Fibonacci number
$N -= $Fib[$i--]
}
# If were aren't finished yet, double Z number
# (equivalent to adding a '0' to the end of a binary number)
If ( $i ) { $ZeckendorfNumber *= 2 }
}
return $ZeckendorfNumber
}

2
Task/Zeckendorf-number-representation/PowerShell/zeckendorf-number-representation-2.psh Normal file
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# Get Zeckendorf numbers through 20, convert to binary for display
0..20 | ForEach { [convert]::ToString( ( Get-ZeckendorfNumber $_ ), 2 ) }

26
Task/Zeckendorf-number-representation/PureBasic/zeckendorf-number-representation.basic Normal file
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Procedure.s zeck(n.i)
Dim f.i(1) : Define i.i=1, o$
f(0)=1 : f(1)=1
While f(i)<n
i+1 : ReDim f(ArraySize(f())+1) : f(i)=f(i-1)+f(i-2)
Wend
For i=i To 1 Step -1
If n>=f(i) : o$+"1" : n-f(i) : Else : o$+"0" : EndIf
Next
If Len(o$)>1 : o$=LTrim(o$,"0") : EndIf
ProcedureReturn o$
EndProcedure
Define n.i, t$
OpenConsole("Zeckendorf number representation")
PrintN(~"\tNr.\tZeckendorf")
For n=0 To 20
t$=zeck(n)
If FindString(t$,"11")
PrintN("Error: n= "+Str(n)+~"\tZeckendorf= "+t$)
Break
Else
PrintN(~"\t"+RSet(Str(n),3," ")+~"\t"+RSet(t$,7," "))
EndIf
Next
Input()

34
Task/Zeckendorf-number-representation/Python/zeckendorf-number-representation-1.py Normal file
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def fib():
memo = [1, 2]
while True:
memo.append(sum(memo))
yield memo.pop(0)
def sequence_down_from_n(n, seq_generator):
seq = []
for s in seq_generator():
seq.append(s)
if s >= n: break
return seq[::-1]
def zeckendorf(n):
if n == 0: return [0]
seq = sequence_down_from_n(n, fib)
digits, nleft = [], n
for s in seq:
if s <= nleft:
digits.append(1)
nleft -= s
else:
digits.append(0)
assert nleft == 0, 'Check all of n is accounted for'
assert sum(x*y for x,y in zip(digits, seq)) == n, 'Assert digits are correct'
while digits[0] == 0:
# Remove any zeroes padding L.H.S.
digits.pop(0)
return digits
n = 20
print('Fibonacci digit multipliers: %r' % sequence_down_from_n(n, fib))
for i in range(n + 1):
print('%3i: %8s' % (i, ''.join(str(d) for d in zeckendorf(i))))

15
Task/Zeckendorf-number-representation/Python/zeckendorf-number-representation-2.py Normal file
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n = 20
def z(n):
if n == 0 : return [0]
fib = [2,1]
while fib[0] < n: fib[0:0] = [sum(fib[:2])]
dig = []
for f in fib:
if f <= n:
dig, n = dig + [1], n - f
else:
dig += [0]
return dig if dig[0] else dig[1:]
for i in range(n + 1):
print('%3i: %8s' % (i, ''.join(str(d) for d in z(i))))

38
Task/Zeckendorf-number-representation/Quackery/zeckendorf-number-representation.quackery Normal file
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[ 2 base put
echo
base release ] is binecho ( n --> )
[ 0 swap ' [ 2 1 ]
[ 2dup 0 peek < iff
[ behead drop ]
done
dup 0 peek
over 1 peek
+ swap join again ]
witheach
[ rot 1 << unrot
2dup < iff drop
else
[ -
dip
[ 1 | ] ] ]
drop ] is n->z ( n --> z )
[ 0 temp put
1 1 rot
[ dup while
dup 1 & if
[ over
temp tally ]
1 >>
dip [ tuck + ]
again ]
2drop drop
temp take ] is z->n ( z --> n )
21 times
[ i^ dup echo
say " -> "
n->z dup binecho
say " -> "
z->n echo cr ]

56
Task/Zeckendorf-number-representation/QuickBASIC/zeckendorf-number-representation.basic Normal file
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' Zeckendorf number representation
DECLARE FUNCTION ToZeckendorf$ (N%)
' The maximum Fibonacci number that can fit in a
' 32 bit number is Fib&(45)
CONST MAXFIBINDEX% = 45, TRUE% = -1, FALSE% = 0
DIM SHARED Fib&(1 TO MAXFIBINDEX%)
Fib&(1) = 1: Fib&(2) = 2
FOR I% = 3 TO MAXFIBINDEX%
Fib&(I%) = Fib&(I% - 1) + Fib&(I% - 2)
NEXT I%
FOR I% = 0 TO 20
SixChars$ = SPACE$(6)
RSET SixChars$ = ToZeckendorf$(I%)
PRINT USING "### "; I%; : PRINT SixChars$
NEXT I%
END
FUNCTION ToZeckendorf$ (N%)
' returns the Zeckendorf representation of N% or "?" if one cannot be found
IF N% = 0 THEN
ToZeckendorf$ = "0"
ELSE
Result$ = ""
FPos% = MAXFIBINDEX%
Rest% = ABS(N%)
' Find the first non-zero Zeckendorf digit
WHILE FPos% > 1 AND Rest% < Fib&(FPos%)
FPos% = FPos% - 1
WEND
' If we found a digit, build the representation
IF FPos% >= 1 THEN ' have a digit
SkipDigit% = FALSE%
WHILE FPos% >= 1
IF Rest% <= 0 THEN
Result$ = Result$ + "0"
ELSEIF SkipDigit% THEN ' we used the previous digit
SkipDigit% = FALSE%
Result$ = Result$ + "0"
ELSEIF Rest% < Fib&(FPos%) THEN ' cannot use the digit at FPos%
SkipDigit% = FALSE%
Result$ = Result$ + "0"
ELSE ' can use this digit
SkipDigit% = TRUE%
Result$ = Result$ + "1"
Rest% = Rest% - Fib&(FPos%)
END IF
FPos% = FPos% - 1
WEND
END IF
IF Rest% = 0 THEN
ToZeckendorf$ = Result$
ELSE
ToZeckendorf$ = "?"
END IF
END IF
END FUNCTION

44
Task/Zeckendorf-number-representation/R/zeckendorf-number-representation.r Normal file
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zeckendorf <- function(number) {
# Get an upper limit on Fibonacci numbers needed to cover number
indexOfFibonacciNumber <- function(n) {
if (n < 1) {
2
} else {
Phi <- (1 + sqrt(5)) / 2
invertClosedFormula <- log(n * sqrt(5)) / log(Phi)
ceiling(invertClosedFormula)
}
}
upperLimit <- indexOfFibonacciNumber(number)
# Return the sequence as digits, sorted descending
fibonacciSequenceDigits <- function(n) {
fibGenerator <- function(f, ...) { c(f[2], sum(f)) }
fibSeq <- Reduce(fibGenerator, 1:n, c(0,1), accumulate=TRUE)
fibNums <- unlist(lapply(fibSeq, head, n=1))
# drop last F0 and F1 and reverse sequence
rev(fibNums[-2:-1])
}
digits <- fibonacciSequenceDigits(upperLimit)
isInNumber <- function(digit) {
if (number >= digit) {
number <<- number - digit
1
} else {
0
}
}
zeckSeq <- Map(isInNumber, digits)
# drop leading 0 and convert to String
gsub("^0+1", "1", paste(zeckSeq, collapse=""))
}
print(unlist(lapply(0:20, zeckendorf)))

22
Task/Zeckendorf-number-representation/REXX/zeckendorf-number-representation-1.rexx Normal file
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/* REXX ***************************************************************
* 11.10.2012 Walter Pachl
**********************************************************************/
fib='13 8 5 3 2 1'
Do i=6 To 1 By -1 /* Prepare Fibonacci Numbers */
Parse Var fib f.i fib /* f.1 ... f.7 */
End
Do n=0 To 20 /* for all numbers in the task */
m=n /* copy of number */
r='' /* result for n */
Do i=6 To 1 By -1 /* loop through numbers */
If m>=f.i Then Do /* f.i must be used */
r=r||1 /* 1 into result */
m=m-f.i /* subtract */
End
Else /* f.i is larger than the rest */
r=r||0 /* 0 into result */
End
r=strip(r,'L','0') /* strip leading zeros */
If r='' Then r='0' /* take care of 0 */
Say right(n,2)': 'right(r,6) /* show result */
End

18
Task/Zeckendorf-number-representation/REXX/zeckendorf-number-representation-2.rexx Normal file
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/*REXX program calculates and displays the first N Zeckendorf numbers. */
numeric digits 100000 /*just in case user gets real ka─razy. */
parse arg N . /*let the user specify the upper limit.*/
if N=='' | N=="," then n=20; w= length(N) /*Not specified? Then use the default.*/
@.1= 1 /*start the array with 1 and 2. */
@.2= 2; do #=3 until #>=N; p= #-1; pp= #-2 /*build a list of Fibonacci numbers. */
@.#= @.p + @.pp /*sum the last two Fibonacci numbers. */
end /*#*/ /* [↑] #: contains a Fibonacci list.*/
do j=0 to N; parse var j x z /*task: process zero ──► N numbers.*/
do k=# by -1 for #; _= @.k /*process all the Fibonacci numbers. */
if x>=_ then do; z= z'1' /*is X>the next Fibonacci #? Append 1.*/
x= x - _ /*subtract this Fibonacci # from index.*/
end
else z= z'0' /*append zero (0) to the Fibonacci #. */
end /*k*/
say ' Zeckendorf' right(j, w) "=" right(z+0, 30) /*display a number.*/
end /*j*/ /*stick a fork in it, we're all done. */

10
Task/Zeckendorf-number-representation/REXX/zeckendorf-number-representation-3.rexx Normal file
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/*REXX program calculates and displays the first N Zeckendorf numbers. */
numeric digits 100000 /*just in case user gets real ka─razy. */
parse arg N . /*let the user specify the upper limit.*/
if N=='' | N=="," then n=20; w= length(N) /*Not specified? Then use the default.*/
z=0 /*the index of a Zeckendorf number. */
do j=0 until z>N; _=x2b( d2x(j) ) /*task: process zero ──► N. */
if pos(11, _) \== 0 then iterate /*are there two consecutive ones (1s) ?*/
say ' Zeckendorf' right(z, w) "=" right(_+0, 30) /*display a number.*/
z= z + 1 /*bump the Zeckendorf number counter.*/
end /*j*/ /*stick a fork in it, we're all done. */

17
Task/Zeckendorf-number-representation/Racket/zeckendorf-number-representation-1.rkt Normal file
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#lang racket (require math)
(define (fibs n)
(reverse
(for/list ([i (in-naturals 2)] #:break (> (fibonacci i) n))
(fibonacci i))))
(define (zechendorf n)
(match/values
(for/fold ([n n] [xs '()]) ([f (fibs n)])
(if (> f n)
(values n (cons 0 xs))
(values (- n f) (cons 1 xs))))
[(_ xs) (reverse xs)]))
(for/list ([n 21])
(list n (zechendorf n)))

21
Task/Zeckendorf-number-representation/Racket/zeckendorf-number-representation-2.rkt Normal file
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'((0 ())
(1 (1))
(2 (1 0))
(3 (1 0 0))
(4 (1 0 1))
(5 (1 0 0 0))
(6 (1 0 0 1))
(7 (1 0 1 0))
(8 (1 0 0 0 0))
(9 (1 0 0 0 1))
(10 (1 0 0 1 0))
(11 (1 0 1 0 0))
(12 (1 0 1 0 1))
(13 (1 0 0 0 0 0))
(14 (1 0 0 0 0 1))
(15 (1 0 0 0 1 0))
(16 (1 0 0 1 0 0))
(17 (1 0 0 1 0 1))
(18 (1 0 1 0 0 0))
(19 (1 0 1 0 0 1))
(20 (1 0 1 0 1 0)))

10
Task/Zeckendorf-number-representation/Raku/zeckendorf-number-representation.raku Normal file
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printf "%2d: %8s\n", $_, zeckendorf($_) for 0 .. 20;
multi zeckendorf(0) { '0' }
multi zeckendorf($n is copy) {
constant FIBS = (1,2, *+* ... *).cache;
[~] map {
$n -= $_ if my $digit = $n >= $_;
+$digit;
}, reverse FIBS ...^ * > $n;
}

27
Task/Zeckendorf-number-representation/Ring/zeckendorf-number-representation.ring Normal file
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# Project : Zeckendorf number representation
see "0 0" + nl
for n = 1 to 20
see "" + n + " " + zeckendorf(n) + nl
next
func zeckendorf(n)
fib = list(45)
fib[1] = 1
fib[2] = 1
i = 2
o = ""
while fib[i] <= n
i = i + 1
fib[i] = fib[i-1] + fib[i-2]
end
while i != 2
i = i - 1
if n >= fib[i]
o = o + "1"
n = n - fib[i]
else
o = o + "0"
ok
end
return o

11
Task/Zeckendorf-number-representation/Ruby/zeckendorf-number-representation-1.rb Normal file
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def zeckendorf
return to_enum(__method__) unless block_given?
x = 0
loop do
bin = x.to_s(2)
yield bin unless bin.include?("11")
x += 1
end
end
zeckendorf.take(21).each_with_index{|x,i| puts "%3d: %8s"% [i, x]}

18
Task/Zeckendorf-number-representation/Ruby/zeckendorf-number-representation-2.rb Normal file
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def zeckendorf(n)
return 0 if n.zero?
fib = [1,2]
fib << fib[-2] + fib[-1] while fib[-1] < n
dig = ""
fib.reverse_each do |f|
if f <= n
dig, n = dig + "1", n - f
else
dig += "0"
end
end
dig.to_i
end
for i in 0..20
puts '%3d: %8d' % [i, zeckendorf(i)]
end

5
Task/Zeckendorf-number-representation/Ruby/zeckendorf-number-representation-3.rb Normal file
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def zeckendorf(n)
0.step.lazy.map { |x| x.to_s(2) }.reject { |z| z.include?("11") }.first(n)
end
zeckendorf(21).each_with_index{ |x,i| puts "%3d: %8s"% [i, x] }

29
Task/Zeckendorf-number-representation/Scala/zeckendorf-number-representation.scala Normal file
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@ -0,0 +1,29 @@
def zNum( n:BigInt ) : String = {
if( n == 0 ) return "0" // Short-circuit this and return zero if we were given zero
val v = n.abs
val fibs : Stream[BigInt] = { def series(i:BigInt,j:BigInt):Stream[BigInt] = i #:: series(j, i+j); series(1,0).tail.tail.tail }
def z( v:BigInt ) : List[BigInt] = if(v == 0) List() else {val m = fibs(fibs.indexWhere(_>v) - 1); m :: z(v-m)}
val zv = z(v)
// Walk the list of fibonacci numbers from the number that matches the most significant down to 1,
// if the zeckendorf matchs then yield '1' otherwise '0'
val s = (for( i <- (fibs.indexWhere(_==zv(0)) to 0 by -1) ) yield {
if( zv.contains(fibs(i))) "1" else "0"
}).mkString
if( n < 0 ) "-" + s // Using a negative-sign instead of twos-complement
else s
}
// A little test...
(0 to 20) foreach( i => print( zNum(i) + "\n" ) )

30
Task/Zeckendorf-number-representation/Scheme/zeckendorf-number-representation.ss Normal file
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(import (rnrs))
(define (getFibList maxNum n1 n2 fibs)
(if (> n2 maxNum)
fibs
(getFibList maxNum n2 (+ n1 n2) (cons n2 fibs))))
(define (getZeckendorf num)
(if (<= num 0)
"0"
(let ((fibs (getFibList num 1 2 (list 1))))
(getZeckString "" num fibs))))
(define (getZeckString zeck num fibs)
(let* ((curFib (car fibs))
(placeZeck (>= num curFib))
(outString (string-append zeck (if placeZeck "1" "0")))
(outNum (if placeZeck (- num curFib) num)))
(if (null? (cdr fibs))
outString
(getZeckString outString outNum (cdr fibs)))))
(let loop ((i 0))
(when (<= i 20)
(for-each
(lambda (item)
(display item))
(list "Z(" i "):\t" (getZeckendorf i)))
(newline)
(loop (+ i 1))))

21
Task/Zeckendorf-number-representation/Sidef/zeckendorf-number-representation.sidef Normal file
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@ -0,0 +1,21 @@
func fib(n) is cached {
n < 2 ? 1
 : (fib(n-1) + fib(n-2))
}
func zeckendorf(n) {
n == 0 && return '0'
var i = 1
++i while (fib(i) <= n)
gather {
while (--i > 0) {
var f = fib(i)
f > n ? (take '0')
 : (take '1'; n -= f)
}
}.join
}
for n (0..20) {
printf("%4d: %8s\n", n, zeckendorf(n))
}

37
Task/Zeckendorf-number-representation/Simula/zeckendorf-number-representation.simula Normal file
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BEGIN
INTEGER N, F0, F1, F2, D;
N := 20;
COMMENT CALCULATE D FROM ANY GIVEN N ;
F1 := 1; F2 := 2; F0 := F1 + F2; D := 2;
WHILE F0 < N DO BEGIN
F1 := F2; F2 := F0; F0 := F1 + F2; D := D + 1;
END;
BEGIN
COMMENT Sinclair ZX81 BASIC Solution ;
TEXT Z1, S1;
INTEGER I, J, Z;
INTEGER ARRAY F(1:D); ! 10 dim f(6) ;
F(1) := 1; ! 20 let f(1)=1 ;
F(2) := 2; ! 30 let f(2)=2 ;
FOR I := 3 STEP 1 UNTIL D DO BEGIN ! 40 for i=3 to 6 ;
F(I) := F(I-2) + F(I-1); ! 50 let f(i)=f(i-2)+f(i-1) ;
END; ! 60 next i ;
FOR I := 0 STEP 1 UNTIL N DO BEGIN ! 70 for i=0 to 20 ;
Z1 :- ""; ! 80 let z$="" ;
S1 :- " "; ! 90 let s$=" " ;
Z := I; ! 100 let z=i ;
FOR J := D STEP -1 UNTIL 1 DO BEGIN ! 110 for j=6 to 1 step -1 ;
IF J=1 THEN S1 :- "0"; ! 120 if j=1 then let s$="0" ;
IF NOT (Z<F(J)) THEN BEGIN ! 130 if z<f(j) then goto 180 ;
Z1 :- Z1 & "1"; ! 140 let z$=z$+"1" ;
Z := Z-F(J); ! 150 let z=z-f(j) ;
S1 :- "0"; ! 160 let s$="0" ;
END ELSE ! 170 goto 190 ;
Z1 :- Z1 & S1; ! 180 let z$=z$+s$ ;
END; ! 190 next j ;
OUTINT(I, 0); OUTCHAR(' '); ! 200 print i ; !" "; !;
IF I<10 THEN OUTCHAR(' '); ! 210 if i<10 then print " "; !;
OUTTEXT(Z1); OUTIMAGE; ! 220 print z$ ;
END; ! 230 next i ;
END;
END

23
Task/Zeckendorf-number-representation/Sinclair-ZX81-BASIC/zeckendorf-number-representation.basic Normal file
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10 DIM F(6)
20 LET F(1)=1
30 LET F(2)=2
40 FOR I=3 TO 6
50 LET F(I)=F(I-2)+F(I-1)
60 NEXT I
70 FOR I=0 TO 20
80 LET Z$=""
90 LET S$=" "
100 LET Z=I
110 FOR J=6 TO 1 STEP -1
120 IF J=1 THEN LET S$="0"
130 IF Z<F(J) THEN GOTO 180
140 LET Z$=Z$+"1"
150 LET Z=Z-F(J)
160 LET S$="0"
170 GOTO 190
180 LET Z$=Z$+S$
190 NEXT J
200 PRINT I;" ";
210 IF I<10 THEN PRINT " ";
220 PRINT Z$
230 NEXT I

33
Task/Zeckendorf-number-representation/Standard-ML/zeckendorf-number-representation-1.ml Normal file
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val zeckList = fn from => fn to =>
let
open IntInf
val rec npow = fn n => fn 0 => fromInt 1 | m => n* (npow n (m-1)) ;
val fib = fn 0 => 1 | 1 => 1 | n => let val rec fb = fn x => fn y => fn 1=>y | n=> fb y (x+y) (n-1) in
fb 0 1 n
end;
val argminfi = fn n => (* lowest k with fibonacci number over n *)
let
val rec afb = fn k => if fib k > n then k else afb (k+1)
in
afb 0
end;
val Zeck = fn n =>
let
val rec calzk = fn (0,z) => (0,z)
| (n,z) => let val k = argminfi n in
calzk ( n - fib (k-1) , z + (npow 10 (k-3) ) )
end
in
#2 (calzk (n,0))
end
in
List.tabulate (toInt ( to - from) ,
fn i:Int.int => ( from + (fromInt i),
Zeck ( from + (fromInt i) )))
end;

25
Task/Zeckendorf-number-representation/Standard-ML/zeckendorf-number-representation-2.ml Normal file
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@ -0,0 +1,25 @@
List.app ( fn e => print ( (IntInf.toString (#1 e)) ^" : "^ (IntInf.toString (#2 e)) ^ "\n" )) (zeckList 1 21) ;
1 : 1
2 : 10
3 : 100
4 : 101
5 : 1000
6 : 1001
7 : 1010
8 : 10000
9 : 10001
10 : 10010
11 : 10100
12 : 10101
13 : 100000
14 : 100001
15 : 100010
16 : 100100
17 : 100101
18 : 101000
19 : 101001
20 : 101010
zeckList 0x21e320a3 0x21e320a4 ;
val it = [(568533155, 100100100101001001001000000100100010100101)]:
: (IntInf.int * IntInf.int) list

29
Task/Zeckendorf-number-representation/Tcl/zeckendorf-number-representation-1.tcl Normal file
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package require Tcl 8.5
# Generates the Fibonacci sequence (starting at 1) up to the largest item that
# is no larger than the target value. Could use tricks to precompute, but this
# is actually a pretty cheap linear operation.
proc fibseq target {
set seq {}; set prev 1; set fib 1
for {set n 1;set i 1} {$fib <= $target} {incr n} {
for {} {$i < $n} {incr i} {
lassign [list $fib [incr fib $prev]] prev fib
}
if {$fib <= $target} {
lappend seq $fib
}
}
return $seq
}
# Produce the given Zeckendorf number.
proc zeckendorf n {
# Special case: only value that begins with 0
if {$n == 0} {return 0}
set zs {}
foreach f [lreverse [fibseq $n]] {
lappend zs [set z [expr {$f <= $n}]]
if {$z} {incr n [expr {-$f}]}
}
return [join $zs ""]
}

3
Task/Zeckendorf-number-representation/Tcl/zeckendorf-number-representation-2.tcl Normal file
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for {set i 0} {$i <= 20} {incr i} {
puts [format "%2d:%9s" $i [zeckendorf $i]]
}

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