Kolakoski sequence

You are encouraged to You are encouraged to solve this task according to the task description, using any language you may know.

The Kolakoski sequence is an infinite sequence of natural numbers, (excluding zero); with the property that:

if you form a new sequence from the counts of runs of the same number in the first sequence, this new sequence is the same as the first sequence.

Example

This is not a Kolakoski sequence:

1,1,2,2,2,1,2,2,1,2,...

Its sequence of run counts, (sometimes called a run length encoding, (RLE); but a true RLE also gives the character that each run encodes), is calculated like this:

Starting from the leftmost number of the sequence we have 2 ones, followed by 3 twos, then 1 ones, 2 twos, 1 one, ...

The above gives the RLE of:

2, 3, 1, 2, 1, ...

The original sequence is different from its RLE in this case. It would be the same for a true Kolakoski sequence.

Creating a Kolakoski sequence

Lets start with the two numbers (1, 2) that we will cycle through; i.e. they will be used in this order:

1,2,1,2,1,2,....

We start the sequence s with the first item from the cycle c :

1 An index, k , into the, (expanding), sequence will step, or index through each item of the sequence s from the first, at its own rate.



We will arrange that the k 'th item of s states how many times the last item of s should appear at the end of s .

We started s with 1 and therefore s[k] states that it should appear only the 1 time.



Increment k Get the next item from c and append it to the end of sequence s . s will then become:

1, 2 k was moved to the second item in the list and s[k] states that it should appear two times, so append another of the last item to the sequence s :

1, 2,2 Increment k Append the next item from the cycle to the list:

1, 2,2, 1 k is now at the third item in the list that states that the last item should appear twice so add another copy of the last item to the sequence s :

1, 2,2, 1,1 increment k

...

Note that the RLE of 1, 2, 2, 1, 1, ... begins 1, 2, 2 which is the beginning of the original sequence. The generation algorithm ensures that this will always be the case.

Task

Create a routine/proceedure/function/... that given an initial ordered list/array/tuple etc of the natural numbers (1, 2) , returns the next number from the list when accessed in a cycle. Create another routine that when given the initial ordered list (1, 2) and the minimum length of the sequence to generate; uses the first routine and the algorithm above, to generate at least the requested first members of the kolakoski sequence. Create a routine that when given a sequence, creates the run length encoding of that sequence (as defined above) and returns the result of checking if sequence starts with the exact members of its RLE. (But note, due to sampling, do not compare the last member of the RLE). Show, on this page, (compactly), the first 20 members of the sequence generated from (1, 2) Check the sequence againt its RLE. Show, on this page, the first 20 members of the sequence generated from (2, 1) Check the sequence againt its RLE. Show, on this page, the first 30 members of the Kolakoski sequence generated from (1, 3, 1, 2) Check the sequence againt its RLE. Show, on this page, the first 30 members of the Kolakoski sequence generated from (1, 3, 2, 1) Check the sequence againt its RLE.

(There are rules on generating Kolakoski sequences from this method that are broken by the last example)

Translation of: Kotlin

#include <stdio.h>

#include <stdlib.h>



#define TRUE 1

#define FALSE 0



typedef int bool ;



int next_in_cycle ( int * c , int len , int index ) {

return c [ index % len ] ;

}



void kolakoski ( int * c , int * s , int clen , int slen ) {

int i = 0 , j , k = 0 ;

while ( TRUE ) {

s [ i ] = next_in_cycle ( c , clen , k ) ;

if ( s [ k ] > 1 ) {

for ( j = 1 ; j < s [ k ] ; ++ j ) {

if ( ++ i == slen ) return ;

s [ i ] = s [ i - 1 ] ;

}

}

if ( ++ i == slen ) return ;

k ++;

}

}



bool possible_kolakoski ( int * s , int len ) {

int i , j = 0 , prev = s [ 0 ] , count = 1 ;

int * rle = calloc ( len , sizeof ( int ) ) ;

bool result = TRUE ;

for ( i = 1 ; i < len ; ++ i ) {

if ( s [ i ] == prev ) {

count ++;

}

else {

rle [ j ++ ] = count ;

count = 1 ;

prev = s [ i ] ;

}

}

/* no point adding final 'count' to rle as we're not going to compare it anyway */

for ( i = 0 ; i < j ; i ++ ) {

if ( rle [ i ] != s [ i ] ) {

result = FALSE ;

break ;

}

}

free ( rle ) ;

return result ;

}



void print_array ( int * a , int len ) {

int i ;

printf ( "[" ) ;

for ( i = 0 ; i < len ; ++ i ) {

printf ( "%d" , a [ i ] ) ;

if ( i < len - 1 ) printf ( ", " ) ;

}

printf ( "]" ) ;

}



int main ( ) {

int i , clen , slen , * s ;

int c0 [ 2 ] = { 1 , 2 } ;

int c1 [ 2 ] = { 2 , 1 } ;

int c2 [ 4 ] = { 1 , 3 , 1 , 2 } ;

int c3 [ 4 ] = { 1 , 3 , 2 , 1 } ;

int * cs [ 4 ] = { c0 , c1 , c2 , c3 } ;

bool p ;

int clens [ 4 ] = { 2 , 2 , 4 , 4 } ;

int slens [ 4 ] = { 20 , 20 , 30 , 30 } ;

for ( i = 0 ; i < 4 ; ++ i ) {

clen = clens [ i ] ;

slen = slens [ i ] ;

s = calloc ( slen , sizeof ( int ) ) ;

kolakoski ( cs [ i ] , s , clen , slen ) ;

printf ( "First %d members of the sequence generated by " , slen ) ;

print_array ( cs [ i ] , clen ) ;

printf ( ":

" ) ;

print_array ( s , slen ) ;

printf ( "

" ) ;

p = possible_kolakoski ( s , slen ) ;

printf ( "Possible Kolakoski sequence? %s



" , p ? "True" : "False" ) ;

free ( s ) ;

}

return 0 ;

}

Output:

First 20 members of the sequence generated by [1, 2]: [1, 2, 2, 1, 1, 2, 1, 2, 2, 1, 2, 2, 1, 1, 2, 1, 1, 2, 2, 1] Possible Kolakoski sequence? True First 20 members of the sequence generated by [2, 1]: [2, 2, 1, 1, 2, 1, 2, 2, 1, 2, 2, 1, 1, 2, 1, 1, 2, 2, 1, 2] Possible Kolakoski sequence? True First 30 members of the sequence generated by [1, 3, 1, 2]: [1, 3, 3, 3, 1, 1, 1, 2, 2, 2, 1, 3, 1, 2, 2, 1, 1, 3, 3, 1, 2, 2, 2, 1, 3, 3, 1, 1, 2, 1] Possible Kolakoski sequence? True First 30 members of the sequence generated by [1, 3, 2, 1]: [1, 3, 3, 3, 2, 2, 2, 1, 1, 1, 1, 1, 3, 3, 2, 2, 1, 1, 3, 2, 1, 1, 1, 1, 3, 3, 3, 2, 2, 1] Possible Kolakoski sequence? False

Translation of: Java

using System ;

using System.Collections.Generic ;

using System.Linq ;

using System.Text ;

using System.Threading.Tasks ;



namespace KolakoskiSequence {

class Crutch {

public readonly int len ;

public int [ ] s ;

public int i ;



public Crutch ( int len ) {

this . len = len ;

s = new int [ len ] ;

i = 0 ;

}



public void Repeat ( int count ) {

for ( int j = 0 ; j < count ; j ++ ) {

if ( ++ i == len ) return ;

s [ i ] = s [ i - 1 ] ;

}

}

}



static class Extension {

public static int NextInCycle ( this int [ ] self, int index ) {

return self [ index % self . Length ] ;

}



public static int [ ] Kolakoski ( this int [ ] self, int len ) {

Crutch c = new Crutch ( len ) ;



int k = 0 ;

while ( c . i < len ) {

c . s [ c . i ] = self . NextInCycle ( k ) ;

if ( c . s [ k ] > 1 ) {

c . Repeat ( c . s [ k ] - 1 ) ;

}

if ( ++ c . i == len ) return c . s ;

k ++;

}

return c . s ;

}



public static bool PossibleKolakoski ( this int [ ] self ) {

int [ ] rle = new int [ self . Length ] ;

int prev = self [ 0 ] ;

int count = 1 ;

int pos = 0 ;

for ( int i = 1 ; i < self . Length ; i ++ ) {

if ( self [ i ] == prev ) {

count ++;

}

else {

rle [ pos ++ ] = count ;

count = 1 ;

prev = self [ i ] ;

}

}

// no point adding final 'count' to rle as we're not going to compare it anyway

for ( int i = 0 ; i < pos ; i ++ ) {

if ( rle [ i ] != self [ i ] ) {

return false ;

}

}

return true ;

}



public static string AsString ( this int [ ] self ) {

StringBuilder sb = new StringBuilder ( "[" ) ;

int count = 0 ;

foreach ( var item in self ) {

if ( count > 0 ) {

sb . Append ( ", " ) ;

}

sb . Append ( item ) ;

count ++;

}

return sb . Append ( "]" ) . ToString ( ) ;

}

}



class Program {

static void Main ( string [ ] args ) {

int [ ] [ ] ias = {

new int [ ] { 1 , 2 } ,

new int [ ] { 2 , 1 } ,

new int [ ] { 1 , 3 , 1 , 2 } ,

new int [ ] { 1 , 3 , 2 , 1 }

} ;

int [ ] lens = { 20 , 20 , 30 , 30 } ;



for ( int i = 0 ; i < ias . Length ; i ++ ) {

int len = lens [ i ] ;

int [ ] kol = ias [ i ] . Kolakoski ( len ) ;



Console . WriteLine ( "First {0} members of the sequence by {1}: " , len, ias [ i ] . AsString ( ) ) ;

Console . WriteLine ( kol . AsString ( ) ) ;

Console . WriteLine ( "Possible Kolakoski sequence? {0}" , kol . PossibleKolakoski ( ) ) ;

Console . WriteLine ( ) ;

}

}

}

}

#include <iostream>

#include <vector>



using Sequence = std :: vector < int > ;



std :: ostream & operator << ( std :: ostream & os, const Sequence & v ) {

os << "[ " ;

for ( const auto & e : v ) {

std :: cout << e << ", " ;

}

os << "]" ;

return os ;

}



int next_in_cycle ( const Sequence & s, size_t i ) {

return s [ i % s. size ( ) ] ;

}



Sequence gen_kolakoski ( const Sequence & s, int n ) {

Sequence seq ;

for ( size_t i = 0 ; seq. size ( ) < n ; ++ i ) {

const int next = next_in_cycle ( s, i ) ;

Sequence nv ( i >= seq. size ( ) ? next : seq [ i ] , next ) ;

seq. insert ( std :: end ( seq ) , std :: begin ( nv ) , std :: end ( nv ) ) ;

}

return { std :: begin ( seq ) , std :: begin ( seq ) + n } ;

}



bool is_possible_kolakoski ( const Sequence & s ) {

Sequence r ;

for ( size_t i = 0 ; i < s. size ( ) ; ) {

int count = 1 ;

for ( size_t j = i + 1 ; j < s. size ( ) ; ++ j ) {

if ( s [ j ] ! = s [ i ] ) break ;

++ count ;

}

r. push_back ( count ) ;

i + = count ;

}

for ( size_t i = 0 ; i < r. size ( ) ; ++ i ) if ( r [ i ] ! = s [ i ] ) return false ;

return true ;

}



int main ( ) {

std :: vector < Sequence > seqs = {

{ 1 , 2 } ,

{ 2 , 1 } ,

{ 1 , 3 , 1 , 2 } ,

{ 1 , 3 , 2 , 1 }

} ;

for ( const auto & s : seqs ) {

auto kol = gen_kolakoski ( s, s. size ( ) > 2 ? 30 : 20 ) ;

std :: cout << "Starting with: " << s << ": " << std :: endl << "Kolakoski sequence: "

<< kol << std :: endl << "Possibly kolakoski? " << is_possible_kolakoski ( kol ) << std :: endl ;

}

return 0 ;

}

Output:

Starting with: [ 1, 2, ]: Kolakoski sequence: [ 1, 2, 2, 1, 1, 2, 1, 2, 2, 1, 2, 2, 1, 1, 2, 1, 1, 2, 2, 1, ] Possibly kolakoski? 1 Starting with: [ 2, 1, ]: Kolakoski sequence: [ 2, 2, 1, 1, 2, 1, 2, 2, 1, 2, 2, 1, 1, 2, 1, 1, 2, 2, 1, 2, ] Possibly kolakoski? 1 Starting with: [ 1, 3, 1, 2, ]: Kolakoski sequence: [ 1, 3, 3, 3, 1, 1, 1, 2, 2, 2, 1, 3, 1, 2, 2, 1, 1, 3, 3, 1, 2, 2, 2, 1, 3, 3, 1, 1, 2, 1, ] Possibly kolakoski? 1 Starting with: [ 1, 3, 2, 1, ]: Kolakoski sequence: [ 1, 3, 3, 3, 2, 2, 2, 1, 1, 1, 1, 1, 3, 3, 2, 2, 1, 1, 3, 2, 1, 1, 1, 1, 3, 3, 3, 2, 2, 1, ] Possibly kolakoski? 0

Translation of: Kotlin

import std. stdio ;



void repeat ( int count , void delegate ( int ) action ) {

for ( int i = 0 ; i < count ; i ++ ) {

action ( i ) ;

}

}



T nextInCycle ( T ) ( T [ ] self , int index ) {

return self [ index % self. length ] ;

}



T [ ] kolakoski ( T ) ( T [ ] self , int len ) {

T [ ] s ;

s. length = len ;

int i ;

int k ;

while ( i < len ) {

s [ i ] = self. nextInCycle ( k ) ;

if ( s [ k ] > 1 ) {

repeat ( s [ k ] - 1 ,

( int j ) {

if ( ++ i == len ) return ;

s [ i ] = s [ i - 1 ] ;

}

) ;

}

if ( ++ i == len ) return s ;

k ++;

}

return s ;

}



bool possibleKolakoski ( T ) ( T [ ] self ) {

auto len = self. length ;

T [ ] rle ;

auto prev = self [ 0 ] ;

int count = 1 ;

foreach ( i ; 1 .. len ) {

if ( self [ i ] == prev ) {

count ++;

} else {

rle ~= count ;

count = 1 ;

prev = self [ i ] ;

}

}

// no point adding final 'count' to rle as we're not going to compare it anyway

foreach ( i ; 0 .. rle . length ) {

if ( rle [ i ] != self [ i ] ) {

return false ;

}

}

return true ;

}



void main ( ) {

auto ias = [ [ 1 , 2 ] , [ 2 , 1 ] , [ 1 , 3 , 1 , 2 ] , [ 1 , 3 , 2 , 1 ] ] ;

auto lens = [ 20 , 20 , 30 , 30 ] ;



foreach ( i , ia ; ias ) {

auto len = lens [ i ] ;

auto kol = ia. kolakoski ( len ) ;

writeln ( "First " , len , " members of the sequence generated by " , ia , ":" ) ;

writeln ( kol ) ;

write ( "Possible Kolakoski sequence? " ) ;

if ( kol. possibleKolakoski ) {

writeln ( "Yes" ) ;

} else {

writeln ( "no" ) ;

}

writeln ;

}

}

Output:

First 20 members of the sequence generated by [1, 2]: [1, 2, 2, 1, 1, 2, 1, 2, 2, 1, 2, 2, 1, 1, 2, 1, 1, 2, 2, 1] Possible Kolakoski sequence? Yes First 20 members of the sequence generated by [2, 1]: [2, 2, 1, 1, 2, 1, 2, 2, 1, 2, 2, 1, 1, 2, 1, 1, 2, 2, 1, 2] Possible Kolakoski sequence? Yes First 30 members of the sequence generated by [1, 3, 1, 2]: [1, 3, 3, 3, 1, 1, 1, 2, 2, 2, 1, 3, 1, 2, 2, 1, 1, 3, 3, 1, 2, 2, 2, 1, 3, 3, 1, 1, 2, 1] Possible Kolakoski sequence? Yes First 30 members of the sequence generated by [1, 3, 2, 1]: [1, 3, 3, 3, 2, 2, 2, 1, 1, 1, 1, 1, 3, 3, 2, 2, 1, 1, 3, 2, 1, 1, 1, 1, 3, 3, 3, 2, 2, 1] Possible Kolakoski sequence? no

Translation of: Kotlin

package main



import "fmt"



func nextInCycle ( c [] int , index int ) int {

return c [ index % len ( c )]

}



func kolakoski ( c [] int , slen int ) [] int {

s := make ([] int , slen )

i , k := 0 , 0

for {

s [ i ] = nextInCycle ( c , k )

if s [ k ] > 1 {

for j := 1 ; j < s [ k ]; j ++ {

i ++

if i == slen {

return s

}

s [ i ] = s [ i - 1 ]

}

}

i ++

if i == slen {

return s

}

k ++

}

}



func possibleKolakoski ( s [] int ) bool {

slen := len ( s )

rle := make ([] int , 0 , slen )

prev := s [ 0 ]

count := 1

for i := 1 ; i < slen ; i ++ {

if s [ i ] == prev {

count ++

} else {

rle = append ( rle , count )

count = 1

prev = s [ i ]

}

}

// no point adding final 'count' to rle as we're not going to compare it anyway

for i := 0 ; i < len ( rle ); i ++ {

if rle [ i ] != s [ i ] {

return false

}

}

return true

}



func printInts ( ia [] int , suffix string ) {

fmt . Print ( "[" )

alen := len ( ia )

for i := 0 ; i < alen ; i ++ {

fmt . Print ( ia [ i ])

if i < alen - 1 {

fmt . Print ( ", " )

}

}

fmt . Printf ( "]%s

" , suffix )

}



func main () {

ias := make ([][] int , 4 )

ias [ 0 ] = [] int { 1 , 2 }

ias [ 1 ] = [] int { 2 , 1 }

ias [ 2 ] = [] int { 1 , 3 , 1 , 2 }

ias [ 3 ] = [] int { 1 , 3 , 2 , 1 }

slens := [] int { 20 , 20 , 30 , 30 }

for i , ia := range ias {

slen := slens [ i ]

kol := kolakoski ( ia , slen )

fmt . Printf ( "First %d members of the sequence generated by " , slen )

printInts ( ia , ":" )

printInts ( kol , "" )

p := possibleKolakoski ( kol )

poss := "Yes"

if ! p {

poss = "No"

}

fmt . Println ( "Possible Kolakoski sequence?" , poss , "

" )

}

}

Output:

First 20 members of the sequence generated by [1, 2]: [1, 2, 2, 1, 1, 2, 1, 2, 2, 1, 2, 2, 1, 1, 2, 1, 1, 2, 2, 1] Possible Kolakoski sequence? Yes First 20 members of the sequence generated by [2, 1]: [2, 2, 1, 1, 2, 1, 2, 2, 1, 2, 2, 1, 1, 2, 1, 1, 2, 2, 1, 2] Possible Kolakoski sequence? Yes First 30 members of the sequence generated by [1, 3, 1, 2]: [1, 3, 3, 3, 1, 1, 1, 2, 2, 2, 1, 3, 1, 2, 2, 1, 1, 3, 3, 1, 2, 2, 2, 1, 3, 3, 1, 1, 2, 1] Possible Kolakoski sequence? Yes First 30 members of the sequence generated by [1, 3, 2, 1]: [1, 3, 3, 3, 2, 2, 2, 1, 1, 1, 1, 1, 3, 3, 2, 2, 1, 1, 3, 2, 1, 1, 1, 1, 3, 3, 3, 2, 2, 1] Possible Kolakoski sequence? No

import Data . List ( group )

import Control . Monad ( forM _ )



replicateAtLeastOne :: Int -> a -> [ a ]

replicateAtLeastOne n x = x : replicate ( n - 1 ) x



zipWithLazy :: ( a -> b -> c ) -> [ a ] -> [ b ] -> [ c ]

zipWithLazy f ~ ( x:xs ) ~ ( y:ys ) = f x y : zipWithLazy f xs ys



kolakoski :: [ Int ] -> [ Int ]

kolakoski items = s

where s = concat $ zipWithLazy replicateAtLeastOne s $ cycle items



rle :: Eq a => [ a ] -> [ Int ]

rle = map length . group



sameAsRleUpTo :: Int -> [ Int ] -> Bool

sameAsRleUpTo n s = r == take ( length r ) prefix

where prefix = take n s

r = init $ rle prefix



main :: IO ( )

main = forM _ [ ( [ 1 , 2 ] , 20 ) ,

( [ 2 , 1 ] , 20 ) ,

( [ 1 , 3 , 1 , 2 ] , 30 ) ,

( [ 1 , 3 , 2 , 1 ] , 30 ) ]

$ \ ( items , n ) -> do

putStrLn $ "First " ++ show n ++ " members of the sequence generated by " ++ show items ++ ":"

let s = kolakoski items

print $ take n s

putStrLn $ "Possible Kolakoski sequence? " ++ show ( sameAsRleUpTo n s )

putStrLn ""

Output:

First 20 members of the sequence generated by [1,2]: [1,2,2,1,1,2,1,2,2,1,2,2,1,1,2,1,1,2,2,1] Possible Kolakoski sequence? True First 20 members of the sequence generated by [2,1]: [2,2,1,1,2,1,2,2,1,2,2,1,1,2,1,1,2,2,1,2] Possible Kolakoski sequence? True First 30 members of the sequence generated by [1,3,1,2]: [1,3,3,3,1,1,1,2,2,2,1,3,1,2,2,1,1,3,3,1,2,2,2,1,3,3,1,1,2,1] Possible Kolakoski sequence? True First 30 members of the sequence generated by [1,3,2,1]: [1,3,3,3,2,2,2,1,1,1,1,1,3,3,2,2,1,1,3,2,1,1,1,1,3,3,3,2,2,1] Possible Kolakoski sequence? False



NB. cyclic



create_cycle_=: 3 : 0

I=: 0

A=: y

N=: # A

)



next_cycle_=: 3 : 0

r=. A {~ N | I

I=: >: I

r

)



NB. kolakoski



kolakoski =: 30 &$: : ( dyad define ) NB. TERMS kolakoski ALPHABET

c=. y conew 'cycle'

s=. i. 0

term=. 0

while. x > # s do.

s=. ( , ( [: #~ next__c ) ` ( term&{ # next__c ) @. ( term < # )) s

term=. >: term

end.

s

)





test=: (( {.~ # ) -: ] ) }:@: ( #;. 1 ~ ( 1 , 2 & ( ~:/\ )))



test cuts the data at a vector of frets where successive pairs are unequal. The groups are tallied, giving run length.

f=: (;~ test)@:kolakoski (; f)&> 1 2 ; 2 1 ; 1 3 1 2 ; 1 3 2 1 ┌───────┬─┬─────────────────────────────────────────────────────────────┐ │1 2 │1│1 2 2 1 1 2 1 2 2 1 2 2 1 1 2 1 1 2 2 1 2 1 1 2 1 2 2 1 1 2 │ ├───────┼─┼─────────────────────────────────────────────────────────────┤ │2 1 │1│2 2 1 1 2 1 2 2 1 2 2 1 1 2 1 1 2 2 1 2 1 1 2 1 2 2 1 1 2 1 1│ ├───────┼─┼─────────────────────────────────────────────────────────────┤ │1 3 1 2│1│1 3 3 3 1 1 1 2 2 2 1 3 1 2 2 1 1 3 3 1 2 2 2 1 3 3 1 1 2 1 │ ├───────┼─┼─────────────────────────────────────────────────────────────┤ │1 3 2 1│0│1 3 3 3 2 2 2 1 1 1 1 1 3 3 2 2 1 1 3 2 1 1 1 1 3 3 3 2 2 1 1│ └───────┴─┴─────────────────────────────────────────────────────────────┘

Translation of: Kotlin

import java.util.Arrays ;



public class Kolakoski {

private static class Crutch {

final int len ;

int [ ] s ;

int i ;



Crutch ( int len ) {

this . len = len ;

s = new int [ len ] ;

i = 0 ;

}



void repeat ( int count ) {

for ( int j = 0 ; j < count ; j ++ ) {

if ( ++ i == len ) return ;

s [ i ] = s [ i - 1 ] ;

}

}

}



private static int nextInCycle ( final int [ ] self, int index ) {

return self [ index % self. length ] ;

}



private static int [ ] kolakoski ( final int [ ] self, int len ) {

Crutch c = new Crutch ( len ) ;



int k = 0 ;

while ( c. i < len ) {

c. s [ c. i ] = nextInCycle ( self, k ) ;

if ( c. s [ k ] > 1 ) {

c. repeat ( c. s [ k ] - 1 ) ;

}

if ( ++ c. i == len ) return c. s ;

k ++;

}

return c. s ;

}



private static boolean possibleKolakoski ( final int [ ] self ) {

int [ ] rle = new int [ self. length ] ;

int prev = self [ 0 ] ;

int count = 1 ;

int pos = 0 ;

for ( int i = 1 ; i < self. length ; i ++ ) {

if ( self [ i ] == prev ) {

count ++;

} else {

rle [ pos ++ ] = count ;

count = 1 ;

prev = self [ i ] ;

}

}

// no point adding final 'count' to rle as we're not going to compare it anyway

for ( int i = 0 ; i < pos ; i ++ ) {

if ( rle [ i ] != self [ i ] ) {

return false ;

}

}

return true ;

}



public static void main ( String [ ] args ) {

int [ ] [ ] ias = new int [ ] [ ] {

new int [ ] { 1 , 2 } ,

new int [ ] { 2 , 1 } ,

new int [ ] { 1 , 3 , 1 , 2 } ,

new int [ ] { 1 , 3 , 2 , 1 }

} ;

int [ ] lens = new int [ ] { 20 , 20 , 30 , 30 } ;



for ( int i = 0 ; i < ias. length ; i ++ ) {

int len = lens [ i ] ;

int [ ] kol = kolakoski ( ias [ i ] , len ) ;



System . out . printf ( "First %d members of the sequence generated by %s:

" , len, Arrays . toString ( ias [ i ] ) ) ;

System . out . printf ( "%s

" , Arrays . toString ( kol ) ) ;

System . out . printf ( "Possible Kolakoski sequence? %s



" , possibleKolakoski ( kol ) ) ;

}

}

}

Output:

First 20 members of the sequence generated by [1, 2]: [1, 2, 2, 1, 1, 2, 1, 2, 2, 1, 2, 2, 1, 1, 2, 1, 1, 2, 2, 1] Possible Kolakoski sequence? true First 20 members of the sequence generated by [2, 1]: [2, 2, 1, 1, 2, 1, 2, 2, 1, 2, 2, 1, 1, 2, 1, 1, 2, 2, 1, 2] Possible Kolakoski sequence? true First 30 members of the sequence generated by [1, 3, 1, 2]: [1, 3, 3, 3, 1, 1, 1, 2, 2, 2, 1, 3, 1, 2, 2, 1, 1, 3, 3, 1, 2, 2, 2, 1, 3, 3, 1, 1, 2, 1] Possible Kolakoski sequence? true First 30 members of the sequence generated by [1, 3, 2, 1]: [1, 3, 3, 3, 2, 2, 2, 1, 1, 1, 1, 1, 3, 3, 2, 2, 1, 1, 3, 2, 1, 1, 1, 1, 3, 3, 3, 2, 2, 1] Possible Kolakoski sequence? false

Translation of: C

function kolakoski(vec, len)

seq = Vector{Int}()

k = 0

denom = length(vec)

while length(seq) < len

n = vec[k % denom + 1]

k += 1

seq = vcat(seq, repeat([n], k > length(seq) ? n : seq[k]))

end

seq[1:len]

end



function iskolakoski(seq)

count = 1

rle = Vector{Int}()

for i in 2:length(seq)

if seq[i] == seq[i - 1]

count += 1

else

push!(rle, count)

count = 1

end

end

rle == seq[1:length(rle)]

end



const tests = [[[1, 2], 20],[[2, 1] ,20], [[1, 3, 1, 2], 30], [[1, 3, 2, 1], 30]]



for t in tests

vec, n = t[1], t[2]

seq = kolakoski(vec, n)

println("Kolakoski from $(vec): first $n numbers are $seq.")

println("\t\tDoes this look like a Kolakoski sequence? ", iskolakoski(seq) ? "Yes" : "No")

end



Output:

Kolakoski from [1, 2]: first 20 numbers are [1, 2, 2, 1, 1, 2, 1, 2, 2, 1, 2, 2, 1, 1, 2, 1, 1, 2, 2, 1]. Does this look like a Kolakoski sequence? Yes Kolakoski from [2, 1]: first 20 numbers are [2, 2, 1, 1, 2, 1, 2, 2, 1, 2, 2, 1, 1, 2, 1, 1, 2, 2, 1, 2]. Does this look like a Kolakoski sequence? Yes Kolakoski from [1, 3, 1, 2]: first 30 numbers are [1, 3, 3, 3, 1, 1, 1, 2, 2, 2, 1, 3, 1, 2, 2, 1, 1, 3, 3, 1, 2, 2, 2, 1, 3, 3, 1, 1, 2, 1]. Does this look like a Kolakoski sequence? Yes Kolakoski from [1, 3, 2, 1]: first 30 numbers are [1, 3, 3, 3, 2, 2, 2, 1, 1, 1, 1, 1, 3, 3, 2, 2, 1, 1, 3, 2, 1, 1, 1, 1, 3, 3, 3, 2, 2, 1]. Does this look like a Kolakoski sequence? No

// Version 1.2.41



fun IntArray. nextInCycle ( index : Int ) = this [ index % this . size ]



fun IntArray. kolakoski ( len : Int ) : IntArray {

val s = IntArray ( len )

var i = 0

var k = 0

while ( true ) {

s [ i ] = this . nextInCycle ( k )

if ( s [ k ] > 1 ) {

repeat ( s [ k ] - 1 ) {

if ( ++i == len ) return s

s [ i ] = s [ i - 1 ]

}

}

if ( ++i == len ) return s

k++

}

}



fun IntArray. possibleKolakoski ( ) : Boolean {

val len = this . size

val rle = mutableListOf < Int > ( )

var prev = this [ 0 ]

var count = 1

for ( i in 1 until len ) {

if ( this [ i ] == prev ) {

count++

}

else {

rle. add ( count )

count = 1

prev = this [ i ]

}

}

// no point adding final 'count' to rle as we're not going to compare it anyway

for ( i in 0 until rle. size ) {

if ( rle [ i ] != this [ i ] ) return false

}

return true

}



fun main ( args : Array < String > ) {

val ias = listOf (

intArrayOf ( 1 , 2 ) , intArrayOf ( 2 , 1 ) ,

intArrayOf ( 1 , 3 , 1 , 2 ) , intArrayOf ( 1 , 3 , 2 , 1 )

)

val lens = intArrayOf ( 20 , 20 , 30 , 30 )

for ( ( i, ia ) in ias. withIndex ( ) ) {

val len = lens [ i ]

val kol = ia. kolakoski ( len )

println ( "First $len members of the sequence generated by ${ia.asList()}:" )

println ( kol. asList ( ) )

val p = kol. possibleKolakoski ( )

println ( "Possible Kolakoski sequence? ${if (p) " Yes " else " No "}

" )

}

}

Output:

First 20 members of the sequence generated by [1, 2]: [1, 2, 2, 1, 1, 2, 1, 2, 2, 1, 2, 2, 1, 1, 2, 1, 1, 2, 2, 1] Possible Kolakoski sequence? Yes First 20 members of the sequence generated by [2, 1]: [2, 2, 1, 1, 2, 1, 2, 2, 1, 2, 2, 1, 1, 2, 1, 1, 2, 2, 1, 2] Possible Kolakoski sequence? Yes First 30 members of the sequence generated by [1, 3, 1, 2]: [1, 3, 3, 3, 1, 1, 1, 2, 2, 2, 1, 3, 1, 2, 2, 1, 1, 3, 3, 1, 2, 2, 2, 1, 3, 3, 1, 1, 2, 1] Possible Kolakoski sequence? Yes First 30 members of the sequence generated by [1, 3, 2, 1]: [1, 3, 3, 3, 2, 2, 2, 1, 1, 1, 1, 1, 3, 3, 2, 2, 1, 1, 3, 2, 1, 1, 1, 1, 3, 3, 3, 2, 2, 1] Possible Kolakoski sequence? No

Translation of: C

function next_in_cycle ( c , length , index )

local pos = index % length

return c [ pos ]

end



function kolakoski ( c , s , clen , slen )

local i = 0

local k = 0



while true do

s [ i ] = next_in_cycle ( c , clen , k )

if s [ k ] > 1 then

for j = 1 , s [ k ] - 1 do

i = i + 1

if i == slen then

return nil

end

s [ i ] = s [ i - 1 ]

end

end

i = i + 1

if i == slen then

return nil

end

k = k + 1

end

return nil

end



function possible_kolakoski ( s , length )

local j = 0

local prev = s [ 0 ]

local count = 1

local rle = { }

local result = "True"



for i = 0 , length do

rle [ i ] = 0

end



for i = 1 , length - 1 do

if s [ i ] == prev then

count = count + 1

else

rle [ j ] = count

j = j + 1

count = 1

prev = s [ i ]

end

end



-- no point adding the final 'count' to rle as we're not going to compare it anyway

for i = 0 , j - 1 do

if rle [ i ] ~= s [ i ] then

result = "False"

break

end

end



return result

end



function print_array ( a )

io.write ( "[" )

for i = 0 ,# a do

if i > 0 then

io.write ( ", " )

end

io.write ( a [ i ] )

end

io.write ( "]" )

end



-- main

local c0 = { [ 0 ] = 1 , [ 1 ] = 2 }

local c1 = { [ 0 ] = 2 , [ 1 ] = 1 }

local c2 = { [ 0 ] = 1 , [ 1 ] = 3 , [ 2 ] = 1 , [ 3 ] = 2 }

local c3 = { [ 0 ] = 1 , [ 1 ] = 3 , [ 2 ] = 2 , [ 3 ] = 1 }



local cs = { [ 0 ] = c0 , [ 1 ] = c1 , [ 2 ] = c2 , [ 3 ] = c3 }

local clens = { [ 0 ] = 2 , [ 1 ] = 2 , [ 2 ] = 4 , [ 3 ] = 4 }

local slens = { [ 0 ] = 20 , [ 1 ] = 20 , [ 2 ] = 30 , [ 3 ] = 30 }



for i = 0 , 3 do

local clen = clens [ i ]

local slen = slens [ i ]

local s = { }



for j = 0 , slen - 1 do

s [ j ] = 0

end



kolakoski ( cs [ i ] , s , clen , slen )

io.write ( string.format ( "First %d members of the sequence generated by " , slen ) )

print_array ( cs [ i ] )

print ( ":" )

print_array ( s )

print ( )



local p = possible_kolakoski ( s , slen )

print ( string.format ( "Possible Kolakoski sequence? %s" , p ) )



print ( )

end

Output:

First 20 members of the sequence generated by [1, 2]: [1, 2, 2, 1, 1, 2, 1, 2, 2, 1, 2, 2, 1, 1, 2, 1, 1, 2, 2, 1] Possible Kolakoski sequence? True First 20 members of the sequence generated by [2, 1]: [2, 2, 1, 1, 2, 1, 2, 2, 1, 2, 2, 1, 1, 2, 1, 1, 2, 2, 1, 2] Possible Kolakoski sequence? True First 30 members of the sequence generated by [1, 3, 1, 2]: [1, 3, 3, 3, 1, 1, 1, 2, 2, 2, 1, 3, 1, 2, 2, 1, 1, 3, 3, 1, 2, 2, 2, 1, 3, 3, 1, 1, 2, 1] Possible Kolakoski sequence? True First 30 members of the sequence generated by [1, 3, 2, 1]: [1, 3, 3, 3, 2, 2, 2, 1, 1, 1, 1, 1, 3, 3, 2, 2, 1, 1, 3, 2, 1, 1, 1, 1, 3, 3, 3, 2, 2, 1] Possible Kolakoski sequence? False

Translation of: Raku

sub kolakoski {

my ( $terms , @seed ) = @_ ;

my @k ;

my $k = $seed [ 0 ] == 1 ? 1 : 0 ;

if ( $k == 1 ) { @k = ( 1 , split //, ( ( $seed [ 1 ] ) x $seed [ 1 ] ) ) }

else { @k = ( $seed [ 0 ] ) x $seed [ 0 ] }

do {

$k ++;

push @k , ( $seed [ $k % @seed ] ) x $k [ $k ] ;

} until $terms <= @k ;

@k [ 0 .. $terms - 1 ]

}



sub rle {

( my $string = join '' , @_ ) =~ s/((.)\2*)/length $1/eg ;

split '' , $string

}



for ( [ 20 , 1 , 2 ] , [ 20 , 2 , 1 ] , [ 30 , 1 , 3 , 1 , 2 ] , [ 30 , 1 , 3 , 2 , 1 ] ) {

$terms = shift @ $_ ;

print "

$terms members of the series generated from [@$_] is:

" ;

print join ( ' ' , @kolakoski = kolakoski ( $terms , @ $_ ) ) . "

" ;

$status = join ( '' , @rle = rle ( @kolakoski ) ) eq join ( '' , @kolakoski [ 0 .. $#rle ] ) ? 'True' : 'False' ;

print "Looks like a Kolakoski sequence?: $status

" ;

}

Output:

20 members of the series generated from [1 2] is: 1 2 2 1 1 2 1 2 2 1 2 2 1 1 2 1 1 2 2 1 Looks like a Kolakoski sequence?: True 20 members of the series generated from [2 1] is: 2 2 1 1 2 1 2 2 1 2 2 1 1 2 1 1 2 2 1 2 Looks like a Kolakoski sequence?: True 30 members of the series generated from [1 3 1 2] is: 1 3 3 3 1 1 1 2 2 2 1 3 1 2 2 1 1 3 3 1 2 2 2 1 3 3 1 1 2 1 Looks like a Kolakoski sequence?: True 30 members of the series generated from [1 3 2 1] is: 1 3 3 3 2 2 2 1 1 1 1 1 3 3 2 2 1 1 3 2 1 1 1 1 3 3 3 2 2 1 Looks like a Kolakoski sequence?: False

Translation of: C

function kolakoski(sequence cycle, integer n)

sequence s = {}

integer k = 1

while length(s)<n do

integer c = cycle[mod(k-1,length(cycle))+1]

s &= repeat(c,iff(k>length(s)?c:s[k]))

k += 1

end while

s = s[1..n]

return s

end function



function possible_kolakoski(sequence s)

integer count = 1

sequence rle = {}

for i=2 to length(s) do

if s[i]==s[i-1] then

count += 1

else

rle &= count

count = 1

end if

end for

-- (final count probably incomplete, so ignore it)

return rle = s[1..length(rle)]

end function



constant cycles = {{1,2},20,

{2,1},20,

{1,3,1,2},30,

{1,3,2,1},30}



for i=1 to length(cycles) by 2 do

{sequence c, integer n} = cycles[i..i+1]

sequence s = kolakoski(c,n)

printf(1,"First %d members of the sequence generated by %s

", {n,sprint(c)})

?s

bool p = possible_kolakoski(s)

printf(1,"Possible Kolakoski sequence? %s



", {iff(p ? "Yes" : "No")})

end for

Output:

First 20 members of the sequence generated by {1,2} {1,2,2,1,1,2,1,2,2,1,2,2,1,1,2,1,1,2,2,1} Possible Kolakoski sequence? Yes First 20 members of the sequence generated by {2,1} {2,2,1,1,2,1,2,2,1,2,2,1,1,2,1,1,2,2,1,2} Possible Kolakoski sequence? Yes First 30 members of the sequence generated by {1,3,1,2} {1,3,3,3,1,1,1,2,2,2,1,3,1,2,2,1,1,3,3,1,2,2,2,1,3,3,1,1,2,1} Possible Kolakoski sequence? Yes First 30 members of the sequence generated by {1,3,2,1} {1,3,3,3,2,2,2,1,1,1,1,1,3,3,2,2,1,1,3,2,1,1,1,1,3,3,3,2,2,1} Possible Kolakoski sequence? No

Python 3.6+

import itertools



def cycler ( start_items ) :

return itertools . cycle ( start_items ) .__next__



def _kolakoski_gen ( start_items ) :

s , k = [ ] , 0

c = cycler ( start_items )

while True :

c_next = c ( )

s. append ( c_next )

sk = s [ k ]

yield sk

if sk > 1 :

s + = [ c_next ] * ( sk - 1 )

k + = 1



def kolakoski ( start_items = ( 1 , 2 ) , length = 20 ) :

return list ( itertools . islice ( _kolakoski_gen ( start_items ) , length ) )



def _run_len_encoding ( truncated_series ) :

return [ len ( list ( group ) ) for grouper , group in itertools . groupby ( truncated_series ) ] [ :- 1 ]



def is_series_eq_its_rle ( series ) :

rle = _run_len_encoding ( series )

return ( series [ : len ( rle ) ] == rle ) if rle else not series



if __name__ == '__main__' :

for start_items , length in [ ( ( 1 , 2 ) , 20 ) , ( ( 2 , 1 ) , 20 ) ,

( ( 1 , 3 , 1 , 2 ) , 30 ) , ( ( 1 , 3 , 2 , 1 ) , 30 ) ] :

print ( f '

## {length} members of the series generated from {start_items} is:' )

s = kolakoski ( start_items , length )

print ( f ' {s}' )

ans = 'YES' if is_series_eq_its_rle ( s ) else 'NO'

print ( f ' Does it look like a Kolakoski sequence: {ans}' )

Output:

## 20 members of the series generated from (1, 2) is: [1, 2, 2, 1, 1, 2, 1, 2, 2, 1, 2, 2, 1, 1, 2, 1, 1, 2, 2, 1] Does it look like a Kolakoski sequence: YES ## 20 members of the series generated from (2, 1) is: [2, 2, 1, 1, 2, 1, 2, 2, 1, 2, 2, 1, 1, 2, 1, 1, 2, 2, 1, 2] Does it look like a Kolakoski sequence: YES ## 30 members of the series generated from (1, 3, 1, 2) is: [1, 3, 3, 3, 1, 1, 1, 2, 2, 2, 1, 3, 1, 2, 2, 1, 1, 3, 3, 1, 2, 2, 2, 1, 3, 3, 1, 1, 2, 1] Does it look like a Kolakoski sequence: YES ## 30 members of the series generated from (1, 3, 2, 1) is: [1, 3, 3, 3, 2, 2, 2, 1, 1, 1, 1, 1, 3, 3, 2, 2, 1, 1, 3, 2, 1, 1, 1, 1, 3, 3, 3, 2, 2, 1] Does it look like a Kolakoski sequence: NO

(formerly Perl 6)

Works with: Rakudo version 2018.04.01

sub kolakoski ( * @seed ) {

my $k = @seed [ 0 ] == 1 ?? 1 !! 0 ;

my @k = flat @seed [ 0 ] == 1 ?? ( 1 , @seed [ 1 ] xx @seed [ 1 ] ) !! @seed [ 0 ] xx @seed [ 0 ] ,

{ $k ++; @seed [ $k % @seed ] xx @k [ $k ] } … *

}



sub rle ( * @series ) { @series . join . subst ( /((.)$0*)/ , -> { $0 . chars } , : g ) . comb » . Int }



# Testing

for [ 1 , 2 ] , 20 ,

[ 2 , 1 ] , 20 ,

[ 1 , 3 , 1 , 2 ] , 30 ,

[ 1 , 3 , 2 , 1 ] , 30

-> @seed , $terms {

say "

## $terms members of the series generated from { @seed.perl } is:

" ,

my @kolakoski = kolakoski ( @seed ) [ ^ $terms ] ;

my @rle = rle @kolakoski ;

say " Looks like a Kolakoski sequence?: " , @rle [ * ] eqv @kolakoski [ ^ @rle ] ;

}

Output:

## 20 members of the series generated from [1, 2] is: [1 2 2 1 1 2 1 2 2 1 2 2 1 1 2 1 1 2 2 1] Looks like a Kolakoski sequence?: True ## 20 members of the series generated from [2, 1] is: [2 2 1 1 2 1 2 2 1 2 2 1 1 2 1 1 2 2 1 2] Looks like a Kolakoski sequence?: True ## 30 members of the series generated from [1, 3, 1, 2] is: [1 3 3 3 1 1 1 2 2 2 1 3 1 2 2 1 1 3 3 1 2 2 2 1 3 3 1 1 2 1] Looks like a Kolakoski sequence?: True ## 30 members of the series generated from [1, 3, 2, 1] is: [1 3 3 3 2 2 2 1 1 1 1 1 3 3 2 2 1 1 3 2 1 1 1 1 3 3 3 2 2 1] Looks like a Kolakoski sequence?: False

def create_generator ( ar )

Enumerator. new do | y |

cycle = ar. cycle

s = [ ]

loop do

t = cycle. next

s. push ( t )

v = s. shift

y << v

( v - 1 ) . times { s. push ( t ) }

end

end

end



def rle ( ar )

ar. slice_when { | a,b | a != b } . map ( & :size )

end



[ [ 20 , [ 1 , 2 ] ] ,

[ 20 , [ 2 , 1 ] ] ,

[ 30 , [ 1 , 3 , 1 , 2 ] ] ,

[ 30 , [ 1 , 3 , 2 , 1 ] ] ] . each do | num,ar |

puts "

First #{num} of the sequence generated by #{ar.inspect}:"

p res = create_generator ( ar ) . take ( num )

puts "Possible Kolakoski sequence? #{res.join.start_with?(rle(res).join)}"

end

Output:

First 20 of the sequence generated by [1, 2]: [1, 2, 2, 1, 1, 2, 1, 2, 2, 1, 2, 2, 1, 1, 2, 1, 1, 2, 2, 1] Possible Kolakoski sequence? true First 20 of the sequence generated by [2, 1]: [2, 2, 1, 1, 2, 1, 2, 2, 1, 2, 2, 1, 1, 2, 1, 1, 2, 2, 1, 2] Possible Kolakoski sequence? true First 30 of the sequence generated by [1, 3, 1, 2]: [1, 3, 3, 3, 1, 1, 1, 2, 2, 2, 1, 3, 1, 2, 2, 1, 1, 3, 3, 1, 2, 2, 2, 1, 3, 3, 1, 1, 2, 1] Possible Kolakoski sequence? true First 30 of the sequence generated by [1, 3, 2, 1]: [1, 3, 3, 3, 2, 2, 2, 1, 1, 1, 1, 1, 3, 3, 2, 2, 1, 1, 3, 2, 1, 1, 1, 1, 3, 3, 3, 2, 2, 1] Possible Kolakoski sequence? false

Translation of: Ruby

func create_generator ( arr ) {

Enumerator ( { | f |

var s = [ ]

var i = 0

loop {

var t = arr [ i ++ % arr. len ]

s << t

f ( var v = s. shift )

s << ( v - 1 ) . of ( t ) ...

}

} )

}



var tests = [

[ 20 , [ 1 , 2 ] ] ,

[ 20 , [ 2 , 1 ] ] ,

[ 30 , [ 1 , 3 , 1 , 2 ] ] ,

[ 30 , [ 1 , 3 , 2 , 1 ] ]

]



for num,arr in ( tests ) {

say "

First #{num} of the sequence generated by #{arr}:"

var res = create_generator ( arr ) . first ( num )

var rle = res. run_length . map { . tail }

say "#{res}

Possible Kolakoski sequence? #{res.first(rle.len) == rle}"

}

Output:

First 20 of the sequence generated by [1, 2]: [1, 2, 2, 1, 1, 2, 1, 2, 2, 1, 2, 2, 1, 1, 2, 1, 1, 2, 2, 1] Possible Kolakoski sequence? true First 20 of the sequence generated by [2, 1]: [2, 2, 1, 1, 2, 1, 2, 2, 1, 2, 2, 1, 1, 2, 1, 1, 2, 2, 1, 2] Possible Kolakoski sequence? true First 30 of the sequence generated by [1, 3, 1, 2]: [1, 3, 3, 3, 1, 1, 1, 2, 2, 2, 1, 3, 1, 2, 2, 1, 1, 3, 3, 1, 2, 2, 2, 1, 3, 3, 1, 1, 2, 1] Possible Kolakoski sequence? true First 30 of the sequence generated by [1, 3, 2, 1]: [1, 3, 3, 3, 2, 2, 2, 1, 1, 1, 1, 1, 3, 3, 2, 2, 1, 1, 3, 2, 1, 1, 1, 1, 3, 3, 3, 2, 2, 1] Possible Kolakoski sequence? false

Translation of: C#

Imports System . Runtime . CompilerServices

Imports System . Text



Module Module1



Class Crutch

Public ReadOnly len As Integer

Public s ( ) As Integer

Public i As Integer



Public Sub New ( len As Integer )

Me . len = len

s = New Integer ( len - 1 ) { }

i = 0

End Sub



Public Sub Repeat ( count As Integer )

For j = 1 To count

i += 1

If i = len Then

Return

End If

s ( i ) = s ( i - 1 )

Next

End Sub

End Class



< Extension ( ) >

Public Function NextInCycle ( self As Integer ( ) , index As Integer ) As Integer

Return self ( index Mod self . Length )

End Function



< Extension ( ) >

Public Function Kolakoski ( self As Integer ( ) , len As Integer ) As Integer ( )

Dim c As New Crutch ( len )



Dim k = 0

While c . i < len

c . s ( c . i ) = self . NextInCycle ( k )

If c . s ( k ) > 1 Then

c . Repeat ( c . s ( k ) - 1 )

End If

c . i += 1

If c . i = len Then

Return c . s

End If

k += 1

End While



Return c . s

End Function



< Extension ( ) >

Public Function PossibleKolakoski ( self As Integer ( ) ) As Boolean

Dim rle ( self . Length ) As Integer

Dim prev = self ( 0 )

Dim count = 1

Dim pos = 0

For i = 2 To self . Length

If self ( i - 1 ) = prev Then

count += 1

Else

rle ( pos ) = count

pos += 1



count = 1

prev = self ( i - 1 )

End If

Next

REM no point adding final 'count' to rle as we're not going to compare it anyway

For i = 1 To pos

If rle ( i - 1 ) <> self ( i - 1 ) Then

Return False

End If

Next

Return True

End Function



< Extension ( ) >

Public Function AsString ( self As Integer ( ) ) As String

Dim sb As New StringBuilder ( "[" )

Dim it = self . GetEnumerator ( )

If it . MoveNext Then

sb . Append ( it . Current )

End If

While it . MoveNext

sb . Append ( ", " )

sb . Append ( it . Current )

End While

Return sb . Append ( "]" ) . ToString

End Function



Sub Main ( )

Dim ias ( ) ( ) As Integer = { New Integer ( ) { 1 , 2 } , New Integer ( ) { 2 , 1 } , New Integer ( ) { 1 , 3 , 1 , 2 } , New Integer ( ) { 1 , 3 , 2 , 1 } }

Dim lens ( ) As Integer = { 20 , 20 , 30 , 30 }



For i = 1 To ias . Length

Dim len = lens ( i - 1 )

Dim kol = ias ( i - 1 ) . Kolakoski ( len )



Console . WriteLine ( "First {0} members of the sequence by {1}: " , len, ias ( i - 1 ) . AsString )

Console . WriteLine ( kol . AsString )

Console . WriteLine ( "Possible Kolakoski sequence? {0}" , kol . PossibleKolakoski )

Console . WriteLine ( )

Next

End Sub



End Module

Output:

First 20 members of the sequence by [1, 2]: [1, 2, 2, 1, 1, 2, 1, 2, 2, 1, 2, 2, 1, 1, 2, 1, 1, 2, 2, 1] Possible Kolakoski sequence? True First 20 members of the sequence by [2, 1]: [2, 2, 1, 1, 2, 1, 2, 2, 1, 2, 2, 1, 1, 2, 1, 1, 2, 2, 1, 2] Possible Kolakoski sequence? True First 30 members of the sequence by [1, 3, 1, 2]: [1, 3, 3, 3, 1, 1, 1, 2, 2, 2, 1, 3, 1, 2, 2, 1, 1, 3, 3, 1, 2, 2, 2, 1, 3, 3, 1, 1, 2, 1] Possible Kolakoski sequence? True First 30 members of the sequence by [1, 3, 2, 1]: [1, 3, 3, 3, 2, 2, 2, 1, 1, 1, 1, 1, 3, 3, 2, 2, 1, 1, 3, 2, 1, 1, 1, 1, 3, 3, 3, 2, 2, 1] Possible Kolakoski sequence? False

Translation of: Python

fcn kolakoski(start_items=List(1,2), length=20){ //-->List

Walker.tweak(fcn(s,rk,cw){ // infinite iterator

s.append( c_next:=cw() );

sk:=s[rk.inc()]; // inc returns previous value, ie k++

if(sk>1) s.extend((List.createLong(sk - 1,c_next))); // list of sk cn's

sk // where we are in s, not end of s

}.fp(List(), Ref(0), Walker.cycle(start_items).next) )

.walk(length); // iterate length times, return list

}

fcn _run_len_encoding(truncated_series){ //List-->List

truncated_series.reduce(fcn(a,b,rm,s){ # if trailing singleton, it is ignored

if(a==b){ rm.inc(); return(b); }

s.append(rm.value);

rm.set(1);

b

}.fp2(Ref(1),s:=List()) );

s

}

fcn is_series_eq_its_rle(series){ //-->Bool

rle:=_run_len_encoding(series);

series[0,rle.len()]==rle

}

foreach sl in (List( L( L(1,2), 20), L( L(2, 1), 20),

L( L(1,3,1,2), 30), L( L(1,3,2,1), 30) )){

start_items, length := sl;

println("First %d members of the series generated from (%s) are:"

.fmt(length,start_items.concat(",")));

println(" (%s)".fmt(( s:=kolakoski(start_items, length) ).concat(",") ));

println(" Does it look like a Kolakoski sequence: ",is_series_eq_its_rle(s) )

}

Output:

First 20 members of the series generated from (1,2) are: (1,2,2,1,1,2,1,2,2,1,2,2,1,1,2,1,1,2,2,1) Does it look like a Kolakoski sequence: True First 20 members of the series generated from (2,1) are: (2,2,1,1,2,1,2,2,1,2,2,1,1,2,1,1,2,2,1,2) Does it look like a Kolakoski sequence: True First 30 members of the series generated from (1,3,1,2) are: (1,3,3,3,1,1,1,2,2,2,1,3,1,2,2,1,1,3,3,1,2,2,2,1,3,3,1,1,2,1) Does it look like a Kolakoski sequence: True First 30 members of the series generated from (1,3,2,1) are: (1,3,3,3,2,2,2,1,1,1,1,1,3,3,2,2,1,1,3,2,1,1,1,1,3,3,3,2,2,1) Does it look like a Kolakoski sequence: False