Kolakoski sequence
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
2ones, followed by3twos, then1ones,2twos,1one, ...
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
swith the first item from the cyclec:
1 - An index,
k, into the, (expanding), sequence will step, or index through each item of the sequencesfrom the first, at its own rate.
We will arrange that the k'th item of s states how many times the last item of sshould 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
kGet the next item from
cand append it to the end of sequences.swill then become:
1, 2kwas moved to the second item in the list ands[k]states that it should appear two times, so append another of the last item to the sequences:
1, 2,2Increment
kAppend the next item from the cycle to the list:
1, 2,2, 1kis 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 sequences:
1, 2,2, 1,1increment 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)
C
<lang c>#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(":\n");
print_array(s, slen);
printf("\n");
p = possible_kolakoski(s, slen);
printf("Possible Kolakoski sequence? %s\n\n", p ? "True" : "False");
free(s);
}
return 0;
}</lang>
- 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
C#
<lang csharp>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();
}
}
}
}</lang>
C++
<lang cpp>#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;
}</lang>
- 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
D
<lang d>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;
}
}</lang>
- 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
Go
<lang go>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\n", 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, "\n")
}
}</lang>
- 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
Haskell
<lang haskell>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)]
$ \(items, n) -> do
putStrLn $ "First " ++ show n ++ " members of the sequence generated by " ++ show items ++ ":"
let s = kolakoski items
print $ take n s
putStrLn $ "Possible Kolakoski sequence? " ++ show (sameAsRleUpTo n s)
putStrLn ""</lang>
- Output:
First 20 members of the sequence generated by [1,2]: [1,2,2,1,1,2,1,2,2,1,2,2,1,1,2,1,1,2,2,1] Possible Kolakoski sequence? True First 20 members of the sequence generated by [2,1]: [2,2,1,1,2,1,2,2,1,2,2,1,1,2,1,1,2,2,1,2] Possible Kolakoski sequence? True First 30 members of the sequence generated by [1,3,1,2]: [1,3,3,3,1,1,1,2,2,2,1,3,1,2,2,1,1,3,3,1,2,2,2,1,3,3,1,1,2,1] Possible Kolakoski sequence? True First 30 members of the sequence generated by [1,3,2,1]: [1,3,3,3,2,2,2,1,1,1,1,1,3,3,2,2,1,1,3,2,1,1,1,1,3,3,3,2,2,1] Possible Kolakoski sequence? False
J
<lang J> NB. cyclic
create_cycle_=: 3 :0
I=: 0 A=: y N=: # A
)
next_cycle_=: 3 :0
r=. A {~ N | I
I=: >: I
r
)
NB. kolakoski
kolakoski =: 30&$: :(dyad define) NB. TERMS kolakoski ALPHABET
c=. y conew'cycle'
s=. i. 0
term=. 0
while. x > # s do.
s=. (, ([: #~ next__c)`(term&{ # next__c)@.(term < #)) s
term=. >: term
end.
s
)
test=: (({.~ #) -: ]) }:@:(#;.1~ (1 , 2&(~:/\)))
</lang>
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│ └───────┴─┴─────────────────────────────────────────────────────────────┘
Java
<lang java>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: \n", len, Arrays.toString(ias[i]));
System.out.printf("%s\n", Arrays.toString(kol));
System.out.printf("Possible Kolakoski sequence? %s\n\n", possibleKolakoski(kol));
}
}
}</lang>
- 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
Julia
<lang julia>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
</lang>
- 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
Kotlin
<lang scala>// 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"}\n")
}
}</lang>
- 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
Lua
<lang lua>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</lang>
- 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
Perl
<lang perl>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 "\n$terms members of the series generated from [@$_] is:\n";
print join(' ', @kolakoski = kolakoski($terms, @$_)) . "\n";
$status = join(, @rle = rle(@kolakoski)) eq join(, @kolakoski[0..$#rle]) ? 'True' : 'False';
print "Looks like a Kolakoski sequence?: $status\n";
}</lang>
- 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
Phix
<lang Phix>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", {n,sprint(c)})
?s
bool p = possible_kolakoski(s)
printf(1,"Possible Kolakoski sequence? %s\n\n", {iff(p ? "Yes" : "No")})
end for</lang>
- 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
Python 3.6+
<lang python>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'\n## {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}')</lang>
- 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
Raku
(formerly Perl 6)
<lang perl6>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 "\n## $terms members of the series generated from { @seed.perl } is:\n ",
my @kolakoski = kolakoski(@seed)[^$terms];
my @rle = rle @kolakoski;
say " Looks like a Kolakoski sequence?: ", @rle[*] eqv @kolakoski[^@rle];
}</lang>
- 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
Ruby
<lang Ruby>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 "\nFirst #{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</lang>
- 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
Sidef
<lang 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 "\nFirst #{num} of the sequence generated by #{arr}:"
var res = create_generator(arr).first(num)
var rle = res.run_length.map{.tail}
say "#{res}\nPossible Kolakoski sequence? #{res.first(rle.len) == rle}"
}</lang>
- 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
Visual Basic .NET
<lang vbnet>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</lang>
- 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
zkl
<lang zkl>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
}</lang> <lang zkl>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
}</lang> <lang zkl>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) )
}</lang>
- 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