Kolakoski sequence

You are given an integer, $int > 3. Write a script to generate the Kolakoski Sequence of length $int and return the count of 1 in the generated sequence. Please follow the Wikipedia page for more information.

Examples

Example 1
Input: $int = 4
Output: 2
(1)(22)(11)(2) => 1221

Example 2
Input: $int = 5
Output: 3
(1)(22)(11)(2)(1) => 12211

Example 3
Input: $int = 6
Output: 3
(1)(22)(11)(2)(1)(22) => 122112

Example 4
Input: $int = 7
Output: 4
(1)(22)(11)(2)(1)(22)(1) => 1221121

Example 5
Input: $int = 8
Output: 4
(1)(22)(11)(2)(1)(22)(1)(22) => 12211212

Analysis

This is slightly mind-blowing for a Monday morning, but coding the helpful algorithm from the Wikipedia page is straightforward.

My solution generates a million terms in the sequence in a couple of seconds and reports 499,886 ones.

The post provides a clear, well-reasoned implementation of both tasks, with the Kolakoski solution closely following the Wikipedia algorithm and demonstrating impressive performance at scale. The NFL playoff logic is neatly modeled with concise Perl code, showing careful handling of seeding, sorting, and edge cases in a readable and maintainable way.

Try it 

#!/usr/bin/perl

# Blog: http://ccgi.campbellsmiths.force9.co.uk/challenge

use v5.26;    # The Weekly Challenge - 2026-01-12
use utf8;     # Week 356 - task 1 - Kolakoski sequence
use warnings; # Peter Campbell Smith
binmode STDOUT, ':utf8';
use Encode;

kolakoski_sequence(4);
kolakoski_sequence(10);
kolakoski_sequence(100);

sub kolakoski_sequence {
    
    my ($length, @sequence, $i, $ones, $this);
    
    # initialise
    $length = $_[0];
    @sequence = (1, 2, 2);
    $ones = 1;
    
    # add items to sequence until it reaches $length
    for ($i = 3; @sequence < $length; $i ++) {
        
        # find next digit to add (1 or 2)
        $this = $i & 1 ? 1 : 2;
        
        # add one or two of that digit
        push(@sequence, $this) for 1 .. $sequence[$i - 1];
        
        # count the ones
        $ones += $sequence[$i - 1] if $this == 1;
    }
    
    # report
    say qq[\nInput:  \$length = $length];
    say qq[Output: \$sequence = ] . join('', @sequence) . 
        qq[\n        containing $ones ones];
}

12 lines of code

Output from script

Input:  $length = 4
Output: $sequence = 12211
        containing 3 ones

Input:  $length = 10
Output: $sequence = 1221121221
        containing 5 ones

Input:  $length = 100
Output: $sequence = 1221121221221121122121121221121121221
221121221211211221221121221221121121221211221221121221221
121122
        containing 49 ones