• Your diagram is easier to work with if you print it top-to-bottom instead of left-to-right, so I made that change.
• No hashing needed, as long as it is OK to do linear scans across all your tracks.
• I used first_index() from List::MoreUtils for clarity; it will be simple to duplicate its functionality in C.
• I wrote this code with *no* understanding of what you are trying to accomplish. Whether or not I got it right, please enlighten us on the root problem you are trying to solve (or mathematical behavior your are trying to explore, etc).

Working, tested code, insofar that I grasp the problem:

#!/usr/bin/env perl
use strict;
use warnings;
use List::MoreUtils qw(first_index);

my $duplicate_original_post_data = 1;

my $generation_limit = 99;
my $r1_count_limit   =  4; # 1..4 elements
my @r1_keys = 0 .. ($r1_count_limit-1);

sub pad { map {$_[$_] || ''} @r1_keys }

my ( $R1, $R2 );
if ( not $duplicate_original_post_data ) {
    $R1 = sub {
        my $n =        1 + int rand $r1_count_limit;
        return   map { 1 + int rand 100 } ( (0) x $n );
    };
    $R2 = sub { return 1 + int rand  20 };
}
else {
    my @fake_r1 = (
        [  17,   1,  20,  12 ],
        [  13,  24,  21      ],
        [  19,  30,  31,  27 ],
        [  22,  34           ],
    );
    my @fake_r2 = ( 4, 6, 3 );
    $generation_limit = @fake_r1;
    $R1 = sub { return @{ shift @fake_r1 } };
    $R2 = sub { return    shift @fake_r2   };
}

my $template = "%5s %5s %5s %5s %5s %5s  ->  %5s %5s %5s %5s\n";
my @last_array = $R1->();

printf $template, qw(Gen R1.1 R1.2 R1.3 R1.4 R2 Trk1 Trk2 Trk3 Trk4);
printf $template,      1, pad( @last_array ),
                  'None', pad( @last_array );


for my $generation ( 2 .. $generation_limit ) {
    my @r1_array = $R1->();
    my $r2       = $R2->();

    my @leftover;
    my @new_array = (0) x $r1_count_limit;
    for my $r1_num (@r1_array) {
        my $target = $r1_num - $r2;
        my $slot_to_use = first_index { $_ != 0 and $_ == $target }
                                      @last_array;

        if ( $slot_to_use == -1 ) {
            push @leftover, $r1_num;
        }
        else {
            $new_array[ $slot_to_use] = $r1_num;
            $last_array[$slot_to_use] = 0;
        }
    }

    my @empty_slots = grep { $new_array[$_] == 0 } @r1_keys;
    while (@leftover) {
        die if not @empty_slots;
        $new_array[ shift @empty_slots ] = shift @leftover;
    }

    printf $template, $generation, pad( @r1_array  ),
                      $r2,         pad( @new_array );

    @last_array = @new_array;
}
[download]

Output:

Gen  R1.1  R1.2  R1.3  R1.4    R2  ->   Trk1  Trk2  Trk3  Trk4
  1    17     1    20    12  None  ->     17     1    20    12
  2    13    24    21           4  ->     21    13    24      
  3    19    30    31    27     6  ->     27    19    30    31
  4    22    34                 3  ->           22          34
[download]

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