It just struck me that this is (the same as) a fixed font text justification algorithm where the As are the words, and the Bs, the number of (extra) spaces to be distributed between the words to make up the line length.

Update: A crude example:

#! perl -slw
use strict;

our $WIDTH ||= 80;

my $buffer = '';
while( <DATA> ) {
    $buffer .= $_;
    $buffer =~ s[\s+][ ]g;
    $buffer =~ s[\. ][.  ]g;
    next unless eof( DATA ) or length( $buffer ) >= $WIDTH;
    while( length $buffer > $WIDTH ) {
        my $line = substr $buffer, 0, 1+rindex( $buffer, ' ', $WIDTH-1
+ )||-1,'';
        my $fill = $WIDTH - length $line;
        my $spaces = $line =~ m[(\s+)(?!$)]g;
        $fill = 0 unless $spaces;
        my $n = int $spaces / 2;
        while( $fill > 0 ) {
            $line =~ s[((?:\s+?\S+){$n})(?<=\S)(\s+)(?=\S)][
                $1 . $2 . ($fill-- > 0 ?  ' ' : '')
            ]ge;
            $n /= 2;
        }
        print $line;
#        printf "%-${WIDTH}s\t\t%d : %d\n", $line, length $line, lengt
+h( $buffer );
    }
}
print $buffer if length $buffer;;
#printf "%-${WIDTH}s\t\t%d : %d\n", $buffer, 0, length( $buffer );

__DATA__
Pickering is seated at the table, putting down some cards and a
tuning-fork which he has been using. Higgins is standing up near
him, closing two or three file drawers which are hanging out. He
appears in the morning light as a robust, vital, appetizing sort
of man of forty or thereabouts, dressed in a professional-looking
black frock-coat with a white linen collar and black silk tie. He
is of the energetic, scientific type, heartily, even violently
interested in everything that can be studied as a scientific
subject, and careless about himself and other people, including
their feelings. He is, in fact, but for his years and size,
rather like a very impetuous baby "taking notice" eagerly and
loudly, and requiring almost as much watching to keep him out of
unintended mischief. His manner varies from genial bullying when
he is in a good humor to stormy petulance when anything goes
wrong; but he is so entirely frank and void of malice that he
remains likeable even in his least reasonable moments.
[download]

C:\test>junk5 -WIDTH=80
Pickering  is  seated  at  the table, putting down some cards and a tu
+ning-fork
which he has been using.  Higgins is standing up near him, closing two
+ or three
file  drawers  which  are  hanging  out.   He appears in the morning l
+ight as a
robust,  vital,  appetizing  sort  of man of forty or thereabouts, dre
+ssed in a
professional-looking  black frock-coat with a white linen collar and b
+lack silk
tie.   He  is  of  the  energetic,  scientific  type,  heartily, even 
+violently
interested  in  everything  that  can  be  studied as a scientific sub
+ject, and
careless  about  himself and other people, including their feelings.  
+He is, in
fact,  but  for  his  years and size, rather like a very impetuous bab
+y "taking
notice"  eagerly  and loudly, and requiring almost as much watching to
+ keep him
out  of unintended mischief.  His manner varies from genial bullying w
+hen he is
in  a  good  humor  to  stormy petulance when anything goes wrong; but
+ he is so
entirely  frank  and  void of malice that he remains likeable even in 
+his least
reasonable moments.

C:\test>junk5 -WIDTH=60
Pickering  is  seated at the table, putting down some cards
and  a  tuning-fork  which  he  has been using.  Higgins is
standing  up  near  him,  closing two or three file drawers
which  are hanging out.  He appears in the morning light as
a  robust,  vital,  appetizing  sort  of  man  of  forty or
thereabouts,   dressed   in  a  professional-looking  black
frock-coat  with  a white linen collar and black silk tie.
He  is  of  the  energetic, scientific type, heartily, even
violently interested in everything that can be studied as a
scientific  subject,  and  careless about himself and other
people,  including their feelings.  He is, in fact, but for
his  years  and  size,  rather  like  a very impetuous baby
"taking notice" eagerly and loudly, and requiring almost as
much  watching to keep him out of unintended mischief.  His
manner  varies  from  genial  bullying when he is in a good
humor  to stormy petulance when anything goes wrong; but he
is  so  entirely  frank  and void of malice that he remains
likeable even in his least reasonable moments.

C:\test>junk5 -WIDTH=40
Pickering   is  seated  at  the  table,
putting   down   some   cards   and   a
tuning-fork  which  he has been using.
Higgins   is   standing  up  near  him,
closing two or three file drawers which
are  hanging  out.   He  appears in the
morning   light  as  a  robust,  vital,
appetizing  sort  of  man  of  forty or
thereabouts,      dressed      in     a
professional-looking  black  frock-coat
with  a  white  linen  collar and black
silk  tie.   He  is  of  the energetic,
scientific    type,    heartily,   even
violently interested in everything that
can be studied as a scientific subject,
and  careless  about  himself and other
people,  including  their feelings.  He
is,  in  fact,  but  for  his years and
size, rather like a very impetuous baby
"taking notice" eagerly and loudly, and
requiring  almost  as  much watching to
keep  him  out of unintended mischief.
His  manner varies from genial bullying
when  he  is  in a good humor to stormy
petulance when anything goes wrong; but
he  is  so  entirely  frank and void of
malice that he remains likeable even in
his least reasonable moments.
[download]