Find words, that are substrings of other words efficiently - regex

Question

I have an Ispell list of english words (nearly 50 000 words), my homework in Perl is to get quickly (like under one minute) list of all strings, that are substrings of some other word. I have tried solution with two foreach cycles comparing all words, but even with some optimalizations, its still too slow. I think, that right solution could be some clever use of regular expressions on array of words. Do you know how to solve this problem quicky (in Perl)?

Answer 1

I have found fast solution, which can find some all these substrings in about 15 seconds on my computer, using just one thread. Basically, for each word, I have created array of every possible substrings (eliminating substrings which differs only in "s" or "'s" endings):
#take word and return list of all valid substrings
sub split_to_all_valid_subwords {
my $word = $_[0];
my #split_list;
my ($i, $j);
for ($i = 0; $i < length($word); ++$i){
for ($j = 1; $j <= length($word) - $i; ++$j){
unless
(
($j == length($word)) or
($word =~ m/s$/ and $i == 0 and $j == length($word) - 1) or
($word =~ m/\'s$/ and $i == 0 and $j == length($word) - 2)
)
{
push(#split_list, substr($word, $i, $j));
}
}
}
return #split_list;
}
Then I just create list of all candidates for substrings and make intersection with words:
my #substring_candidates;
foreach my $word (#words) {
push( #substring_candidates, split_to_all_valid_subwords($word));
}
#make intersection between substring candidates and words
my %substring_candidates=map{$_ =>1} #substring_candidates;
my %words=map{$_=>1} #words;
my #substrings = grep( $substring_candidates{$_}, #words );
Now in substrings I have array of all words, that are substrings of some other words.

Answer 2

Perl regular expressions will optimize patterns like foo|bar|baz into an Aho-Corasick match - up to a certain limit of total compiled regex length. Your 50000 words will probably exceed that length, but could be broken into smaller groups. (Indeed, you probably want to break them up by length and only check words of length N for containing words of length 1 through N-1.)
Alternatively, you could just implement Aho-Corasick in your perl code - that's kind of fun to do.

Answer 3

update
Ondra supplied a beautiful solution in his answer; I leave my post here as an example of overthinking a problem and failed optimisation techniques.
My worst case kicks in for a word that doesn't match any other word in the input. In that case, it goes quadratic. The OPT_PRESORT was a try to advert the worst case for most words. The OPT_CONSECUTIVE was a linear-complexity filter that reduced the total number of items in the main part of the algorithm, but it is just a constant factor when considering the complexity. However, it is still useful with Ondras algorithm and saves a few seconds, as building his split list is more expensive than comparing two consecutive words.
I updated the code below to select ondras algorithm as a possible optimisation. Paired with zero threads and the presort optimisation, it yields maximum performance.
I would like to share a solution I coded. Given an input file, it outputs all those words that are a substring of any other word in the same input file. Therefore, it computes the opposite of ysth's ideas, but I took the idea of optimisation #2 from his answer. There are the following three main optimisations that can be deactivated if required.
Multithreading
The questions "Is word A in list L? Is word B in L?" can be easily parallelised.
Pre-sorting all the words for their length
I create an array that points to the list of all words that are longer than a certain length, for every possible length. For long words, this can cut down the number of possible words dramatically, but it trades quite a lot of space, as one word of length n appears in all lists from length 1 to length n.
Testing consecutive words
In my /usr/share/dict/words, most consecutive lines look quite similar:
Abby
Abby's
for example. As every word that would match the first word also matches the second one, I immediately add the first word to the list of matching words, and only keep the second word for further testing. This saved about 30% of words in my test cases. Because I do that before optimisation No 2, this also saves a lot of space. Another trade-off is that the output will not be sorted.
The script itself is ~120 lines long; I explain each sub before showing it.
head
This is just a standard script header for multithreading. Oh, and you need perl 5.10 or better to run this. The configuration constants define the optimisation behaviour. Add the number of processors of your machine in that field. The OPT_MAX variable can take the number of words you want to process, however this is evaluated after the optimisations have taken place, so the easy words will already have been caught by the OPT_CONSECUTIVE optimisation. Adding anything there will make the script seemingly slower. $|++ makes sure that the status updates are shown immediately. I exit after the main is executed.
#!/usr/bin/perl
use strict; use warnings; use feature qw(say); use threads;
$|=1;
use constant PROCESSORS => 0; # (false, n) number of threads
use constant OPT_MAX => 0; # (false, n) number of words to check
use constant OPT_PRESORT => 0; # (true / false) sorts words by length
use constant OPT_CONSECUTIVE => 1; # (true / false) prefilter data while loading
use constant OPT_ONDRA => 1; # select the awesome Ondra algorithm
use constant BLABBER_AT => 10; # (false, n) print progress at n percent
die q(The optimisations Ondra and Presort are mutually exclusive.)
if OPT_PRESORT and OPT_ONDRA;
exit main();
main
Encapsulates the main logic, and does multi-threading. The output of n words will be matched will be considerably smaller than the number of input words, if the input was sorted. After I have selected all matched words, I print them to STDOUT. All status updates etc. are printed to STDERR, so that they don't interfere with the output.
sub main {
my #matching; # the matching words.
my #words = load_words(\#matching); # the words to be searched
say STDERR 0+#words . " words to be matched";
my $prepared_words = prepare_words(#words);
# do the matching, possibly multithreading
if (PROCESSORS) {
my #threads =
map {threads->new(
\&test_range,
$prepared_words,
#words[$$_[0] .. $$_[1]] )
} divide(PROCESSORS, OPT_MAX || 0+#words);
push #matching, $_->join for #threads;
} else {
push #matching, test_range(
$prepared_words,
#words[0 .. (OPT_MAX || 0+#words)-1]);
}
say STDERR 0+#matching . " words matched";
say for #matching; # print out the matching words.
0;
}
load_words
This reads all the words from the input files which were supplied as command line arguments. Here the OPT_CONSECUTIVE optimisation takes place. The $last word is either put into the list of matching words, or into the list of words to be matched later. The -1 != index($a, $b) decides if the word $b is a substring of word $a.
sub load_words {
my $matching = shift;
my #words;
if (OPT_CONSECUTIVE) {
my $last;
while (<>) {
chomp;
if (defined $last) {
push #{-1 != index($_, $last) ? $matching : \#words}, $last;
}
$last = $_;
}
push #words, $last // ();
} else {
#words = map {chomp; $_} <>;
}
#words;
}
prepare_words
This "blows up" the input words, sorting them after their length into each slot, that has the words of larger or equal length. Therefore, slot 1 will contain all words. If this optimisation is deselected, it is a no-op and passes the input list right through.
sub prepare_words {
if (OPT_ONDRA) {
my $ondra_split = sub { # evil: using $_ as implicit argument
my #split_list;
for my $i (0 .. length $_) {
for my $j (1 .. length($_) - ($i || 1)) {
push #split_list, substr $_, $i, $j;
}
}
#split_list;
};
return +{map {$_ => 1} map &$ondra_split(), #_};
} elsif (OPT_PRESORT) {
my #prepared = ([]);
for my $w (#_) {
push #{$prepared[$_]}, $w for 1 .. length $w;
}
return \#prepared;
} else {
return [#_];
}
}
test
This tests if the word $w is a substring in any of the other words. $wbl points to the data structure that was created by the previous sub: Either a flat list of words, or the words sorted by length. The appropriate algorithm is then selected. Nearly all of the running time is spent in this loop. Using index is much faster than using a regex.
sub test {
my ($w, $wbl) = #_;
my $l = length $w;
if (OPT_PRESORT) {
for my $try (#{$$wbl[$l + 1]}) {
return 1 if -1 != index $try, $w;
}
} else {
for my $try (#$wbl) {
return 1 if $w ne $try and -1 != index $try, $w;
}
}
return 0;
}
divide
This just encapsulates an algorithm that guarantees a fair distribution of $items items into $parcels buckets. It outputs the bounds of a range of items.
sub divide {
my ($parcels, $items) = #_;
say STDERR "dividing $items items into $parcels parcels.";
my ($min_size, $rest) = (int($items / $parcels), $items % $parcels);
my #distributions =
map [
$_ * $min_size + ($_ < $rest ? $_ : $rest),
($_ + 1) * $min_size + ($_ < $rest ? $_ : $rest - 1)
], 0 .. $parcels - 1;
say STDERR "range division: #$_" for #distributions;
return #distributions;
}
test_range
This calls test for each word in the input list, and is the sub that is multithreaded. grep selects all those elements in the input list where the code (given as first argument) return true. It also regulary outputs a status message like thread 2 at 10% which makes waiting for completition much easier. This is a psychological optimisation ;-).
sub test_range {
my $wbl = shift;
if (BLABBER_AT) {
my $range = #_;
my $step = int($range / 100 * BLABBER_AT) || 1;
my $i = 0;
return
grep {
if (0 == ++$i % $step) {
printf STDERR "... thread %d at %2d%%\n",
threads->tid,
$i / $step * BLABBER_AT;
}
OPT_ONDRA ? $wbl->{$_} : test($_, $wbl)
} #_;
} else {
return grep {OPT_ONDRA ? $wbl->{$_} : test($_, $wbl)} #_;
}
}
invocation
Using bash, I invoked the script like
$ time (head -n 1000 /usr/share/dict/words | perl script.pl >/dev/null)
Where 1000 is the number of lines I wanted to input, dict/words was the word list I used, and /dev/null is the place I want to store the output list, in this case, throwing the output away. If the whole file should be read, it can be passed as an argument, like
$ perl script.pl input-file >output-file
time just tells us how long the script ran. Using 2 slow processors and 50000 words, it executed in just over two minutes in my case, which is actually quite good.
update: more like 6–7 seconds now, with the Ondra + Presort optimisation, and no threading.
further optimisations
update: overcome by better algorithm. This section is no longer completely valid.
The multithreading is awful. It allocates quite some memory and isn't exactly fast. This isn't suprising considering the amount of data. I considered using a Thread::Queue, but that thing is slow like $#*! and therefore is a complete no-go.
If the inner loop in test was coded in a lower-level language, some performance might be gained, as the index built-in wouldn't have to be called. If you can code C, take a look at the Inline::C module. If the whole script were coded in a lower language, array access would also be faster. A language like Java would also make the multithreading less painful (and less expensive).