NAME
List::BinarySearch - Binary Search a sorted list or array.
VERSION
Version 0.02
Stable release.
SYNOPSIS
This module performs a binary search on an array passed by reference, or on an array or list passed as a flat list.
Examples:
use List::BinarySearch qw( :all );
use List::BinarySearch qw(
bsearch_str bsearch_num bsearch_general
bsearch_custom bsearch_transform
);
my @num_array = ( 100, 200, 300, 400, 500 );
my $index;
# Find the first index of element containing the number 300.
$index = bsearch_num 300, @num_array;
$index = bsearch_general 300, @num_array;
$index = bsearch_custom { $_[0] <=> $_[1] } 300, @num_array;
$index = bsearch_transform { $_[0] } 300, @num_array;
my @str_array = qw( Brahms Beethoven Schubert Mozart Bach );
# Find the first index of element containing the string 'Mozart'.
$index = bsearch_str 'Mozart', @str_array;
$index = bsearch_general 'Mozart', @str_array;
$index = bsearch_custom { $_[0] cmp $_[1] } 'Mozart', @str_array;
$index = bsearch_transform { $_[0] } 'Mozart', @str_array;
# All functions return 'undef' if nothing is found:
$index = bsearch_str 'Meatloaf', @str_array; # not found: returns undef
$index = bsearch_num 42, @num_array; # not found: returns undef
# Complex data structures:
my @complex = (
[ 'one', 1 ],
[ 'two', 2 ],
[ 'three', 3 ],
[ 'four' , 4 ],
[ 'five' , 5 ],
);
# Find 'one' from the structure above:
$index = bsearch_custom { $_[0] cmp $_[1][0] } 'one', @complex;
$index = besarch_custom { $_[1][0] } 'one', @complex;DESCRIPTION
A binary search searches sorted lists using a divide and conquer technique. On each iteration the search domain is cut in half, until the result is found. The computational complexity of a binary search is O(log n).
The binary search algorithm implemented in this module is known as a Deferred Detection variant on the traditional Binary Search. Deferred Detection provides stable searches. Stable binary search algorithms have the following characteristics, contrasted with their unstable binary search cousins:
In the case of non-unique keys, a stable binary search will always return the lowest-indexed matching element. An unstable binary search would return the first one found, which may not be the chronological first.
Best and worst case time complexity is always O(log n). Unstable searches may find the target in fewer iterations in the best case, but in the worst case would still be O(log n).
Stable binary searches only require one relational comparison of a given pair of data elements per iteration, where unstable binary searches require two comparisons per iteration.
The net result is that although an unstable binary search might have a better "best case" time complexity, the fact that a stable binary search gets away with fewer comparisons per iteration gives it better performance in the worst case, and approximately equal performance in the average case. By trading away slightly better "best case" performance, the stable search gains the guarantee that the element found will always be the lowest-indexed element in a range of non-unique keys.
RATIONALE
Quoting from Wikipedia: When Jon Bentley assigned it as a problem in a course for professional programmers, he found that an astounding ninety percent failed to code a binary search correctly after several hours of working on it, and another study shows that accurate code for it is only found in five out of twenty textbooks. Furthermore, Bentley's own implementation of binary search, published in his 1986 book Programming Pearls, contains an error that remained undetected for over twenty years.
So the answer to the question "Why use a module for this?" is "Because it has already been written and tested. You don't have to write, test, and debug your own implementation.
Nevertheless, before using this module the user should weigh the other options: linear searches ( grep or List::Util::first ), or hash based searches. A binary search only makes sense if the data set is already sorted in ascending order, and if it is determined that the cost of a linear search, or the linear-time conversion to a hash-based container is too inefficient or demands too much memory. So often, it just doesn't make sense to try to optimize beyond what Perl's tools natively provide.
However, there are cases where, a binary search may be an excellent choice. Finding the first matching element in a list of 1,000,000 items with a linear search would have a worst-case of 1,000,000 iterations, whereas the worst case for a binary search of 1,000,000 elements is about 20 iterations. In fact, if many lookups will be performed on a seldom-changed list, the savings of O(log n) lookups may outweigh the cost of sorting or performing occasional ordered inserts.
Profile, then benchmark, then consider (and benchmark) the options, and finally, optimize.
EXPORT
Nothing is exported by default. Upon request will export bsearch_custom, bsearch_general, or both functions by specifying :all.
SUBROUTINES/METHODS
bsearch_str STRING_TARGET ARRAY
$first_found_ix = bsearch $target, $array_ref;Finds the string specified by $target in the array @array. Return value is an index to the first (lowest numbered) matching element in @array, or undef if nothing is found. String comparisons are used. The target must be an exact and complete match.
bsearch_num NUMERIC_TARGET ARRAY
$first_found_ix = bsearch $target, $array_ref;Finds the numeric needle $target in the haystack @array. Return value is an index to the first (lowest numbered) matching element in @array, or undef if $target isn't found.
The comparison type is numeric.
bsearch_general TARGET ARRAY
$first_found_ix = bsearch_general $target, @array;Detects whether $target is a string or number, and performs the appropriate comparisons to find $target in the haystack @array. Return value is an index to the first (lowest numbered) matching element in @array.
The comparison type is automatically detected for numbers or strings. This extra magic is a convenience that does incur a small performance penalty.
If $target isn't found, the return value will be undef.
bsearch_custom CODE TARGET ARRAY
$first_found_ix = bsearch_custom { $_[0] cmp $_[1] } $target, @array;
$first_found_ix = bsearch_custom \&comparator, $target, @array;Pass a code block or subref, a search target, and an array to search. Uses the subroutine suppled in the code block or subref callback to test target against elements in @array.
Return value is the index of the first element equalling $target. If no element is found, undef is returned.
Beware a potential 'gotcha': When dealing with complex data structures, the callback function will have an asymmetrical look to it, which is easy to get wrong. The target will always be referred to by $_[0], but the right hand side of the comparison must refer to the $_[1]..., where ... is the portion of the data structure to be used in the comparison: $_[1][$n], or $_[1]{$k}, for example.
bsearch_transform CODE TARGET ARRAY
$first_found_ix = bsearch_transform { $_[0] } $target, @array;
$first_found_ix = bsearch_transform \&transformer, $target, @array );Pass a transform code block or subref, a target to find, and an array to find it in. Return value is the lowest numbered index to an element matching $target, or undef if nothing is found.
This algorithm detects whether $target looks like a number or a string. If it looks like a number, numeric comparisons are performed. Otherwise, stringwise comparisons are used. The transform code block or coderef is used to transform each element of the search array to a value that can be compared against the target. This is useful if @array contains a complex data structure, and less prone to user error in such cases than bsearch_custom.
If no transformation is needed, use bsearch_str, bsearch_num, or bsearch_custom.
\&comparator
(callback)
Comparator functions are used by bsearch_custom.
Comparators are references to functions that accept as parameters a target, and a list element, returning the result of the relational comparison of the two values. A good example would be the code block in a sort function, except that our comparators get their input from @_, where sort's comparator functions get their input from $a and $b.
Basic comparators might be defined like this:
# Numeric comparisons:
$comp = sub {
my( $target, $list_item ) = @_;
return $target <=> $list_item;
};
# Non-numeric (stringwise) comparisons:
$comp = sub {
my( $target, $list_item ) = @_;
return $target cmp $list_item;
};The first parameter passed to the comparator will be the target. The second parameter will be the contents of the element being tested. This leads to an asymetry that might be prone to "gotchas" when writing custom comparators for searching complex data structures. As an example, consider the following data structure:
my @structure = (
[ 100, 'ape' ],
[ 200, 'frog' ],
[ 300, 'dog' ],
[ 400, 'cat' ]
);A numeric custom comparator for such a data structure would look like this:
sub{ $_[0] <=> $_[1][0]; }...or more explicitly...
sub{
my( $target, $list_item ) = @_;
return $target <=> $list_item->[0];
}Therefore, a call to bsearch_custom where the target is to solve for $unknown such that $structure[$unknown][0] == 200 might look like this:
my $found_ix = bsearch_custom { $_[0] <=> $_[1][0] }, 200, @structure;
print $structure[$found_ix][1], "\n" if defined $found_ix;
# prints 'frog'\&transform
(callback)
The transform callback routine is used by bsearch_transform() to transform a given search list element into something that can be compared against $target. As an example, consider the following complex data structure:
my @structure = (
[ 100, 'ape' ],
[ 200, 'frog' ],
[ 300, 'dog' ],
[ 400, 'cat' ]
);If the goal is do a numeric search using the first element of each integer/string pair, the transform sub might be written like this:
sub transform {
return $_[0][0]; # Returns 100, 200, 300, etc.
}Or if the goal is instead to search by the second element of each int/str pair, the sub would instead look like this:
sub transform {
return $_[0][1];
}A transform sub that results in each list element being compared as-is against the target would be:
sub transform { $_[0] }This will be recognized, of course, as an identity sub.
DATA SET REQUIREMENTS
A well written general algorithm should place as few demands on its data as practical. The three requirements that these Binary Search algorithms impose are:
The lists must be in ascending sorted order.
This is a big one. Keep in mind that the best sort routines run in O(n log n) time. It makes no sense to sort a list in O(n log n), and then perform a single O(log n) binary search when List::Util
firstcould accomplish the same thing in O(n) time. A Binary Search only makes sense if there are other good reasons for keeping the data set sorted in the first place.Passing an unsorted list to these Binary Search algorithms will result in undefined behavior.
A Binary Search consumes O(log n) time. It would, therefore, be foolish for these algorithms to pre-check the list for sortedness, as that would require linear, or O(n) time. Since no sortedness testing is done, there can be no guarantees as to what will happen if an unsorted list is passed to a binary search.
Data that is more complex than simple numeric or string lists will require a custom comparator.
CONFIGURATION AND ENVIRONMENT
This module should run under any Perl from 5.6.0 onward. There are no special environment or configuration concerns to address. In the future, an XS plugin will be implemented, and at that time there may be additional configuration details in this section.
DEPENDENCIES
This module uses Exporter and Scalar::Util, both of which are core modules. Installation requires Test::More, which is also a core module.
INCOMPATIBILITIES
This module hasn't been tested on Perl versions that predate Perl 5.6.0.
AUTHOR
David Oswald, <davido at cpan.org>
If the documentation fails to answer your question, or if you have a comment or suggestion, send me an email.
DIAGNOSTICS
BUGS AND LIMITATIONS
Please report any bugs or feature requests to bug-list-binarysearch at rt.cpan.org, or through the web interface at http://rt.cpan.org/NoAuth/ReportBug.html?Queue=List-BinarySearch. I will be notified, and then you'll automatically be notified of progress on your bug as I make changes.
SUPPORT
You can find documentation for this module with the perldoc command.
perldoc List::BinarySearchThis module is maintained in a public repo at Github. You may look for information at:
Github: Development is hosted on Github at:
RT: CPAN's request tracker (report bugs here)
AnnoCPAN: Annotated CPAN documentation
CPAN Ratings
Search CPAN
ACKNOWLEDGEMENTS
Necessity, who is the mother of invention. -- plato.
Although the basic idea of binary search is comparatively straightforward, the details can be surprisingly tricky... -- Donald Knuth
LICENSE AND COPYRIGHT
Copyright 2012 David Oswald.
This program is free software; you can redistribute it and/or modify it under the terms of either: the GNU General Public License as published by the Free Software Foundation; or the Artistic License.
See http://dev.perl.org/licenses/ for more information.