++ed by:
2 non-PAUSE users

# NAME

Set::IntSpan::Fast - Fast handling of sets containing integer spans.

# VERSION

This document describes Set::IntSpan::Fast version 1.15

# SYNOPSIS

``````    use Set::IntSpan::Fast;

my \$set = Set::IntSpan::Fast->new();
print \$set->as_string(), "\n";    # prints 1,3,5,7,9,100-1000000``````

# DESCRIPTION

`Set::IntSpan::Fast` represents sets of integers. It is optimised for sets that contain contiguous runs of values.

``    1-1000, 2000-10000      # Efficiently handled``

Sets that don't have this characteristic may still be represented but some of the performance and storage space advantages will be lost. Consider using bit vectors if your set does not typically contain clusters of values.

Sets may be infinite - assuming you're prepared to accept that infinity is actually no more than a fairly large integer. Specifically the constants `Set::IntSpan::Fast::NEGATIVE_INFINITY` and `Set::IntSpan::Fast::POSITIVE_INFINITY` are defined to be -(2^31-1) and (2^31-2) respectively. To create an infinite set invert an empty one:

``    my \$inf = Set::IntSpan::Fast->new()->complement();``

Sets need only be bounded in one direction - for example this is the set of all positive integers (assuming you accept the slightly feeble definition of infinity we're using):

``````    my \$pos_int = Set::IntSpan::Fast->new();

## Set representation

The internal representation used is extremely simple: a set is represented as a list of integers. Integers in even numbered positions (0, 2, 4 etc) represent the start of a run of numbers while those in odd numbered positions represent the ends of runs. As an example the set (1, 3-7, 9, 11, 12) would be represented internally as (1, 2, 3, 8, 11, 13).

## Comparision with Set::IntSpan

The `Set::IntSpan` module represents sets of integers as a number of inclusive ranges, for example '1-10,19-23,45-48'. Because many of its operations involve linear searches of the list of ranges its overall performance tends to be proportional to the number of distinct ranges. This is fine for small sets but suffers compared to other possible set representations (bit vectors, hash keys) when the number of ranges grows large.

This module also represents sets as ranges of values but stores those ranges in order and uses a binary search for many internal operations so that overall performance tends towards O log N where N is the number of ranges.

## `Set::IntSpan::Fast::XS`

If Set::IntSpan::Fast::XS is installed it will automatically be used when a new `Set::IntSpan::Fast` is created. There is no need to change any code; the XS module is automatically detected and loaded.

If you have a C compiler consider installing `Set::IntSpan::Fast::XS` for even better performance.

# INTERFACE

## `new`

Create a new set. Any arguments will be processed by a call to `add_from_string`:

``    my \$set = Set::IntSpan::Fast->new( '1, 3, 5, 10-100' );``

Because `add_from_string` handles multiple arguments this will work:

``````    my @nums = ( 1, 2, 3, 4, 5 );
my \$set = Set::IntSpan::Fast->new( @nums );``````

Bear in mind though that this validates each element of the array is it would if you called `add_from_string` so for large sets it will be slightly more efficient to create an empty set and then call `add`.

## `invert`

Complement the set. Because our notion of infinity is actually disappointingly finite inverting a finite set results in another finite set. For example inverting the empty set makes it contain all the integers between `NEGATIVE_INFINITY` and `POSITIVE_INFINITY` inclusive.

As noted above `NEGATIVE_INFINITY` and `POSITIVE_INFINITY` are actually just big integers.

## `copy`

Return an identical copy of the set.

``    my \$new_set = \$set->copy();``

## `add( \$number ... )`

Add the specified integers to the set. Any number of arguments may be specified in any order. All arguments must be integers between `Set::IntSpan::NEGATIVE_INFINITY` and `Set::IntSpan::POSITIVE_INFINITY` inclusive.

## `remove( \$number ... )`

Remove the specified integers from the set. It is not an error to remove non-members. Any number of arguments may be specified.

## `add_range( \$from, \$to )`

Add the inclusive range of integers to the set. Multiple ranges may be specified:

``    \$set->add_range(1, 10, 20, 22, 15, 17);``

Each pair of arguments constitute a range. The second argument in each pair must be greater than or equal to the first.

## `add_from_string( \$string )`

Add items to a set from a string representation, of the same form as `as_string`. Multiple strings may be supplied:

``    \$set->add_from_string( '1-10, 30-40', '100-200' );``

is equivalent to

``    \$set->add_from_string( '1-10, 30-40, 100-200' );``

By default items are separated by ',' and ranges delimited by '-'. You may select different punctuation like this:

``````    \$set->add_from_string(
{ sep => ';', range => ':' },
'1;3;5;7:11;19:27'
);
``````

When supplying an options hash in this way the `sep` and `range` option may be either a regular expression or a literal string.

``````    \$set->add_from_string(
{ sep => qr/:+/, range => qr/[.]+/ },
'1::3::5:7...11:19..27'
);``````

Any embedded whitespace in the string will be ignored.

## `remove_range( \$from, \$to )`

Remove the inclusive range of integers from the set. Multiple ranges may be specified:

``    \$set->remove_range(1, 10, 20, 22, 15, 17);``

Each pair of arguments constitute a range. The second argument in each pair must be greater than or equal to the first.

## `remove_from_string( \$string )`

Remove items to a set from a string representation, of the same form as `as_string`. As with `add_from_string` the punctuation characters may be specified.

## `merge( \$set ... )`

Merge the members of the supplied sets into this set. Any number of sets may be supplied as arguments.

Empty a set.

## Operators

### `complement`

Returns a new set that is the complement of this set. See the comments about our definition of infinity above.

### `union( \$set ... )`

Return a new set that is the union of this set and all of the supplied sets.

``    \$un = \$set->union( \$other_set );``

### `intersection( \$set )`

Return a new set that is the intersection of this set and all the supplied sets.

``    \$in = \$set->intersection( \$other_set );``

### `xor( \$set )`

Return a new set that contains all of the members that are in this set or the supplied set but not both. Can actually handle more than two sets in which case it returns a set that contains all the members that are in some of the sets but not all of the sets.

### `diff( \$set )`

Return a set containing all the elements that are in this set but not the supplied set.

## Tests

### `is_empty`

Return true if the set is empty.

### `contains( \$number )`

Return true if the specified number is contained in the set.

### `contains_any(\$number, \$number, \$number ...)`

Return true if the set contains any of the specified numbers.

### `contains_all(\$number, \$number, \$number ...)`

Return true if the set contains all of the specified numbers.

### `contains_all_range( \$low, \$high )`

Return true if all the numbers in the range `\$low` to `\$high` (inclusive) are in the set.

### `cardinality( [ \$clip_lo, \$clip_hi ] )`

Returns the number of members in the set. If a clipping range is supplied return the count of members that fall within that inclusive range.

### `superset( \$set )`

Returns true if this set is a superset of the supplied set. A set is always a superset of itself, or in other words

``````    \$set->superset( \$set )
``````

returns true.

### `subset( \$set )`

Returns true if this set is a subset of the supplied set. A set is always a subset of itself, or in other words

``````    \$set->subset( \$set )
``````

returns true.

### `equals( \$set )`

Returns true if this set is identical to the supplied set.

## Getting set contents

### `as_array`

Return an array containing all the members of the set in ascending order.

### `as_string`

Return a string representation of the set.

``````    my \$set = Set::IntSpan::Fast->new();
print \$set->as_string(), "\n";    # prints 1,3,5,7,9,100-1000000``````

You may optionally supply a hash containing `sep` and `range` options:

``````    print \$set->as_string({ sep => ';', range => '*' ), "\n";
# prints 1;3;5;7;9;100*1000000``````

### `iterate_runs( [ \$clip_lo, \$clip_hi ] )`

Returns an iterator that returns each run of integers in the set in ascending order. To iterate all the members of the set do something like this:

``````    my \$iter = \$set->iterate_runs();
while (my ( \$from, \$to ) = \$iter->()) {
for my \$member (\$from .. \$to) {
print "\$member\n";
}
}``````

If a clipping range is specified only those members that fall within the range will be returned.

## Constants

The constants `NEGATIVE_INFINITY` and `POSITIVE_INFINITY` are exposed. As noted above these are infinitely smaller than infinity but they're the best we've got. They're not exported into the caller's namespace so if you want to use them you'll have to use their fully qualified names:

``    \$set->add_range(1, Set::IntSpan::Fast::POSITIVE_INFINITY);``

# DIAGNOSTICS

### `Range list must have an even number of elements`

The lists of ranges passed to `add_range` and `remove_range` consist of a number of pairs of integers each of which specify the start and end of a range.

### `Range limits must be integers`

You may only add integers to sets.

### `Range limits must be in ascending order`

When specifying a range in a call to `add_range` or `remove_range` the range bounds must be in ascending order. Multiple ranges don't need to be in any particular order.

### `Value out of range`

Sets may only contain values in the range `NEGATIVE_INFINITY` to `POSITIVE_INFINITY` inclusive.

### `That's very kind of you - but I expect you meant complement()`

The method that complements a set is called `complement`.

### `I need two sets to compare`

`superset` and `subset` need two sets to compare. They may be called either as a function:

``````    \$ss = Set::IntSpan::Fast::subset( \$s1, \$s2 )
``````

or as a method:

``    \$ss = \$s1->subset( \$s2 );``

### `Invalid Range String`

The range string must only contain a comma separated list of ranges, with a hyphen used as the range limit separator. e.g. "1,5,8-12,15-29".

# CONFIGURATION AND ENVIRONMENT

Set::IntSpan::Fast requires no configuration files or environment variables.

# DEPENDENCIES

``````    Data::Types
List::Util``````

# INCOMPATIBILITIES

Although this module was conceived as a replacement for `Set::IntSpan` it isn't a drop-in replacement.

# BUGS AND LIMITATIONS

No bugs have been reported.

Please report any bugs or feature requests to `bug-set-intspan-fast@rt.cpan.org`, or through the web interface at http://rt.cpan.org.

# AUTHOR

Andy Armstrong `<andy@hexten.net>`

# CREDITS

K. J. Cheetham http://www.shadowcatsystems.co.uk/ for add_from_string, remove_from_string. I butchered his code so any errors are mine.

Copyright (c) 2006-2008, Andy Armstrong `<andy@hexten.net>`. All rights reserved.