- NAME
- SYNOPSIS
- DESCRIPTION
- METHODS
- CONSTANTS
- POS_INF
- NEG_INF
- EMPTY_STRING
- INTERFACE: Set creation
- new
- valid
- clear
- INTERFACE: Set contents
- edges_ref
- edges
- edge_size
- span_size
- as_string
- as_array
- INTERFACE: Span contents
- ranges
- spans
- sets
- runlists
- INTERFACE: Set cardinality
- cardinality
- is_empty
- is_not_empty
- is_neg_inf
- is_pos_inf
- is_infinite
- is_finite
- is_universal
- INTERFACE: Membership test
- contains_all
- contains_any
- INTERFACE: Member operations
- add_pair
- add_range
- add_runlist
- add
- invert
- remove_range
- remove
- merge
- subtract
- INTERFACE: Set operations
- copy
- union
- complement
- diff
- intersect
- xor
- INTERFACE: Set comparison
- equal
- subset
- superset
- smaller_than
- larger_than
- INTERFACE: Indexing
- at
- index
- slice
- INTERFACE: Extrema
- min
- max
- INTERFACE: Utils
- grep_set
- map_set
- substr_span
- INTERFACE: Spans operations
- banish_span
- cover
- holes
- inset
- trim
- pad
- excise
- fill
- INTERFACE: Inter-set operations
- overlap
- distance
- INTERFACE: Islands
- find_islands
- nearest_island
- at_island
- INTERFACE: Aliases

- AUTHOR
- COPYRIGHT AND LICENSE

# NAME

AlignDB::IntSpan - Handling of sets containing integer spans.

# SYNOPSIS

```
use AlignDB::IntSpan;
my $set = AlignDB::IntSpan->new;
$set->add(1, 2, 3, 5, 7, 9);
$set->add_range(100, 1_000_000);
print $set->as_string, "\n"; # 1-3,5,7,9,100-1000000
```

## Operator overloads

```
if ($set) { ... } # true if $set is not empty
print "$set\n"; # stringizes to the run list
```

# DESCRIPTION

The `AlignDB::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.

The internal representation used by this module 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).

Sets may be infinite - assuming you're prepared to accept that infinity is actually no more than a fairly large integer. Specifically the constants `$NEG_INF`

and `$POS_INF`

are defined to be -(2^31-1) and (2^31-2) respectively. To create an infinite set invert an empty one:

` my $inf = AlignDB::IntSpan->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 = AlignDB::IntSpan->new;
$pos_int->add_range(1, $pos_int->POS_INF);
```

Many codes come from Set::IntSpan, Set::IntSpan::Fast and Set::IntSpan::Island.

# METHODS

**CONSTANTS**

## POS_INF

Normally used in construction of infinite sets

## NEG_INF

Normally used in construction of infinite sets

## EMPTY_STRING

**INTERFACE: Set creation**

## new

```
my $set = AlignDB::Intspan->new; # empty set
my $set = AlignDB::Intspan->new($set_spec); # the content of $set_spec
my $set = AlignDB::Intspan->new(@set_specs); # the union of @set_specs
```

Creates and returns an AlignDB::IntSpan object.

## valid

` my $ok = AlignDB::IntSpan->valid($runlist);`

Returns true if $runlist is a valid run list.

## clear

` $set->clear;`

Clear all contents of $set

**INTERFACE: Set contents**

## edges_ref

Return the internal used ArrayRef representing the set.

I don't think you should use this method.

## edges

Return the internal used Array representing the set.

I don't think you should use this method.

## edge_size

Return the number of edges

## span_size

Return the number of spans

## as_string

Return a string representation of the set.

## as_array

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

**INTERFACE: Span contents**

## ranges

Returns the runs in $set, as a list of ($lower, $upper)

## spans

Returns the runs in $set, as a list of [$lower, $upper]

## sets

Returns the runs in $set, as a list of AlignDB::IntSpan objects. The sets in the list are in order.

## runlists

Returns the runs in $set, as a list of "$lower-$upper"

**INTERFACE: Set cardinality**

## cardinality

Returns the number of elements in $set.

## is_empty

Return true if the set is empty.

## is_not_empty

Return true if the set is not empty.

## is_neg_inf

Return true if the set is negtive infinite.

## is_pos_inf

Return true if the set is positive infinite.

## is_infinite

Return true if the set is infinite.

## is_finite

Return true if the set is finite.

## is_universal

Return true if the set contains all integers.

**INTERFACE: Membership test**

## contains_all

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

## contains_any

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

**INTERFACE: Member operations**

## add_pair

` $set->add_pair($lower, $upper);`

Add a pair of inclusive integers to the set.

A pair of arguments constitute a range

## add_range

` $set->add_range($lower, $upper);`

Add the inclusive range of integers to the set.

Multiple ranges may be specified. Each pair of arguments constitute a range

## add_runlist

` $set->add_runlist($runlist);`

Add the specified runlist to the set.

## add

```
$set->add($number1, $number2, $number3 ...)
$set->add($runlist);
```

Add the specified integers or a runlist to the set.

## invert

` $set = $set->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 $NEG_INF and $POS_INF inclusive.

As noted above $NEG_INF and $POS_INF are actually just big integers.

## remove_range

$set->remove_range($lower, $upper);

Remove the inclusive range of integers to the set.

Multiple ranges may be specified. Each pair of arguments constitute a range.

## remove

```
$set->remove($number1, $number2, $number3 ...);
$set->remove($runlist);
```

Remove the specified integers or a runlist to the set.

## merge

```
$set->merge($another_set);
$set->merge($set_spec);
```

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

## subtract

```
$set->subtract($another_set);
$set->subtract($set_spec);
```

Subtract the members of the supplied sets or set_specs out of this set. Any number of sets may be supplied as arguments.

**INTERFACE: Set operations**

## copy

` my $new_set = $set->copy;`

Return an identical copy of the set.

## union

Be called either as a method

` my $new_set = $set->union( $other_set );`

or as a function:

` my $new_set = AlignDB::IntSpan::union( $set1, $set2, $set3 );`

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

## complement

` my $new_set = $set->complement;`

Returns a new set that is the complement of this set.

## diff

` my $new_set = $set->diff( $other_set );`

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

## intersect

Be called either as a method

` my $new_set = $set->intersect( $other_set );`

or as a function:

` my $new_set = AlignDB::IntSpan::intersect( $set1, $set2, $set3 );`

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

## xor

Be called either as a method

` my $new_set = $set->xor( $other_set );`

or as a function:

` my $new_set = AlignDB::IntSpan::xor( $set1, $set2, $set3 );`

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 setsin which case it returns a set that contains all the members that are in some of the sets but not all of the sets.

**INTERFACE: Set comparison**

## equal

Returns true if $set and $set_spec contain the same elements.

## subset

Returns true if $set is a subset of $set_spec.

## superset

Returns true if $set is a superset of $set_spec.

## smaller_than

Returns true if $set is smaller than $set_spec.

## larger_than

Returns true if $set is larger than $set_spec.

**INTERFACE: Indexing**

## at

Returns the indexth element of set, index start from "1". Negtive indices count backwards from the end of the set.

## index

Returns the index fo a element in the set, index start from "1"

## slice

Give two indexes, return a subset. These indexes must be positive.

**INTERFACE: Extrema**

## min

Returns the smallest element of $set, or undef if there is none.

## max

Returns the largest element of $set, or undef if there is none.

**INTERFACE: Utils**

## grep_set

Evaluates the $code_ref for each integer in $set (locally setting $_ to each integer) and returns an AlignDB::IntSpan object containing those integers for which the $code_ref returns TRUE.

## map_set

Evaluates the $code_ref for each integer in $set (locally setting $_ to each integer) and returns an AlignDB::IntSpan object containing all the integers returned as results of all those evaluations.

Evaluates the $code_ref in list context, so each element of $set may produce zero, one, or more elements in the returned set. The elements may be returned in any order, and need not be disjoint.

## substr_span

` my $substring = $set->substr_span($string);`

**INTERFACE: Spans operations**

## banish_span

## cover

Returns a set consisting of a single span from $set->min to $set->max.

## holes

Returns a set containing all the holes in $set, that is, all the integers that are in-between spans of $set.

## inset

inset returns a set constructed by removing $n integers from each end of each span of $set. If $n is negative, then -$n integers are added to each end of each span.

In the first case, spans may vanish from the set; in the second case, holes may vanish.

## trim

trim is provided as a synonym for inset.

## pad

pad $set $n is the same as $set->inset( -$n )

## excise

` my $new_set = $set->excise( $minlength )`

Removes all spans within $set smaller than $minlength

## fill

` my $new_set = $set->fill( $maxlength )`

Fills in all holes in $set smaller than $maxlength

**INTERFACE: Inter-set operations**

## overlap

` my $overlap_amount = $set->overlap( $another_set );`

Returns the size of intersection of two sets. Equivalent to

` $set->intersect( $another_set )->size;`

## distance

` my $distance = $set->distance( $another_set );`

Returns the distance between sets, measured as follows.

If the sets overlap, then the distance is negative and given by

` $d = - $set->overlap( $another_set )`

If the sets do not overlap, $d is positive and given by the distance on the integer line between the two closest islands of the sets.

**INTERFACE: Islands**

## find_islands

```
my $island = $set->find_islands( $integer );
my $new_set = $set->find_islands( $another_set );
```

Returns a set containing the island in $set containing $integer. If $integer is not in $set, an empty set is returned. Returns a set containing all islands in $set intersecting $another_set. If $set and $another_set have an empty intersection, an empty set is returned.

## nearest_island

```
my $island = $set->nearest_island( $integer );
my $island = $set->nearest_island( $another_set );
```

Returns the nearest island(s) in $set that contains, but does not overlap with, $integer. If $integer lies exactly between two islands, then the returned set contains these two islands.

Returns the nearest island(s) in $set that intersects, but does not overlap with, $another_set. If $another_set lies exactly between two islands, then the returned set contains these two islands.

## at_island

` my $island = $set->at_island( $island_index );`

Returns the island indexed by $island_index. Islands are 1-indexed. For a set with N islands, the first island (ordered left-to-right) has index 1 and the last island has index N. If $island_index is negative, counting is done back from the last island (c.f. negative indexes of Perl arrays).

**INTERFACE: Aliases**

```
runlist => as_string
elements => as_array
size, count => cardinality
contains => contains_all
intersection => intersect
equals => equal
```

# AUTHOR

Qiang Wang <wang-q@outlook.com>

# COPYRIGHT AND LICENSE

This software is copyright (c) 2008 by Qiang Wang.

This is free software; you can redistribute it and/or modify it under the same terms as the Perl 5 programming language system itself.