Set::IntSpan - Manages sets of integers use Set::IntSpan qw(grep_set map_set); $Set::IntSpan::Empty_String = $string; $set = new Set::IntSpan $set_spec; $valid = valid Set::IntSpan $run_list; $set = copy $set $set_spec; $run_list = run_list $set; @elements = elements $set; @spans = spans $set; $u_set = union $set $set_spec; $i_set = intersect $set $set_spec; $x_set = xor $set $set_spec; $d_set = diff $set $set_spec; $c_set = complement $set; equal $set $set_spec; equivalent $set $set_spec; superset $set $set_spec; subset $set $set_spec; $n = cardinality $set; empty $set; finite $set; neg_inf $set; pos_inf $set; infinite $set; universal $set; member $set $n; insert $set $n; remove $set $n; $min = min $set; $max = max $set; $subset = grep_set { ... } $set; $mapset = map_set { ... } $set; for ($element=$set->first; defined $element; $element=$set->next) { ... } for ($element=$set->last ; defined $element; $element=$set->prev) { ... } $element = $set->start($n); $element = $set->current;

@EXPORT
Nothing

@EXPORT_OK
"grep_set", "map_set" "Set::IntSpan" manages sets of integers. It is optimized for sets that have long runs of consecutive integers. These arise, for example, in .newsrc files, which maintain lists of articles: alt.foo: 1-21,28,31 alt.bar: 1-14192,14194,14196-14221 Sets are stored internally in a run-length coded form. This provides for both compact storage and efficient computation. In particular, set operations can be performed directly on the encoded representation. "Set::IntSpan" is designed to manage finite sets. However, it can also represent some simple infinite sets, such as {x | x>n}. This allows operations involving complements to be carried out consistently, without having to worry about the actual value of INT_MAX on your machine. Many of the methods take a set specification. There are four kinds of set specifications.

Empty
If a set specification is omitted, then the empty set is assumed. Thus, $set = new Set::IntSpan; creates a new, empty set. Similarly, copy $set; removes all elements from $set.

Object reference
If an object reference is given, it is taken to be a "Set::IntSpan" object.

Array reference
If an array reference is given, then the elements of the array are taken to be the elements of the set. The array may contain duplicate elements. The elements of the array may be in any order.

Run list
If a string is given, it is taken to be a run list. A run list specifies a set using a syntax similar to that in newsrc files. A run list is a comma-separated list of runs. Each run specifies a set of consecutive integers. The set is the union of all the runs. Runs may be written in any of several forms.

Finite forms
{ n } {x | a<=x && x<=b}

Infinite forms
{x | x<=n} {x | x>=n} The set of all integers

Empty forms
The empty set is consistently written as '' (the null string). It is also denoted by the special form '-' (a single dash).

Restrictions
The runs in a run list must be disjoint, and must be listed in increasing order. Valid characters in a run list are 0-9, '(', ')', '-' and ','. White space and underscore (_) are ignored. Other characters are not allowed.

Examples
{ } { 1 } { 1, 2 } { -5, -4, -3, -2, -1 } the integers the negative integers { 1, 2, 3, 4, 18, 19, 20, 21 } Each set has a single iterator, which is shared by all calls to "first", "last", "start", "next", "prev", and "current". At all times, the iterator is either an element of the set, or "undef". "first", "last", and "start" set the iterator; "next", and "prev" move it; and "current" returns it. Calls to these methods may be freely intermixed. Using "next" and "prev", a single loop can move both forwards and backwards through a set. Using "start", a loop can iterate over portions of an infinite set.

Creation
Creates and returns a "Set::IntSpan" object. The initial contents of the set are given by $set_spec. Returns true if $run_list is a valid run list. Otherwise, returns false and leaves an error message in $@. Copies $set_spec into $set. The previous contents of $set are lost. For convenience, "copy" returns $set. Returns a run list that represents $set. The run list will not contain white space. $set is not affected. By default, the empty set is formatted as '-'; a different string may be specified in $Set::IntSpan::Empty_String. Returns an array containing the elements of $set. The elements will be sorted in numerical order. In scalar context, returns an array reference. $set is not affected. Returns the runs in $set, as a list of the form ([$a1, $b1], [$a2, $b2], ... [$aN, $bN]) If a run contains only a single integer, then the upper and lower bounds of the corresponding span will be equal. If the set has no lower bound, then $a1 will be "undef". Similarly, if the set has no upper bound, then $bN will be "undef".

Set operations
Returns the set of integers in either $set or $set_spec. Returns the set of integers in both $set and $set_spec. Returns the set of integers in $set or $set_spec, but not both. Returns the set of integers in $set but not in $set_spec. Returns the set of integers that are not in $set. For all set operations, a new "Set::IntSpan" object is created and returned. The operands are not affected.

Comparison
Returns true iff $set and $set_spec contain the same elements. Returns true iff $set and $set_spec contain the same number of elements. All infinite sets are equivalent. Returns true iff $set is a superset of $set_spec. Returns true iff $set is a subset of $set_spec.

Cardinality
Returns the number of elements in $set. Returns -1 for infinite sets. Returns true iff $set is empty. Returns true iff $set is finite. Returns true iff $set contains {x | x<n} for some n. Returns true iff $set contains {x | x>n} for some n. Returns true iff $set is infinite. Returns true iff $set contains all integers.

Membership
Returns true iff the integer $n is a member of $set. Inserts the integer $n into $set. Does nothing if $n is already a member of $set. Removes the integer $n from $set. Does nothing if $n is not a member of $set.

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

Iterators
Sets the iterator for $set to the smallest element of $set. If there is no smallest element, sets the iterator to "undef". Returns the iterator. Sets the iterator for $set to the largest element of $set. If there is no largest element, sets the iterator to "undef". Returns the iterator. Sets the iterator for $set to $n. If $n is not an element of $set, sets the iterator to "undef". Returns the iterator. Sets the iterator for $set to the next element of $set. If there is no next element, sets the iterator to "undef". Returns the iterator. "next" will return "undef" only once; the next call to "next" will reset the iterator to the smallest element of $set. Sets the iterator for $set to the previous element of $set. If there is no previous element, sets the iterator to "undef". Returns the iterator. "prev" will return "undef" only once; the next call to "prev" will reset the iterator to the largest element of $set. Returns the iterator for $set. Evaluates the BLOCK for each integer in $set (locally setting $_ to each integer) and returns a "Set::IntSpan" object containing those integers for which the BLOCK returns TRUE. Returns "undef" if $set is infinite. Evaluates the BLOCK for each integer in $set (locally setting $_ to each integer) and returns a "Set::IntSpan" object containg all the integers returned as results of all those evaluations. Evaluates the BLOCK in list context, so each element of $set may produce zero, one, or more elements in the returned set. Returns "undef" if $set is infinite. $Set::IntSpan::Empty_String contains the string that is returned when "run_list" is called on the empty set. $Empty_String is initially '-'; alternatively, it may be set to ''. Other values should be avoided, to ensure that "run_list" always returns a valid run list. "run_list" accesses $Empty_String through a reference stored in $set->{"empty_string"}. Subclasses that wish to override the value of $Empty_String can reassign this reference. Any method (except "valid") will "die" if it is passed an invalid run list. (F) $run_list has bad syntax (F) $run_list has overlapping runs or runs that are out of order. (F) An infinte set was passed to "elements". (X) "elements" $set can generate an "Out of memory!" message on sufficiently large finite sets.

Traps
Beware of forms like union $set [1..5]; This passes an element of @set to union, which is probably not what you want. To force interpretation of $set and [1..5] as separate arguments, use forms like union $set +[1..5]; or $set->union([1..5]);

Cardinality
You cannot use the obvious comparison routine { $a->cardinality <=> $b->cardinality } to sort sets by size, because "cardinality" returns -1 for infinte sets. (All the non-negative integers were taken. Sorry.) Instead, you have to write something like { my $a_card = $a->cardinality; my $b_card = $b->cardinality; $a_card == $b_card and return 0; $a_card < 0 and return 1; $b_card < 0 and return -1; $a_card <=> $b_card }

grep_set and map_set
"grep_set" and "map_set" make it easy to construct sets for which the internal representation used by "Set::IntSpan" is not small. Consider: $billion = new Set::IntSpan '0-1_000_000_000'; # OK $odd = grep_set { $_ & 1 } $billion; # trouble $even = map_set { $_ * 2 } $billion; # double trouble

Error handling
There are two common approaches to error handling: exceptions and return codes. There seems to be some religion on the topic, so "Set::IntSpan" provides support for both. To catch exceptions, protect method calls with an eval: $run_list = <STDIN>; eval { $set = new Set::IntSpan $run_list }; $@ and print "$@: try again\n"; To check return codes, use an appropriate method call to validate arguments: $run_list = <STDIN>; if (valid Set::IntSpan $run_list) { $set = new Set::IntSpan $run_list } else { print "$@ try again\n" } Similarly, use "finite" to protect calls to "elements": finite $set and @elements = elements $set; Calling "elements" on a large, finite set can generate an "Out of memory!" message, which cannot (easily) be trapped. Applications that must retain control after an error can use "intersect" to protect calls to "elements": @elements = elements { intersect $set "-1_000_000 - 1_000_000" }; or check the size of $set first: finite $set and cardinality $set < 2_000_000 and @elements = elements $set;

Limitations
Although "Set::IntSpan" can represent some infinite sets, it does not perform infinite-precision arithmetic. Therefore, finite elements are restricted to the range of integers on your machine.

Roots
The sets implemented here are based on a Macintosh data structure called a region. See Inside Macintosh for more information. Steven McDougall <swmcd@world.std.com> Martin Krzywinski <martink@bcgsc.ca> Copyright 1996-2004 by Steven McDougall. This module is free software; you can redistribute it and/or modify it under the same terms as Perl itself.