1Math::Cartesian::ProducUts(e3rpmC)ontributed Perl DocumeMnattaht:i:oCnartesian::Product(3pm)
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6 Math::Cartesian::Product - Generate the Cartesian product of zero or
7 more lists.
8
10 use Math::Cartesian::Product;
11 cartesian {print "@_\n"} [qw(a b c)], [1..2];
13 # a 1
15 # a 2
16 # b 1
17 # b 2
18 # c 1
19 # c 2
20 cartesian {print "@_\n"} ([0..1]) x 8;
22 # 0 0 0 0 0 0 0 0
24 # 0 0 0 0 0 0 0 1
25 # 0 0 0 0 0 0 1 0
26 # ...
27 # 1 1 1 1 1 1 1 0
28 # 1 1 1 1 1 1 1 1
29 print "@$_\n" for
31 cartesian {"@{[reverse @_]}" eq "@_"}
32 ([' ', '*']) x 8;
33 # * *
35 # * *
36 # * * * *
37 # * *
38 # * * * *
39 # * * * *
40 # * * * * * *
41 # * *
42 # * * * *
43 # * * * *
44 # * * * * * *
45 # * * * *
46 # * * * * * *
47 # * * * * * *
48 # * * * * * * * *
49
51 Generate the Cartesian product of zero or more lists.
52 Given two lists, say: [a,b] and [1,2,3], the Cartesian product is the
54 set of all ordered pairs:
55 (a,1), (a,2), (a,3), (b,1), (b,2), (b,3)
57 which select their first element from all the possibilities listed in
59 the first list, and select their second element from all the
60 possibilities in the second list.
61 The idea can be generalized to n-tuples selected from n lists where all
63 the elements of the first list are combined with all the elements of
64 the second list, the results of which are then combined with all the
65 member of the third list and so on over all the input lists.
66 It should be noted that Cartesian product of one or more lists where
68 one or more of the lists are empty (representing the empty set) is the
69 empty set and thus has zero members; and that the Cartesian product of
70 zero lists is a set with exactly one member, namely the empty set.
71 cartesian() takes the following parameters:
73 1. A block of code to process each n-tuple. this code should return
75 true if the current n-tuple should be included in the returned value of
76 the cartesian() function, otherwise false.
77 2. Zero or more lists.
79 cartesian() returns an array of references to all the n-tuples selected
81 by the code block supplied as parameter 1 if called in list context,
82 else it returns a count of the selected n-tuples.
83 cartesian() croaks if you try to form the Cartesian product of
85 something other than lists of things or prior Cartesian products.
86 The cartesian product of lists A,B,C is associative, that is:
88 (A X B) X C = A X (B X C)
90 cartesian() respects associativity by allowing you to include a
92 Cartesian product produced by an earlier call to cartesian() in the set
93 of lists whose Cartesian product is to be formed, at the cost of a
94 performance penalty if this option is chosen.
95 use Math::Cartesian::Product;
97 my $a = [qw(a b)];
99 my $b = [cartesian {1} $a, $a];
100 cartesian {print "@_\n"} $b, $b;
101 # a a a a
103 # a a a b
104 # a a b a
105 # ...
106 cartesian() is easy to use and fast. It is written in 100% Pure Perl.
108
110 The cartesian() function is exported.
111
113 Standard Module::Build process for building and installing modules:
114 perl Build.PL
116 ./Build
117 ./Build test
118 ./Build install
119 Or, if you're on a platform (like DOS or Windows) that doesn't require
121 the "./" notation, you can do this:
122 perl Build.PL
124 Build
125 Build test
126 Build install
127
129 Philip R Brenan at gmail dot com
130 http://www.appaapps.com
132
134 With much help and good natured advice from Philipp Rumpf and Justin
135 Case to whom I am indebted.
136
138 Math::Disarrange::List
139 Math::Permute::List
140 Math::Permute::Lists
141 Math::Permute::Partitions
142 Math::Subsets::List
143 Math::Transform::List
144
146 Copyright (c) 2009-2015 Philip R Brenan.
147 This module is free software. It may be used, redistributed and/or
149 modified under the same terms as Perl itself.
150perl v5.38.0 2023-07-20 Math::Cartesian::Product(3pm)