Add 2D binary indexed trees

[algorithm-bit-xs.git] / lib / Algorithm / BIT2D / XS.pm

diff --git a/lib/Algorithm/BIT2D/XS.pm b/lib/Algorithm/BIT2D/XS.pm
new file mode 100644 (file)
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+++ b/lib/Algorithm/BIT2D/XS.pm
@@ -0,0 +1,111 @@
+package Algorithm::BIT2D::XS;
+
+use 5.014000;
+use strict;
+use warnings;
+
+our $VERSION = '0.001';
+
+use Algorithm::BIT::XS;
+
+sub new {
+       my ($class, $n, $m) = @_;
+       create($n, $m);
+}
+
+sub get {
+       my ($b, $i1, $i2) = @_;
+       $b->query($i1, $i2) + $b->query($i1 - 1, $i2 - 1)
+         - $b->query($i1 - 1, $i2) - $b->query($i1, $i2 - 1);
+}
+
+sub set {
+       my ($b, $i1, $i2, $value) = @_;
+       $b->update($i1, $i2, $value - $b->get($i1, $i2))
+}
+
+1;
+__END__
+
+=encoding utf-8
+
+=head1 NAME
+
+Algorithm::BIT2D::XS - 2D Binary indexed trees / Fenwick trees
+
+=head1 SYNOPSIS
+
+  use Algorithm::BIT2D::XS;
+  my $bit = Algorithm::BIT2D::XS->new(100, 100);
+  $bit->update(1, 2, 5);  # bit[1][2] += 5
+  $bit->update(3, 3, 6);  # bit[3][3] += 6
+  say 'bit[1..2][1..10]  == ', $bit->query(2, 10);  # 5
+  say 'bit[1..3][1..2]   == ', $bit->query(3, 2);  # 5
+  say 'bit[1..20][1..10] == ', $bit->query(20, 10); # 11
+
+  $bit->update(3, 1, 10); # bit[3][1] += 10
+  say 'bit[1..3][1..3]  == ', $bit->query(3, 3);  # 21
+  say 'bit[3][3] == ', $bit->get(3, 3); # 6
+
+  $bit->set(3, 3, 10); # bit[3][3] = 10
+  say 'bit[3][3] == ', $bit->get(3, 3); # 10
+
+  $bit->clear;
+  say 'bit[1..100][1..10] == ', $bit->query(100, 10); # 0
+  $bit->set(100, 10, 5);
+  say 'bit[1..100][1..10] == ', $bit->query(100, 10); # 5
+
+=head1 DESCRIPTION
+
+A binary indexed tree is a data structure similar to an array of integers.
+The two main operations are updating an element and calculating a
+prefix sum, both of which run in time logarithmic in the size of the tree.
+
+=over
+
+=item Algorithm::BIT2D::XS->B<new>(I<$n>, I<$m>)
+
+Create a new 2D binary indexed tree of length I<$n> x I<$m>. As binary
+indexed trees are 1-indexed, its indexes are [1..I<$n>][1..I<$m>].
+It is initially filled with zeroes.
+
+=item $bit->B<clear>()
+
+Clears the binary indexed tree (sets all elements to 0).
+
+=item $bit->B<query>(I<$i1>, I<$i2>)
+
+Returns the rectangle sum from I<$bit>[1][1] to I<$bit>[I<$i1>][I<$i2>].
+
+=item $bit->B<update>(I<$i1>, I<$i2>, I<$value>)
+
+Adds I<$value> to I<$bit>[I<$i1>][I<$i2>].
+
+=item $bit->B<get>(I<$i1>, I<$i2>)
+
+Returns the value of I<$bit>[I<$i1>][I<$i2>].
+
+=item $bit->B<set>(I<$i1>, I<$i2>, I<$value>)
+
+Sets I<$bit>[I<$i1>][I<$i2>] to I<$value>.
+
+=back
+
+=head1 SEE ALSO
+
+L<Algorithm::BIT>, L<Algorithm::BIT::XS>, L<https://en.wikipedia.org/wiki/Fenwick_tree>
+
+=head1 AUTHOR
+
+Marius Gavrilescu, E<lt>marius@ieval.roE<gt>
+
+=head1 COPYRIGHT AND LICENSE
+
+Copyright (C) 2017 by Marius Gavrilescu
+
+This library is free software; you can redistribute it and/or modify
+it under the same terms as Perl itself, either Perl version 5.24.1 or,
+at your option, any later version of Perl 5 you may have available.
+
+
+=cut