Good luck (*) with IntervalTree.

The idea is that you insert your items in a tree, their interval being the discriminating characteristic.

Traversing the tree will be in the same order as if you lined up all those intervals (on a line).

In traverse()'s order, calculate distance between an item's "before" and "after" neighbour and develop the logic to merge them or not.

Here is a quick demo, notice the line-up of the items at the end:

#!/usr/bin/perl

#
# author: Bliako
# date: 10/09/2018
# for: https://perlmonks.org/?node_id=1222031
#

use strict;
use warnings;

use IntervalTree;
use Data::Dumper;

# create the tree
my $tree = IntervalTree->new();

while(<DATA>){
        chomp;
        next if $_ =~ /^\s*$/;
        my @items = split /\s+/;
        $tree->insert(@items[1,2,3]);
}
close(DATA);
print_tree($tree);

# print all the intervals
sub     print_tree {
        my $atree = shift;
        $atree->traverse(
                # specify a func to be run on every node as returned b
+y traverse()
                sub {
                        my $anode = $_[0];
                        print "traverse() : ".$anode->{interval}." => 
+".$anode->str()."\n";
                }
        );
}

__DATA__
Chr1 30000 32000 A3
Chr1 28000 29000 B2
Chr1 12000 18500 B1
Chr1 1000 4000 A1
Chr1 42000 44000 A4
Chr1 15000 22000 A2
[download]

Result:

traverse() : (A1) => Node(1000, 4000)
traverse() : (B1) => Node(12000, 18500)
traverse() : (A2) => Node(15000, 22000)
traverse() : (B2) => Node(28000, 29000)
traverse() : (A3) => Node(30000, 32000)
traverse() : (A4) => Node(42000, 44000)
[download]

(*) : personally I found this module very frustrating to work with as it mixes together Node objects, Interval objects and Interval names. I had to modify the source of _seek_left and _seek_right to save $self rather than $self->{interval}. But for your modest need, the above will do nicely. There are even worst alternatives, search at cpan.

If you are a Bioinformatician and have more serious bioinformatics needs I am available for hire - in the spirit of appeasing and keeping content the general anonymous public. If you are not, well I can always help for free when I can as I always do.

bw, bliako

Edit - Clarification: my program lines up all your items in a line wrt their intervals (compare Result above and your sample output A1, B1, A2, B2, A3, A4.). The program will not do the merging as I was too lazy to read your requirements and translate to code. Now all you have to do is to check each item with its 2 or 4 neighbours (for when A neighbours A) following your rules. The important thing is that the "line-up" is done using the Interval Tree in O(n log n) time and will persist for classifying unknown intervals too.

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