moritz's post, or rather his discussion of it on the ChatterBox, made me think, and it inspired me to come up with a related yet different solution.

My solution is based on the idea of a step function, often spelled "µ" in math, and adding them together (function of x, edge at t):

    µ(x, t) = 0 if x < t
            = 1 if x > t
            = ?? if x == t (often 1/2 in continuous math functions)

As this is about discrete values, I'd rather make that

    µ(x, t) = 0 if x < t
            = 1 if x > t
            = 1 if x == t (for discrete input)

That way, the added value for a range, say [20, 50], can be

    µ(x, 20) - µ(x, 51)

So, just as with moritz's solution, you can store the value for a range as 2 tuples for each edge:

%step = ( 20 => 1, 50+1 => -1 );
[download]

You can imagine this to represent a number of Dirac pulses; the combination of step functions is the integral of this set of pulses, or, because we're in the discrete case, the sum of amplitudes of every pulse on its left.

For each range you add, in the same hash, you can then increment the value for the lower edge, and decrement for the upper edge + 1.

my %step;
foreach(@range) {
    $step{ $_->[0] }++;
    $step{ $_->[1]+1 }--;
}
[download]

Now, the next step is to convert this data structure to the final outcome. If you need a complete data structure for the whole spectrum, you'll have to loop through the full range once, on each edge, adding the value for $step{$edge} to the previous accumulated value and assigning that to the range:

my @edge = sort { $a <=> $b } keys %step;
my $step = 0;
my $x = shift @edge;
for(my $i = $x; defined $x; $i++) {
    if($i == $x) {
        $step += $step{$x};
        $x = shift @edge;
    }
    $arr[$i] += $step;
}
[download]

Tested with

@arr = (0) x 120;
@range = ([20, 50], [30, 100]);
[download]

The end result of print "@arr\n"; is:

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 
+2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
+ 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 
+0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
[download]

---

---

Posts are HTML formatted. Put <p> </p> tags around your paragraphs. Put <code> </code> tags around your code and data!

Titles consisting of a single word are discouraged, and in most cases are disallowed outright.

Read Where should I post X? if you're not absolutely sure you're posting in the right place.

Please read these before you post! —

• How do I compose an effective node title?
• How do I post a question effectively?
• Markup in the Monastery

Posts may use any of the Perl Monks Approved HTML tags:

a, abbr, b, big, blockquote, br, caption, center, col, colgroup, dd, del, details, div, dl, dt, em, font, h1, h2, h3, h4, h5, h6, hr, i, ins, li, ol, p, pre, readmore, small, span, spoiler, strike, strong, sub, summary, sup, table, tbody, td, tfoot, th, thead, tr, tt, u, ul, wbr

You may need to use entities for some characters, as follows. (Exception: Within code tags, you can put the characters literally.)

	For:		Use:
	&		&
	<		&lt;
	>		&gt;
	[		&#91;
	]		&#93;

Link using PerlMonks shortcuts! What shortcuts can I use for linking?

See Writeup Formatting Tips and other pages linked from there for more info.