1234567890 coordinate
----------
+++        range (1,3)
 ++++++    range (2,7)
++       + range (0,2)
----------
5557753113 size of smallest window...

##</code><code>##

use 5.012;
use List::Util qw (min max);


my $max_length = 10;
my @ranges = ( [ 1, 3 ], [ 2, 7 ], [ 10, 2 ] );

# foreach $i in 1 .. $max_length: $res_a->[$i] ==  half size of
# smallest odd-sized window which is centered at $i and not covered
# by any range
my $res_a = ranges_a_to_min_uncovered_a(\@ranges);
foreach my $i (1 .. $max_length) {
	print $res_a->[$i]*2+1, " "; # print full size 
								 # just to be consistent with the original post
								 # prints '5 5 5 7 7 5 3 1 1 3'
}


# gets an array of ranges
# returns a ref to an arr hich satisfies:
# foreach $i in 1 .. $max_length $ret->[$i] ==
# half size of smallest odd-sized window which is centered at $i and not covered
# by any range
sub ranges_a_to_min_uncovered_a {
	my $ranges_a = shift // die;

	# default value is zero - a coordiante is not covered by any range
	# arrat length is $max_length+1 since the first position (0) is never used
	# (coordinates start from 1)
	my @min_uncovered_window_half_sizes = (0) x ( $max_length + 1 );

	foreach my $range ( @{$ranges_a} ) {
		my $start = $range->[0];
		my $end   = $range->[1];

		# iterate all coordinates in range

		if ( $start <= $end ) {    # simple range
			for my $i ( $start .. $end ) {
				ranges_a_to_min_uncovered_a_helper( $i, $range, \@min_uncovered_window_half_sizes );
			}
		}

		else {                     # wrapped range
			for my $i ( $start .. $max_length, 1 .. $end ) {
				ranges_a_to_min_uncovered_a_helper( $i, $range, \@min_uncovered_window_half_sizes );
			}
		}
	}    # foreach my $range

	return \@min_uncovered_window_half_sizes;
}

# gets a range, a coordinate within it and $min_uncovered_a
# updates $min_uncovered_a[$coordinate] if needed
sub ranges_a_to_min_uncovered_a_helper {
	my $coordinate      = shift // die;
	my $range           = shift // die;
	my $min_uncovered_a = shift // die;

	my $dist = min( dist( $range->[0], $coordinate ), dist( $coordinate, $range->[1] ) );

	if ( $dist > $min_uncovered_a->[$coordinate] ) {
		$min_uncovered_a->[$coordinate] = $dist;
	}

}

# returns the length covered between $start and $end (both inclusive)
sub dist {
	my $start = shift // die;
	my $end   = shift // die;

	if ( $end >= $start ) {    # simple range
		return $end - $start + 1;
	}

	# warpped range
	return $max_length - $start + 1 + $end;

}