Speaking mathematically, the sum of the empty set is a perfectly valid sum of consecutive integers, and its value is 0. But you can change the problem to exclude the empty sum as follows:
#! /usr/bin/perl -w
use strict;
my @array = @ARGV ? @ARGV : qw(3 2 8 9 -25 5 8 4 4 -3 5 3 -10);
my $cur = my $best_start = my $best_end = my $cur_start = 0;
my $best = $array[0];
for (0..$#array) {
$cur += $array[$_];
if ($best < $cur) {
$best = $cur;
$best_start = $cur_start;
$best_end = $_;
}
if ($cur < 0) {
$cur = 0;
$cur_start = $_ + 1;
}
}
print qq(Start: $best_start
End: $best_end
Sum: $best
Numbers: @array[$best_start..$best_end]
);