I simply can't believe how complicated people's attempts at an O(n) solution are. It is as simple as this: 
#! /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 = my $best_start = my $cur_start = 0;
my $best_end = -1;

for (0..$#array) {
  $cur += $array[$_];
  if ($cur < 0) {
    $cur = 0;
    $cur_start = $_ + 1;
  }
  elsif ($best < $cur) {
    $best = $cur;
    $best_start = $cur_start;
    $best_end = $_;
  }
}

print qq(Start: $best_start
End: $best_end
Sum: $best
Numbers: @array[$best_start..$best_end]
);

[download]
Update: I was asked in chatter about the -1. Yes, it has a purpose, and were I the instructor I would ding the code for not providing a comment explaining it.

In reply to Re: Largest Sum of Consecutive Integers by tilly
in thread Largest Sum of Consecutive Integers by OverlordQ

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