# TADM2E 8.21

From Algorithm Wiki

#### 1

Sum every range and keep track of the maximum.

Given a set of numbers N = { x0, x1 ... xn } M = 0 for i in (0 .. n) S[i, i] = xi for j in (i + 1 .. n) S[i, j] = S[i, j - 1] + xj if M < S[i, j] M = S[i, j]

#### 2

Sum from each end, resetting the prefix or suffix (i.e., discarding the summed numbers) if it goes negative.

#!/usr/bin/perl sub max_range { my @numbers = @_; my $prefix = 0; my $suffix = 0; for (my ($l, $r) = (0, @numbers - 1); $l <= $r; $l ++, $r --) { $prefix += $numbers[$l]; $prefix = 0 if $prefix < 0; $suffix += $numbers[$r] if $l < $r; $suffix = 0 if $suffix < 0; } return $prefix + $suffix; } my $max = max_range 31, -41, 59, 26, -53, 58, 97, -93, -23, 84;

print $max, "\n";