Array Sum (Linear Scan)

Walk an array once, accumulating each element into a running total. This is the canonical single-pass linear scan and the simplest possible loop invariant: after step i, total equals the sum of arr[0..i].

Algorithm

Trace Output

basic.pl

use strict; use warnings;
my @arr = (3, 1, 4, 1, 5, 9, 2, 6);
my $total = 0;
my $i = 0;
while ($i < scalar @arr) {
	$total = $total + $arr[$i];
	$i = $i + 1;
}
print "$total\n";

trace.pl

use strict; use warnings;
my @arr = (3, 1, 4, 1, 5, 9, 2, 6);
my $total = 0;
my $i = 0;
while ($i < scalar @arr) {
	my $before = $total;
	$total = $total + $arr[$i];
	printf("step %d: arr(%d)=%d total %d -> %d\n", $i, $i, $arr[$i], $before, $total);
	$i = $i + 1;
}
printf("final total = %d\n", $total);

Complexity

Time: O(n)
Space: O(1)

Implementation notes

Perl: use the explicit while ($i < scalar @arr) loop with $total = 0 and a manual 0-based index. The stdlib does not ship a one-call sum for arrays — List::Util::sum would hide the loop the lesson is teaching and would also require a CPAN-style use.
my @arr = (3, 1, 4, 1, 5, 9, 2, 6); documents the fixed-content array; the manual $i = $i + 1 step keeps the iteration without leaning on foreach my $val (@arr) that hides the running index.
use strict; use warnings; at the top keeps the lesson on the typo-safe path; every $total / $i / @arr reference is my-declared.
The replay shows i, arr[i], and total before and after each addition, matching the lesson spec's state-transition table.

linear scan Visit each element exactly once in index order.

running total `total` accumulates the sum as the loop advances.