Sorting

Quick Sort (Lomuto)

Choose the last item as a pivot, partition smaller values to its left, then recurse on the two sides.

Algorithm

The checked-in replay follows the same small input and final output across all 21 DSA books, so this Perl DSA implementation can be compared directly with the other languages.

pivot The final element is moved to the boundary between smaller and larger values.
partition One scan rearranges the current range before the recursive calls.

Visual walkthrough

The pinned first partition uses [4, 1, 5, 2, 3] with pivot 3. The diagrams track the boundary, swaps, and recursive ranges.

Step 1 - Choose the last value as pivot

The pivot is arr[4] = 3, and i starts just before the current range.

Initial partition state for [4, 1, 5, 2, 3].i0i1i2i3i441523j startspivot

Step 2 - Swap small values left

1 and 2 are <= pivot, so they move into the left partition.

After scanning values before the pivot: [1, 2, 5, 4, 3].i0i1i2i3i412543<= 3<= 3> 3> 3pivot

Step 3 - Place pivot, then recurse

Swapping pivot 3 into index 2 gives [1, 2, 3, 4, 5]; recurse on [1, 2] and [4, 5].

Pivot lands at index 2 and splits the remaining work.left rangepivotright range[1, 2]3 at i2[4, 5]quick_sort(0,1)fixedquick_sort(3,4)

Basic Implementation

basic.pl 
use strict; use warnings;
sub partition {
	my ($arr, $low, $high) = @_;
	my $pivot = $arr->[$high];
	my $i = $low - 1;
	for (my $j = $low; $j < $high; $j++) {
		if ($arr->[$j] <= $pivot) {
			$i++;
			@$arr[$i, $j] = @$arr[$j, $i];
		}
	}
	@$arr[$i + 1, $high] = @$arr[$high, $i + 1];
	return $i + 1;
}

sub quick_sort {
	my ($arr, $low, $high) = @_;
	if ($low < $high) {
		my $pivot_index = partition($arr, $low, $high);
		quick_sort($arr, $low, $pivot_index - 1);
		quick_sort($arr, $pivot_index + 1, $high);
	}
}

my @arr = (4, 1, 5, 2, 3);
quick_sort(\@arr, 0, $#arr);
print "[" . join(", ", @arr) . "]
";

Complexity

  • Time: O(n^2) worst, O(n log n) average
  • Space: O(log n) average call stack
  • Stable: no

Implementation notes

  • my @arr = (4, 1, 5, 2, 3) declares the pinned Perl array with the @ sigil.
  • quick_sort(\@arr, 0, $#arr) passes an array reference plus zero-based bounds; $#arr is the last valid index.
  • partition unpacks its parameters with my ($arr, $low, $high) = @_, so $arr is a scalar reference to the array.
  • Array elements are read through the reference, such as $arr->[$high] and $arr->[$j].
  • Lomuto pivot selection is my $pivot = $arr->[$high], so the first pivot is the final value 3.
  • my $i = $low - 1 starts the smaller-value boundary at -1 for the first partition.
  • The partition scan is for (my $j = $low; $j < $high; $j++), so it compares indexes 0 through 3 and leaves the pivot at index 4 until the final placement.
  • The comparison is numeric and inclusive: if ($arr->[$j] <= $pivot).
  • Swaps use Perl slice/list assignment on the referenced array: @$arr[$i, $j] = @$arr[$j, $i].
  • In the trace, 4 <= 3 is false, so 4 stays on the right side and i remains -1.
  • 1 <= 3 is true, so i becomes 0 and the array changes to [1, 4, 5, 2, 3].
  • 5 <= 3 is false, leaving [1, 4, 5, 2, 3].
  • 2 <= 3 is true, so i becomes 1 and the array changes to [1, 2, 5, 4, 3].
  • Final pivot placement uses another slice assignment: @$arr[$i + 1, $high] = @$arr[$high, $i + 1], putting 3 at index 2 and producing [1, 2, 3, 4, 5].
  • quick_sort recurses only when $low < $high; the replay then summarizes the already-sorted left side [1, 2] and right side [4, 5] instead of expanding every base-case call.
  • The final print concatenates "[", join(", ", @arr), and a closing bracket string that includes the newline, producing [1, 2, 3, 4, 5].