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 PHP 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.php 
<?php
function partition(&$arr, $low, $high) {
	$pivot = $arr[$high];
	$i = $low - 1;
	for ($j = $low; $j < $high; $j++) {
		if ($arr[$j] <= $pivot) {
			$i++;
			$tmp = $arr[$i]; $arr[$i] = $arr[$j]; $arr[$j] = $tmp;
		}
	}
	$tmp = $arr[$i + 1]; $arr[$i + 1] = $arr[$high]; $arr[$high] = $tmp;
	return $i + 1;
}

function quick_sort(&$arr, $low, $high) {
	if ($low < $high) {
		$pivot_index = partition($arr, $low, $high);
		quick_sort($arr, $low, $pivot_index - 1);
		quick_sort($arr, $pivot_index + 1, $high);
	}
}

$arr = [4, 1, 5, 2, 3];
quick_sort($arr, 0, count($arr) - 1);
echo "[" . implode(", ", $arr) . "]
";

Complexity

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

Implementation notes

  • $arr is the pinned PHP array literal [4, 1, 5, 2, 3].
  • quick_sort(&$arr, $low, $high) and partition(&$arr, $low, $high) take $arr by reference, so swaps mutate the same array that is later printed.
  • The pivot is the last slot in the active range: $pivot = $arr[$high].
  • Lomuto's left boundary starts as $i = $low - 1, then $j scans from $low up to $high - 1.
  • The comparison is $arr[$j] <= $pivot; values 1 and 2 move left of pivot 3, while 4 and 5 stay on the right in the first partition trace.
  • Swaps use a temporary variable: $tmp = $arr[$i]; $arr[$i] = $arr[$j]; $arr[$j] = $tmp;, then the pivot swaps into $i + 1.
  • The replay shows [4, 1, 5, 2, 3] becoming [1, 4, 5, 2, 3], then [1, 2, 5, 4, 3], then [1, 2, 3, 4, 5] when pivot 3 lands at index 2.
  • Recursive calls then cover $low..$pivot_index - 1 and $pivot_index + 1..$high; the trace records left [1, 2] and right [4, 5] already sorted.
  • The final echo concatenates [ + implode(", ", $arr) + ], then closes the quoted string after a literal newline, so it prints [1, 2, 3, 4, 5].