Sorting

Bubble Sort

Repeatedly walk the array comparing adjacent pairs and swapping any that are out of order. After pass k, the k largest elements are in their final positions at the end. Stop early when a full pass makes zero swaps.

Algorithm

Canonical input [5, 1, 4, 2, 8] finishes after three passes: two with swaps, then a clean pass that triggers the early exit. Final array [1, 2, 4, 5, 8].

Basic Implementation

basic.php 
<?php
$arr = [5, 1, 4, 2, 8];
$n = count($arr);
$i = 0;
$done = false;
while ($i < $n - 1 && !$done) {
	$swapped = false;
	$j = 0;
	while ($j < $n - $i - 1) {
		if ($arr[$j] > $arr[$j + 1]) {
			$tmp = $arr[$j];
			$arr[$j] = $arr[$j + 1];
			$arr[$j + 1] = $tmp;
			$swapped = true;
		}
		$j = $j + 1;
	}
	if (!$swapped) {
		$done = true;
	}
	$i = $i + 1;
}
echo "[" . implode(", ", $arr) . "]\n";

Complexity

  • Time: O(n^2) worst and average; O(n) best (already sorted with early exit)
  • Space: O(1)
  • Stable: yes

Implementation notes

  • PHP: explicit while loops with $i, $j, $done, and $swapped so the early-exit flow stays visible. The stdlib sort($arr) would hide the comparison-and-swap the lesson is teaching, and a break 2; inside a foreach would collapse the $done flag into a control-flow shortcut.
  • The explicit $tmp = $arr[$j]; $arr[$j] = $arr[$j+1]; $arr[$j+1] = $tmp; three-line swap keeps the move visible without leaning on list destructuring like [$arr[$j], $arr[$j+1]] = [$arr[$j+1], $arr[$j]];.
  • The replay distinguishes compare frames from swap frames so the moving pivot value is visible. The pass number and $swapped flag appear in the trace.
adjacent-pair compare and swap Inner loop walks `$j` from `0` to `$n - $i - 2` comparing `$arr[$j]` and `$arr[$j + 1]`.
early exit A `$swapped` flag set `false` at the start of each pass. If no swap happened, flip a `$done` flag and break out of the outer loop.