Sorting

Merge Sort (Top-Down)

Split the array recursively, sort each half, then merge two sorted runs into one sorted result.

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.

divide and conquer Each recursive call solves a smaller sorted subproblem.
merge step Two sorted halves are combined by repeatedly taking the smaller front item.

Visual walkthrough

The pinned input is [5, 1, 4, 2, 8]. The diagrams show the split into recursive halves, the sorted subarrays, and the final merge choices.

Step 1 - Split the input

The first midpoint splits [5, 1, 4, 2, 8] into left [5, 1] and right [4, 2, 8].

Top-down split used by merge_sort.[5,1,4,2,8]mid = 2[5,1]left[4,2,8]right

Step 2 - Sorted halves return

Recursive calls return [1, 5] and [2, 4, 8] before the final merge begins.

Returned subarrays before the final merge.sidebefore sortafter sortleft[5, 1][1, 5]right[4, 2, 8][2, 4, 8]

Step 3 - Merge by taking smaller fronts

Take 1 from left, then 2 and 4 from right, then the remaining 5 and 8.

Final merge produces [1, 2, 4, 5, 8].choiceleft frontright frontmergedtake 112[1]take 252[1, 2]take 454[1, 2, 4]extend58[1, 2, 4, 5, 8]

Basic Implementation

basic.php 
<?php
function merge_sort($values) {
	if (count($values) <= 1) return $values;
	$mid = intdiv(count($values), 2);
	$left = merge_sort(array_slice($values, 0, $mid));
	$right = merge_sort(array_slice($values, $mid));
	$merged = [];
	$i = 0; $j = 0;
	while ($i < count($left) && $j < count($right)) {
		if ($left[$i] <= $right[$j]) $merged[] = $left[$i++];
		else $merged[] = $right[$j++];
	}
	return array_merge($merged, array_slice($left, $i), array_slice($right, $j));
}

$arr = [5, 1, 4, 2, 8];
echo "[" . implode(", ", merge_sort($arr)) . "]
";

Complexity

  • Time: O(n log n)
  • Space: O(n)
  • Stable: yes

Implementation notes

  • $arr is the pinned PHP array literal [5, 1, 4, 2, 8].
  • merge_sort($values) returns a sorted array; it does not mutate $arr in place.
  • The base case is if (count($values) <= 1) return $values;.
  • $mid = intdiv(count($values), 2) splits the array with integer division.
  • array_slice($values, 0, $mid) creates the left half, and array_slice($values, $mid) creates the right half.
  • $merged = [] collects output while $i and $j index the sorted left and right arrays.
  • The merge comparison is $left[$i] <= $right[$j], so equal values would keep the left-side value first.
  • Appends use $merged[] = ..., and leftovers are joined with array_merge($merged, array_slice($left, $i), array_slice($right, $j)).
  • The trace shows top-level halves [5, 1] and [4, 2, 8], sorted as [1, 5] and [2, 4, 8], then merged into [1, 2, 4, 5, 8].
  • The final echo concatenates [ + implode(", ", merge_sort($arr)) + ], then closes the quoted string after a literal newline, so the output is one bracketed row.