MergeSort Algorithm with PHP

index.php

<?php

require_once './Merge.php';

$a = [15, 5, 24, 8, 1, 3, 16, 10, 20];

Merge::display($a); // output: [15, 5, 24, 8, 1, 3, 16, 10, 20]
Merge::sort($a, 0, count($a) - 1);
Merge::display($a); // output: [1, 3, 5, 8, 10, 15, 16, 20, 24]

Merge.php

<?php

/**
 * class Merge
 */
class Merge {
    /**
     * sort
     * @param  array &$a (Pointer)
     * @param  int   $lb
     * @param  int   $ub
     * @return void
     */
    public static function sort(array &$a, int $lb, int $ub): void {
        if ($lb < $ub) {
            $mid = intval(($lb + $ub) / 2);
            Merge::sort($a, $lb, $mid);
            Merge::sort($a, $mid + 1, $ub);
            Merge::concat($a, $lb, $mid, $ub);
        }
    }
    /**
     * concat
     * @param  array &$a (Pointer)
     * @param  int   $lb
     * @param  int   $mid
     * @param  int   $ub
     * @return void
     */
    public static function concat(array &$a, int $lb, int $mid, int $ub): void {
        $i = $lb;
        $j = $mid + 1;
        $k = $lb;
        
        $b = [];
        
        while ($i <= $mid && $j <= $ub) {
            if ($a[$i] <= $a[$j]) {
                $b[$k] = $a[$i++];
            } else {
                $b[$k] = $a[$j++];
            }
            $k++;
        }
        
        if ($i > $mid) {
            while ($j <= $ub) {
                $b[$k++] = $a[$j++];
            }
        } else {
            while ($i <= $mid) {
                $b[$k++] = $a[$i++];
            }
        }
                
        for ($k = $lb; $k <= $ub; $k++) {
            $a[$k] = $b[$k];
        }
    }
    /**
     * concat
     * @param  array &$a (Pointer)
     * @return void
     */
    public static function display(array &$a): void {
        $data = join(', ', $a);
        echo '['. $data .']';
    }
}