Dutch National Flag Partition in PHP

<?php
declare(strict_types=1);
// Dutch National Flag Partition in PHP
//
// PURPOSE
// Three-way partition groups zeros, ones, and twos in one pass. The same idea is useful for
// grouping values around a pivot.
//
// METHOD
// Keep a zero prefix, a one middle, an unknown interval, and a two suffix. Swap a zero left,
// advance past a one, or swap a two right and re-examine the incoming unknown value.
//
// COMPLEXITY
// O(n) time and O(1) auxiliary space. Not stable.
//
// CONTRACT
// Every value must be 0, 1, or 2. Mutates the array into sorted order and returns 0.
// Public APIs infer array lengths except in C, which accepts pointer/length pairs. Vertex
// counts and matrix dimensions remain explicit. Arrays must contain signed 32-bit integers.
// Sorted order, correct tree topology, and caller-owned data-structure invariants are
// preconditions; checking them on every query would change query complexity.
// Scalar and shape checks are included. Value-range checks are included where needed to
// prevent invalid indexing or nontermination. Allocation sizes are capped at 4,000,000
// workspace entries. Arithmetic outside Python raises an error on 32-bit overflow; Python
// uses arbitrary precision. Native allocation failures propagate. In-place outputs may be
// partly updated after arithmetic failure. These are single-threaded, in-memory
// implementations.
//
// LANGUAGE DETAILS
// PHP 8.1+ on a 64-bit runtime: packed arrays, strict scalar types, read-only inputs by
// value using copy-on-write, references only for outputs, and checked 32-bit arithmetic.
// Invalid input and overflow throw exceptions. PHP arrays have higher overhead than native
// packed buffers in C/Java.
//
// EXAMPLE
// Expected return: 0.
// Expected a after call: [0, 0, 1, 2, 2].
// Run: php example.php
// Tests for this exact source artifact run before publication. The accompanying source
// archive includes unit cases, runtime results, and source hashes.

function alg_require(bool $valid): void { if (!$valid) throw new InvalidArgumentException("invalid algorithm input"); }
function alg_checked(int|float $v): int { if ($v < -2147483648 || $v > 2147483647 || floor($v) != $v) throw new OverflowException("32-bit result overflow"); return (int)$v; }
function alg_add(int $a,int $b): int { return alg_checked($a+$b); }
function alg_sub(int $a,int $b): int { return alg_checked($a-$b); }
function alg_mul(int $a,int $b): int { return alg_checked($a*$b); }
function alg_size(int $n): int { alg_require($n>=0 && $n<=4000000); return $n; }

function dutch_flag(array &$a): int {
    alg_require(array_is_list($a));
    $n = count($a);
    alg_require((($n >= 0) && ($n <= 1000000)));
    alg_require((count($a) == $n));
    for ($alg_i = 0; $alg_i < count($a); $alg_i++) {
        $alg_value = $a[$alg_i];
        alg_require((($alg_value >= 0) && ($alg_value <= 2)));
    }
    $low = 0;
    $mid = 0;
    $high = alg_sub($n, 1);
    $temp = 0;
    while (($mid <= $high)) {
        if (($a[$mid] == 0)) {
            $temp = $a[$low];
            $a[$low] = $a[$mid];
            $a[$mid] = $temp;
            $low = alg_add($low, 1);
            $mid = alg_add($mid, 1);
        } else {
            if (($a[$mid] == 1)) {
                $mid = alg_add($mid, 1);
            } else {
                $temp = $a[$mid];
                $a[$mid] = $a[$high];
                $a[$high] = $temp;
                $high = alg_sub($high, 1);
            }
        }
    }
    return 0;
}

$a = [2, 0, 1, 2, 0];
$result = dutch_flag($a);
echo $result, PHP_EOL;
echo json_encode($a), PHP_EOL;
// Expected a: [0, 0, 1, 2, 2]