Iterative Binary Tree Preorder in PHP

<?php
declare(strict_types=1);
// Iterative Binary Tree Preorder in PHP
//
// PURPOSE
// Preorder traversal visits each binary-tree node once without recursion.
//
// METHOD
// Keep a stack of nodes and visit states. State zero descends left, state one descends
// right, and state two exits. Emit the node at the traversal-specific state.
//
// COMPLEXITY
// O(n) time and O(n) allocated stack space; live stack usage is O(tree height).
//
// CONTRACT
// Parallel left_child and right_child arrays contain -1 or node IDs. root=-1 means empty.
// The structure must be a valid tree, not cyclic or shared. output has n entries; writes
// node IDs and returns visited count.
// 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: 3.
// Expected output after call: [0, 1, 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 tree_preorder(array $left_child, array $right_child, int $root, array &$output): int {
    alg_require(array_is_list($left_child));
    alg_require(array_is_list($right_child));
    alg_require(array_is_list($output));
    $n = count($left_child);
    alg_require((($n >= 0) && ($n <= 1000000)));
    alg_require((count($left_child) == $n));
    alg_require((count($right_child) == $n));
    alg_require((count($output) == $n));
    alg_require((($root >= alg_sub(0, 1)) && ($root < $n)));
    for ($alg_i = 0; $alg_i < count($left_child); $alg_i++) {
        $alg_value = $left_child[$alg_i];
        alg_require((($alg_value >= alg_sub(0, 1)) && ($alg_value < $n)));
    }
    for ($alg_i = 0; $alg_i < count($right_child); $alg_i++) {
        $alg_value = $right_child[$alg_i];
        alg_require((($alg_value >= alg_sub(0, 1)) && ($alg_value < $n)));
    }
    $stack = array_fill(0, alg_size(alg_add($n, 1)), 0);
    $state = array_fill(0, alg_size(alg_add($n, 1)), 0);
    $top = 0;
    $u = 0;
    $phase = 0;
    $count = 0;
    if (($root == alg_sub(0, 1))) {
        return 0;
    }
    $stack[0] = $root;
    $top = 1;
    while (($top > 0)) {
        $u = $stack[alg_sub($top, 1)];
        $phase = $state[alg_sub($top, 1)];
        if (($phase == 0)) {
            $output[$count] = $u;
            $count = alg_add($count, 1);
        }
        if (($phase == 0)) {
            $state[alg_sub($top, 1)] = 1;
            if (($left_child[$u] != alg_sub(0, 1))) {
                $stack[$top] = $left_child[$u];
                $state[$top] = 0;
                $top = alg_add($top, 1);
            }
        } else {
            if (($phase == 1)) {
                $state[alg_sub($top, 1)] = 2;
                if (($right_child[$u] != alg_sub(0, 1))) {
                    $stack[$top] = $right_child[$u];
                    $state[$top] = 0;
                    $top = alg_add($top, 1);
                }
            } else {
                $top = alg_sub($top, 1);
            }
        }
    }
    return $count;
}

$left_child = [1, -1, -1];
$right_child = [2, -1, -1];
$root = 0;
$output = [0, 0, 0];
$result = tree_preorder($left_child, $right_child, $root, $output);
echo $result, PHP_EOL;
// Expected output: [0, 1, 2]
echo json_encode($output), PHP_EOL;