Binary Search Tree Lookup in PHP

<?php
declare(strict_types=1);
// Binary Search Tree Lookup in PHP
//
// PURPOSE
// A binary search tree chooses a branch by comparing the target with the current node key.
//
// METHOD
// At each node return on equality, otherwise follow the left child for a smaller target or
// the right child for a larger target.
//
// COMPLEXITY
// O(height) time and O(1) auxiliary space; height is O(log n) only when the tree is
// balanced.
//
// CONTRACT
// keys,left_child,right_child have n entries; -1 means absent. Must be a valid BST. Returns
// node ID or -1.
// 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: 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 bst_lookup(array $keys, array $left_child, array $right_child, int $root, int $target): int {
    alg_require(array_is_list($keys));
    alg_require(array_is_list($left_child));
    alg_require(array_is_list($right_child));
    $n = count($keys);
    alg_require((($n >= 0) && ($n <= 1000000)));
    alg_require((count($keys) == $n));
    alg_require((count($left_child) == $n));
    alg_require((count($right_child) == $n));
    alg_require((($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 < $n)));
    }
    while (($root != alg_sub(0, 1))) {
        if (($keys[$root] == $target)) {
            return $root;
        }
        if (($target < $keys[$root])) {
            $root = $left_child[$root];
        } else {
            $root = $right_child[$root];
        }
    }
    return alg_sub(0, 1);
}

$keys = [4, 2, 6];
$left_child = [1, -1, -1];
$right_child = [2, -1, -1];
$root = 0;
$target = 6;
$result = bst_lookup($keys, $left_child, $right_child, $root, $target);
echo $result, PHP_EOL;