Warshall Transitive Closure in PHP

<?php
declare(strict_types=1);
// Warshall Transitive Closure in PHP
//
// PURPOSE
// Transitive closure records whether every vertex can reach every other vertex. Warshall is
// the Boolean counterpart of Floyd-Warshall.
//
// METHOD
// Mark each vertex reachable from itself. For every intermediate k, mark i-to-j reachable
// whenever i reaches k and k reaches j. The matrix accumulates reachability through the
// processed intermediates.
//
// COMPLEXITY
// O(n cubed) time and O(1) auxiliary space beyond the caller-owned matrix.
//
// CONTRACT
// Mutates a flattened n by n 0/1 adjacency matrix to reflexive transitive closure. Returns
// 0. A vertex reaches itself via a path of zero edges.
// 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 graph after call: [1, 1, 1, 0, 1, 1, 0, 0, 1].
// 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 transitive_closure(array &$graph, int $n): int {
    alg_require(array_is_list($graph));
    alg_require((($n >= 0) && ($n <= 1000000)));
    alg_require((count($graph) == alg_mul($n, $n)));
    $i = 0;
    $j = 0;
    $k = 0;
    while (($i < $n)) {
        $graph[alg_add(alg_mul($i, $n), $i)] = 1;
        $i = alg_add($i, 1);
    }
    while (($k < $n)) {
        $i = 0;
        while (($i < $n)) {
            $j = 0;
            while (($j < $n)) {
                if ((($graph[alg_add(alg_mul($i, $n), $k)] != 0) && ($graph[alg_add(alg_mul($k, $n), $j)] != 0))) {
                    $graph[alg_add(alg_mul($i, $n), $j)] = 1;
                }
                $j = alg_add($j, 1);
            }
            $i = alg_add($i, 1);
        }
        $k = alg_add($k, 1);
    }
    return 0;
}

$graph = [0, 1, 0, 0, 0, 1, 0, 0, 0];
$n = 3;
$result = transitive_closure($graph, $n);
echo $result, PHP_EOL;
echo json_encode($graph), PHP_EOL;
// Expected graph: [1, 1, 1, 0, 1, 1, 0, 0, 1]