Kosaraju Strongly Connected Components in PHP

<?php
declare(strict_types=1);
// Kosaraju Strongly Connected Components in PHP
//
// PURPOSE
// Strongly connected components group vertices that can reach each other in both directions.
//
// METHOD
// First perform iterative DFS to record finishing order. Traverse vertices in reverse
// finishing order using incoming edges, counting each newly discovered component.
//
// COMPLEXITY
// O(n squared) time for the dense matrix and O(n) auxiliary space.
//
// CONTRACT
// Flattened n by n directed 0/1 matrix. Returns number of components; empty graph returns
// zero.
// 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 scc_count(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)));
    $seen = array_fill(0, alg_size(alg_add($n, 1)), 0);
    $stack = array_fill(0, alg_size(alg_add($n, 1)), 0);
    $next_vertex = array_fill(0, alg_size(alg_add($n, 1)), 0);
    $order = array_fill(0, alg_size(alg_add($n, 1)), 0);
    $source = 0;
    $top = 0;
    $finished = 0;
    $u = 0;
    $v = 0;
    $count = 0;
    while (($source < $n)) {
        if (($seen[$source] == 0)) {
            $stack[0] = $source;
            $top = 1;
            $seen[$source] = 1;
            while (($top > 0)) {
                $u = $stack[alg_sub($top, 1)];
                if (($next_vertex[$u] == $n)) {
                    $order[$finished] = $u;
                    $finished = alg_add($finished, 1);
                    $top = alg_sub($top, 1);
                } else {
                    $v = $next_vertex[$u];
                    $next_vertex[$u] = alg_add($next_vertex[$u], 1);
                    if ((($graph[alg_add(alg_mul($u, $n), $v)] != 0) && ($seen[$v] == 0))) {
                        $seen[$v] = 1;
                        $stack[$top] = $v;
                        $top = alg_add($top, 1);
                    }
                }
            }
        }
        $source = alg_add($source, 1);
    }
    $source = 0;
    while (($source < $n)) {
        $seen[$source] = 0;
        $source = alg_add($source, 1);
    }
    while (($finished > 0)) {
        $finished = alg_sub($finished, 1);
        $source = $order[$finished];
        if (($seen[$source] == 0)) {
            $count = alg_add($count, 1);
            $stack[0] = $source;
            $top = 1;
            $seen[$source] = 1;
            while (($top > 0)) {
                $top = alg_sub($top, 1);
                $u = $stack[$top];
                $v = 0;
                while (($v < $n)) {
                    if ((($graph[alg_add(alg_mul($v, $n), $u)] != 0) && ($seen[$v] == 0))) {
                        $seen[$v] = 1;
                        $stack[$top] = $v;
                        $top = alg_add($top, 1);
                    }
                    $v = alg_add($v, 1);
                }
            }
        }
    }
    return $count;
}

$graph = [0, 1, 0, 1, 0, 1, 0, 0, 0];
$n = 3;
$result = scc_count($graph, $n);
echo $result, PHP_EOL;