Kahn Topological Cycle Detection in PHP

<?php
declare(strict_types=1);
// Kahn Topological Cycle Detection in PHP
//
// PURPOSE
// Kahn algorithm repeatedly removes vertices with no incoming edges. A directed graph has a
// topological ordering exactly when all vertices can be removed this way.
//
// METHOD
// Compute indegrees, queue every zero-indegree vertex, then remove its outgoing edges.
// Enqueue a neighbor when its indegree becomes zero. Compare the number removed with n.
//
// COMPLEXITY
// O(n squared) time with an adjacency matrix and O(n) auxiliary space. Adjacency lists give
// O(V+E).
//
// CONTRACT
// Flattened n by n 0/1 directed matrix. Returns 1 for a DAG and 0 for a cycle. Empty graph
// is a DAG. This variant reports existence rather than returning an ordering.
// 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: 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 is_dag(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)));
    $indegree = array_fill(0, alg_size(alg_add($n, 1)), 0);
    $queue = array_fill(0, alg_size(alg_add($n, 1)), 0);
    $u = 0;
    $v = 0;
    $head = 0;
    $tail = 0;
    while (($u < $n)) {
        $v = 0;
        while (($v < $n)) {
            if (($graph[alg_add(alg_mul($u, $n), $v)] != 0)) {
                $indegree[$v] = alg_add($indegree[$v], 1);
            }
            $v = alg_add($v, 1);
        }
        $u = alg_add($u, 1);
    }
    $v = 0;
    while (($v < $n)) {
        if (($indegree[$v] == 0)) {
            $queue[$tail] = $v;
            $tail = alg_add($tail, 1);
        }
        $v = alg_add($v, 1);
    }
    while (($head < $tail)) {
        $u = $queue[$head];
        $head = alg_add($head, 1);
        $v = 0;
        while (($v < $n)) {
            if (($graph[alg_add(alg_mul($u, $n), $v)] != 0)) {
                $indegree[$v] = alg_sub($indegree[$v], 1);
                if (($indegree[$v] == 0)) {
                    $queue[$tail] = $v;
                    $tail = alg_add($tail, 1);
                }
            }
            $v = alg_add($v, 1);
        }
    }
    if (($tail == $n)) {
        return 1;
    }
    return 0;
}

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