Bipartite Graph Coloring in PHP

<?php
declare(strict_types=1);
// Bipartite Graph Coloring in PHP
//
// PURPOSE
// A graph is bipartite when its vertices can be colored with two colors so that each edge
// joins opposite colors.
//
// METHOD
// BFS every uncolored component. Give neighbors the opposite color and reject any edge
// joining equal colors.
//
// COMPLEXITY
// O(n squared) time with this dense matrix, O(n) auxiliary space.
//
// CONTRACT
// Symmetric flattened n by n 0/1 matrix. Returns 1 or 0. Self-loops make a graph non-
// bipartite.
// 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_bipartite(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)));
    $color = array_fill(0, alg_size(alg_add($n, 1)), 0);
    $queue = array_fill(0, alg_size(alg_add($n, 1)), 0);
    $source = 0;
    $head = 0;
    $tail = 0;
    $u = 0;
    $v = 0;
    while (($source < $n)) {
        if (($color[$source] == 0)) {
            $head = 0;
            $tail = 1;
            $queue[0] = $source;
            $color[$source] = 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), $v)] != 0)) {
                        if (($color[$v] == $color[$u])) {
                            return 0;
                        }
                        if (($color[$v] == 0)) {
                            $color[$v] = alg_sub(3, $color[$u]);
                            $queue[$tail] = $v;
                            $tail = alg_add($tail, 1);
                        }
                    }
                    $v = alg_add($v, 1);
                }
            }
        }
        $source = alg_add($source, 1);
    }
    return 1;
}

$graph = [0, 1, 1, 0];
$n = 2;
$result = is_bipartite($graph, $n);
echo $result, PHP_EOL;