Prim Minimum Spanning Tree in PHP

<?php
declare(strict_types=1);
// Prim Minimum Spanning Tree in PHP
//
// PURPOSE
// Prim grows a minimum spanning tree by choosing the cheapest edge that connects an
// unvisited vertex to the current tree. The cut property justifies each greedy choice.
//
// METHOD
// Keep the cheapest connection cost for every unvisited vertex. Select the cheapest one, add
// its cost, and update neighbors. If no finite connection remains before all vertices are
// added, the graph is disconnected.
//
// COMPLEXITY
// O(n squared) time and O(n) auxiliary space for a dense adjacency matrix.
//
// CONTRACT
// n >= 1; symmetric flattened matrix for an undirected graph. -1 means absent, weights are
// nonnegative and < 1,000,000,000. Total must fit. Returns MST weight or -1 if disconnected.
// 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: 6.
// 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 prim_mst(array $graph, int $n): int {
    alg_require(array_is_list($graph));
    alg_require((($n >= 0) && ($n <= 1000000)));
    alg_require((count($graph) == alg_mul($n, $n)));
    alg_require(($n >= 1));
    for ($alg_i = 0; $alg_i < count($graph); $alg_i++) {
        $alg_value = $graph[$alg_i];
        alg_require((($alg_value >= alg_sub(0, 1)) && ($alg_value < 1000000000)));
    }
    $cost = array_fill(0, alg_size($n), 0);
    $used = array_fill(0, alg_size($n), 0);
    $i = 0;
    $v = 0;
    $u = 0;
    $best = 0;
    $total = 0;
    while (($i < $n)) {
        $cost[$i] = 1000000000;
        $i = alg_add($i, 1);
    }
    $cost[0] = 0;
    $i = 0;
    while (($i < $n)) {
        $u = alg_sub(0, 1);
        $best = 1000000000;
        $v = 0;
        while (($v < $n)) {
            if ((($used[$v] == 0) && ($cost[$v] < $best))) {
                $best = $cost[$v];
                $u = $v;
            }
            $v = alg_add($v, 1);
        }
        if (($u == alg_sub(0, 1))) {
            return alg_sub(0, 1);
        }
        $used[$u] = 1;
        $total = alg_add($total, $cost[$u]);
        $v = 0;
        while (($v < $n)) {
            if (($graph[alg_add(alg_mul($u, $n), $v)] >= 0)) {
                $cost[$v] = min($cost[$v], $graph[alg_add(alg_mul($u, $n), $v)]);
            }
            $v = alg_add($v, 1);
        }
        $i = alg_add($i, 1);
    }
    return $total;
}

$graph = [0, 4, 10, 4, 0, 2, 10, 2, 0];
$n = 3;
$result = prim_mst($graph, $n);
echo $result, PHP_EOL;