Kruskal Minimum Spanning Tree in PHP

<?php
declare(strict_types=1);
// Kruskal Minimum Spanning Tree in PHP
//
// PURPOSE
// Kruskal adds edges in ascending weight order whenever they join different components.
//
// METHOD
// Sort edge indices by weight using a stable bottom-up merge. Use union by size and path
// halving to accept edges joining different roots. Stop after n-1 accepted edges.
//
// COMPLEXITY
// O(E log E + V) time and O(V+E) auxiliary space.
//
// CONTRACT
// n>=1, parallel edge arrays have m entries and valid vertex IDs. Weights nonnegative; total
// fits signed 32-bit. Returns -1 for a disconnected graph.
// 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 kruskal(array $from_vertex, array $to_vertex, array $weight, int $n): int {
    alg_require(array_is_list($from_vertex));
    alg_require(array_is_list($to_vertex));
    alg_require(array_is_list($weight));
    $m = count($from_vertex);
    alg_require((($n >= 0) && ($n <= 1000000)));
    alg_require((($m >= 0) && ($m <= 1000000)));
    alg_require((count($from_vertex) == $m));
    alg_require((count($to_vertex) == $m));
    alg_require((count($weight) == $m));
    alg_require(($n >= 1));
    for ($alg_i = 0; $alg_i < count($from_vertex); $alg_i++) {
        $alg_value = $from_vertex[$alg_i];
        alg_require((($alg_value >= 0) && ($alg_value < $n)));
    }
    for ($alg_i = 0; $alg_i < count($to_vertex); $alg_i++) {
        $alg_value = $to_vertex[$alg_i];
        alg_require((($alg_value >= 0) && ($alg_value < $n)));
    }
    $order = array_fill(0, alg_size(alg_add($m, 1)), 0);
    $buffer = array_fill(0, alg_size(alg_add($m, 1)), 0);
    $parent = array_fill(0, alg_size($n), 0);
    $size = array_fill(0, alg_size($n), 0);
    $i = 0;
    $j = 0;
    $k = 0;
    $width = 1;
    $left = 0;
    $mid = 0;
    $right = 0;
    $edge = 0;
    $u = 0;
    $v = 0;
    $temp = 0;
    $accepted = 0;
    $total = 0;
    while (($i < $m)) {
        $order[$i] = $i;
        $i = alg_add($i, 1);
    }
    while (($width < $m)) {
        $left = 0;
        while (($left < $m)) {
            $mid = min(alg_add($left, $width), $m);
            $right = min(alg_add($left, alg_mul(2, $width)), $m);
            $i = $left;
            $j = $mid;
            $k = $left;
            while (($k < $right)) {
                if ((($i < $mid) && (($j >= $right) || ($weight[$order[$i]] <= $weight[$order[$j]])))) {
                    $buffer[$k] = $order[$i];
                    $i = alg_add($i, 1);
                } else {
                    $buffer[$k] = $order[$j];
                    $j = alg_add($j, 1);
                }
                $k = alg_add($k, 1);
            }
            $left = alg_add($left, alg_mul(2, $width));
        }
        $i = 0;
        while (($i < $m)) {
            $order[$i] = $buffer[$i];
            $i = alg_add($i, 1);
        }
        $width = alg_mul($width, 2);
    }
    $i = 0;
    while (($i < $n)) {
        $parent[$i] = $i;
        $size[$i] = 1;
        $i = alg_add($i, 1);
    }
    while ((($edge < $m) && ($accepted < alg_sub($n, 1)))) {
        $u = $from_vertex[$order[$edge]];
        $v = $to_vertex[$order[$edge]];
        while (($parent[$u] != $u)) {
            $parent[$u] = $parent[$parent[$u]];
            $u = $parent[$u];
        }
        while (($parent[$v] != $v)) {
            $parent[$v] = $parent[$parent[$v]];
            $v = $parent[$v];
        }
        if (($u != $v)) {
            if (($size[$u] < $size[$v])) {
                $temp = $u;
                $u = $v;
                $v = $temp;
            }
            $parent[$v] = $u;
            $size[$u] = alg_add($size[$u], $size[$v]);
            $accepted = alg_add($accepted, 1);
            $total = alg_add($total, $weight[$order[$edge]]);
        }
        $edge = alg_add($edge, 1);
    }
    if (($accepted != alg_sub($n, 1))) {
        return alg_sub(0, 1);
    }
    return $total;
}

$from_vertex = [0, 1, 0];
$to_vertex = [1, 2, 2];
$weight = [4, 2, 10];
$n = 3;
$result = kruskal($from_vertex, $to_vertex, $weight, $n);
echo $result, PHP_EOL;