Disjoint Set Union in PHP

<?php
declare(strict_types=1);
// Disjoint Set Union in PHP
//
// PURPOSE
// Disjoint set union maintains connected components as a forest of parent links. Union by
// size and path compression keep repeated operations nearly constant in amortized time.
//
// METHOD
// Start with each vertex as its own component. Find each edge endpoint root with path
// halving. If roots differ, attach the smaller tree to the larger and decrease the component
// count.
//
// COMPLEXITY
// O(n + m alpha(n)) amortized time and O(n) auxiliary space, where alpha is the inverse
// Ackermann function.
//
// CONTRACT
// n >= 0; edge arrays u_edges and v_edges have m valid vertex indices each. Treats edges as
// undirected. Returns component count; isolated vertices count separately.
// 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 component_count(array $u_edges, array $v_edges, int $n): int {
    alg_require(array_is_list($u_edges));
    alg_require(array_is_list($v_edges));
    $m = count($u_edges);
    alg_require((($n >= 0) && ($n <= 1000000)));
    alg_require((($m >= 0) && ($m <= 1000000)));
    alg_require((count($u_edges) == $m));
    alg_require((count($v_edges) == $m));
    for ($alg_i = 0; $alg_i < count($u_edges); $alg_i++) {
        $alg_value = $u_edges[$alg_i];
        alg_require((($alg_value >= 0) && ($alg_value < $n)));
    }
    for ($alg_i = 0; $alg_i < count($v_edges); $alg_i++) {
        $alg_value = $v_edges[$alg_i];
        alg_require((($alg_value >= 0) && ($alg_value < $n)));
    }
    $parent = array_fill(0, alg_size(alg_add($n, 1)), 0);
    $size = array_fill(0, alg_size(alg_add($n, 1)), 0);
    $i = 0;
    $edge = 0;
    $u = 0;
    $v = 0;
    $temp = 0;
    $count = $n;
    while (($i < $n)) {
        $parent[$i] = $i;
        $size[$i] = 1;
        $i = alg_add($i, 1);
    }
    while (($edge < $m)) {
        $u = $u_edges[$edge];
        $v = $v_edges[$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]);
            $count = alg_sub($count, 1);
        }
        $edge = alg_add($edge, 1);
    }
    return $count;
}

$u_edges = [0, 1, 3];
$v_edges = [1, 2, 4];
$n = 5;
$result = component_count($u_edges, $v_edges, $n);
echo $result, PHP_EOL;