Bellman Ford Shortest Path in PHP

<?php
declare(strict_types=1);
// Bellman Ford Shortest Path in PHP
//
// PURPOSE
// Bellman-Ford permits negative edge weights and detects negative cycles reachable from the
// source. Repeated edge relaxation finds progressively longer optimal paths.
//
// METHOD
// Relax every edge up to n-1 times, stopping early if nothing changes. Perform one extra
// pass to detect a reachable negative cycle. Guard unreachable endpoints before adding
// weights.
//
// COMPLEXITY
// O(VE) time and O(V) auxiliary space.
//
// CONTRACT
// Edge arrays from_vertex, to_vertex, weight each have m entries; n >= 1. Finite distances
// and all relaxed sums stay strictly between -1,000,000,000 and 1,000,000,000. Returns
// distance, INF if unreachable, or -INF for any reachable negative cycle (even if it cannot
// reach target).
// 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 bellman_ford(array $from_vertex, array $to_vertex, array $weight, int $n, int $source, int $target): int {
    alg_require(array_is_list($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) && ($source >= 0) && ($source < $n)));
    alg_require((($target >= 0) && ($target < $n)));
    for ($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)));
    }
    $distance = array_fill(0, alg_size($n), 0);
    $i = 0;
    $edge = 0;
    $iteration = 0;
    $changed = 0;
    $u = 0;
    $v = 0;
    while (($i < $n)) {
        $distance[$i] = 1000000000;
        $i = alg_add($i, 1);
    }
    $distance[$source] = 0;
    while (($iteration < alg_sub($n, 1))) {
        $changed = 0;
        $edge = 0;
        while (($edge < $m)) {
            $u = $from_vertex[$edge];
            $v = $to_vertex[$edge];
            if ((($distance[$u] != 1000000000) && (alg_add($distance[$u], $weight[$edge]) < $distance[$v]))) {
                $distance[$v] = alg_add($distance[$u], $weight[$edge]);
                $changed = 1;
            }
            $edge = alg_add($edge, 1);
        }
        if (($changed == 0)) {
            break;
        }
        $iteration = alg_add($iteration, 1);
    }
    $edge = 0;
    while (($edge < $m)) {
        $u = $from_vertex[$edge];
        $v = $to_vertex[$edge];
        if ((($distance[$u] != 1000000000) && (alg_add($distance[$u], $weight[$edge]) < $distance[$v]))) {
            return alg_sub(0, 1000000000);
        }
        $edge = alg_add($edge, 1);
    }
    return $distance[$target];
}

$from_vertex = [0, 1, 0];
$to_vertex = [1, 2, 2];
$weight = [4, -2, 9];
$n = 3;
$source = 0;
$target = 2;
$result = bellman_ford($from_vertex, $to_vertex, $weight, $n, $source, $target);
echo $result, PHP_EOL;