Monotonic Deque Sliding Maximum in PHP

<?php
declare(strict_types=1);
// Monotonic Deque Sliding Maximum in PHP
//
// PURPOSE
// A monotonic deque returns every fixed-window maximum in linear time.
//
// METHOD
// Keep candidate indices in decreasing value order. Discard expired indices from the front
// and dominated candidates from the back; the front is the current maximum.
//
// COMPLEXITY
// O(n) time; O(n) allocated index-buffer space in this linear-buffer implementation, with at
// most k live candidates.
//
// CONTRACT
// 1 <= k <= n. output has n-k+1 entries. Writes maximum values and returns output length.
// 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.
// Expected output after call: [3, 3, 5, 5, 6, 7].
// 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 sliding_maximum(array $a, int $k, array &$output): int {
    alg_require(array_is_list($a));
    alg_require(array_is_list($output));
    $n = count($a);
    alg_require((($n >= 0) && ($n <= 1000000)));
    alg_require((count($a) == $n));
    alg_require((count($output) == alg_add(alg_sub($n, $k), 1)));
    alg_require((($k >= 1) && ($k <= $n)));
    $queue = array_fill(0, alg_size($n), 0);
    $head = 0;
    $tail = 0;
    $i = 0;
    while (($i < $n)) {
        while ((($head < $tail) && ($queue[$head] <= alg_sub($i, $k)))) {
            $head = alg_add($head, 1);
        }
        while ((($head < $tail) && ($a[$queue[alg_sub($tail, 1)]] <= $a[$i]))) {
            $tail = alg_sub($tail, 1);
        }
        $queue[$tail] = $i;
        $tail = alg_add($tail, 1);
        if (($i >= alg_sub($k, 1))) {
            $output[alg_add(alg_sub($i, $k), 1)] = $a[$queue[$head]];
        }
        $i = alg_add($i, 1);
    }
    return alg_add(alg_sub($n, $k), 1);
}

$a = [1, 3, -1, -3, 5, 3, 6, 7];
$k = 3;
$output = [0, 0, 0, 0, 0, 0];
$result = sliding_maximum($a, $k, $output);
echo $result, PHP_EOL;
// Expected output: [3, 3, 5, 5, 6, 7]
echo json_encode($output), PHP_EOL;