Rod Cutting in PHP

<?php
declare(strict_types=1);
// Rod Cutting in PHP
//
// PURPOSE
// Rod cutting chooses cuts that maximize the sale value of a rod. It considers every first
// piece and reuses the optimal solution for the remaining length.
//
// METHOD
// Set the value of length zero to zero. For each length, try each possible first cut and
// combine its price with the already computed remainder value.
//
// COMPLEXITY
// O(n squared) time and O(n) auxiliary space.
//
// CONTRACT
// prices[i] is the nonnegative price for length i+1 and contains n entries. Returns maximum
// revenue for length n. Revenue must fit.
// 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: 10.
// 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 rod_cutting(array $prices, int $n): int {
    alg_require(array_is_list($prices));
    alg_require((($n >= 0) && ($n <= 1000000)));
    $dp = array_fill(0, alg_size(alg_add($n, 1)), 0);
    $length = 1;
    $cut = 0;
    while (($length <= $n)) {
        $cut = 1;
        while (($cut <= $length)) {
            $dp[$length] = max($dp[$length], alg_add($prices[alg_sub($cut, 1)], $dp[alg_sub($length, $cut)]));
            $cut = alg_add($cut, 1);
        }
        $length = alg_add($length, 1);
    }
    return $dp[$n];
}

$prices = [1, 5, 8, 9];
$n = 4;
$result = rod_cutting($prices, $n);
echo $result, PHP_EOL;