0-1 Knapsack in PHP

<?php
declare(strict_types=1);
// 0-1 Knapsack in PHP
//
// PURPOSE
// Knapsack chooses items with maximum total value under a weight limit, using each item at
// most once. The one-dimensional table stores the best value for each capacity.
//
// METHOD
// Process items one at a time and capacities downward. Compare skipping the item with adding
// its value to the previous best at the remaining capacity. Descending capacities prevent
// reusing the current item.
//
// COMPLEXITY
// O(n * capacity) time and O(capacity) auxiliary space; pseudo-polynomial.
//
// CONTRACT
// Weights are positive, values nonnegative, capacity >= 0. Both arrays have n entries.
// Returns best value, not the chosen item set.
// 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: 9.
// 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 knapsack(array $weights, array $values, int $capacity): int {
    alg_require(array_is_list($weights));
    alg_require(array_is_list($values));
    $n = count($weights);
    alg_require((($n >= 0) && ($n <= 1000000)));
    alg_require((count($weights) == $n));
    alg_require((count($values) == $n));
    alg_require((($capacity >= 0) && ($capacity <= 1000000)));
    for ($alg_i = 0; $alg_i < count($weights); $alg_i++) {
        $alg_value = $weights[$alg_i];
        alg_require(($alg_value > 0));
    }
    for ($alg_i = 0; $alg_i < count($values); $alg_i++) {
        $alg_value = $values[$alg_i];
        alg_require(($alg_value >= 0));
    }
    $dp = array_fill(0, alg_size(alg_add($capacity, 1)), 0);
    $i = 0;
    $c = 0;
    while (($i < $n)) {
        $c = $capacity;
        while (($c >= $weights[$i])) {
            $dp[$c] = max($dp[$c], alg_add($dp[alg_sub($c, $weights[$i])], $values[$i]));
            $c = alg_sub($c, 1);
        }
        $i = alg_add($i, 1);
    }
    return $dp[$capacity];
}

$weights = [2, 3, 4];
$values = [4, 5, 7];
$capacity = 5;
$result = knapsack($weights, $values, $capacity);
echo $result, PHP_EOL;