Longest Palindromic Subsequence in PHP

<?php
declare(strict_types=1);
// Longest Palindromic Subsequence in PHP
//
// PURPOSE
// A longest palindromic subsequence may skip tokens while preserving order. It differs from
// a contiguous palindromic substring.
//
// METHOD
// Scan left endpoints backward and right endpoints forward. Equal endpoints extend the inner
// solution by two; otherwise discard one endpoint. Retain one row and the old diagonal.
//
// COMPLEXITY
// O(n squared) time, O(n) auxiliary space.
//
// CONTRACT
// Integer tokens. Returns length; empty input returns 0.
// 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: 5.
// 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 palindromic_subsequence(array $a): int {
    alg_require(array_is_list($a));
    $n = count($a);
    alg_require((($n >= 0) && ($n <= 1000000)));
    alg_require((count($a) == $n));
    $dp = array_fill(0, alg_size(alg_add($n, 1)), 0);
    $left = alg_sub($n, 1);
    $right = 0;
    $diagonal = 0;
    $old = 0;
    while (($left >= 0)) {
        $dp[$left] = 1;
        $diagonal = 0;
        $right = alg_add($left, 1);
        while (($right < $n)) {
            $old = $dp[$right];
            if (($a[$left] == $a[$right])) {
                $dp[$right] = alg_add($diagonal, 2);
            } else {
                $dp[$right] = max($dp[$right], $dp[alg_sub($right, 1)]);
            }
            $diagonal = $old;
            $right = alg_add($right, 1);
        }
        $left = alg_sub($left, 1);
    }
    if (($n == 0)) {
        return 0;
    }
    return $dp[alg_sub($n, 1)];
}

$a = [1, 2, 3, 2, 1];
$result = palindromic_subsequence($a);
echo $result, PHP_EOL;