Egg Dropping by Number of Moves in PHP

<?php
declare(strict_types=1);
// Egg Dropping by Number of Moves in PHP
//
// PURPOSE
// Instead of trying every floor, this DP counts how many floors can be distinguished with a
// given number of moves and eggs.
//
// METHOD
// For each move, update egg counts downward using
// reachable[e]=reachable[e]+reachable[e-1]+1. Stop when the available egg count covers all
// floors.
//
// COMPLEXITY
// O(eggs * moves) time and O(eggs) space, where moves is the answer.
//
// CONTRACT
// 1<=eggs<=30, 0<=floors<=1000000. Returns the minimum worst-case number of drops.
// Reachability is capped at floors to avoid unnecessary growth.
// 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: 14.
// 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 egg_drop(int $eggs, int $floors): int {
    alg_require((($eggs >= 1) && ($eggs <= 30) && ($floors >= 0) && ($floors <= 1000000)));
    $reachable = array_fill(0, alg_size(alg_add($eggs, 1)), 0);
    $moves = 0;
    $e = 0;
    while (($reachable[$eggs] < $floors)) {
        $moves = alg_add($moves, 1);
        $e = $eggs;
        while (($e > 0)) {
            $reachable[$e] = min($floors, alg_add(alg_add($reachable[$e], $reachable[alg_sub($e, 1)]), 1));
            $e = alg_sub($e, 1);
        }
    }
    return $moves;
}

$eggs = 2;
$floors = 100;
$result = egg_drop($eggs, $floors);
echo $result, PHP_EOL;