Trapping Rain Water in PHP

<?php
declare(strict_types=1);
// Trapping Rain Water in PHP
//
// PURPOSE
// Two boundary maxima determine trapped water above each bar.
//
// METHOD
// Process the side with the smaller boundary maximum, because the opposite side already
// provides a sufficiently high boundary. Accumulate that side's maximum minus its bar
// height.
//
// COMPLEXITY
// O(n) time, O(1) auxiliary space.
//
// CONTRACT
// Heights are nonnegative. Total volume must fit signed 32-bit.
// 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.
// 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 trapped_water(array $a): int {
    alg_require(array_is_list($a));
    $n = count($a);
    alg_require((($n >= 0) && ($n <= 1000000)));
    alg_require((count($a) == $n));
    for ($alg_i = 0; $alg_i < count($a); $alg_i++) {
        $alg_value = $a[$alg_i];
        alg_require(($alg_value >= 0));
    }
    $left = 0;
    $right = alg_sub($n, 1);
    $left_max = 0;
    $right_max = 0;
    $total = 0;
    while (($left <= $right)) {
        if (($left_max <= $right_max)) {
            $left_max = max($left_max, $a[$left]);
            $total = alg_add($total, alg_sub($left_max, $a[$left]));
            $left = alg_add($left, 1);
        } else {
            $right_max = max($right_max, $a[$right]);
            $total = alg_add($total, alg_sub($right_max, $a[$right]));
            $right = alg_sub($right, 1);
        }
    }
    return $total;
}

$a = [0, 1, 0, 2, 1, 0, 1, 3, 2, 1, 2, 1];
$result = trapped_water($a);
echo $result, PHP_EOL;