Greedy Interval Scheduling in PHP

<?php
declare(strict_types=1);
// Greedy Interval Scheduling in PHP
//
// PURPOSE
// Earliest-finish-time scheduling selects a maximum-size collection of non-overlapping
// intervals.
//
// METHOD
// Process intervals sorted by finish time. Accept the next interval whenever its start is at
// least the finish of the last accepted interval.
//
// COMPLEXITY
// O(n) scan time and O(1) auxiliary space once sorted; sorting unsorted intervals first
// costs O(n log n).
//
// CONTRACT
// start and finish arrays have n entries; finish is nondecreasing and start[i]<finish[i].
// Half-open intervals allow touching endpoints. Returns selected count.
// 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: 4.
// 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 interval_schedule(array $start, array $finish): int {
    alg_require(array_is_list($start));
    alg_require(array_is_list($finish));
    $n = count($start);
    alg_require((($n >= 0) && ($n <= 1000000)));
    alg_require((count($start) == $n));
    alg_require((count($finish) == $n));
    $count = 0;
    $end = 0;
    $i = 0;
    while (($i < $n)) {
        if ((($count == 0) || ($start[$i] >= $end))) {
            $count = alg_add($count, 1);
            $end = $finish[$i];
        }
        $i = alg_add($i, 1);
    }
    return $count;
}

$start = [1, 3, 0, 5, 8, 5];
$finish = [2, 4, 6, 7, 9, 9];
$result = interval_schedule($start, $finish);
echo $result, PHP_EOL;