Project Euler 92: Investigating a square digits number chain with a surprising property. How many starting numbers below ten million will arrive at 89?

euler92.php

<?php
declare(strict_types=1);

ini_set('memory_limit', '1G');
ini_set('max_execution_time', '0');

/**
 * Maps the given number to array of its digits.
 *
 * @param int $number
 * @return int[]|false
 */
function num_split(int $number): array
{
    $chars = str_split((string)$number);
    if (!is_array($chars)) {
        return false;
    }
    $digits = [];
    foreach ($chars as $char) {
        $digits[] = (int)$char;
    }

    return $digits;
}

// assert(count(array_diff([4, 4], num_split(44))) === 0);
// assert(count(array_diff([8, 9], num_split(89))) === 0);
// assert(count(array_diff([1, 0, 0, 0, 0, 0, 0, 0], num_split(10000000))) === 0);

/**
 * Reduces the given number to the square of its digits.
 *
 * @param int $number
 * @return int
 */
function square_digits(int $number): int
{
    $digits = num_split($number);
    $total = 0;
    foreach ($digits as $digit) {
        $total += $digit ** 2;
    }

    return $total;
}

// assert(square_digits(44) === 32);
// assert(square_digits(85) === 89);
// assert(square_digits(10000000) === 1);

/**
 * Return the termination value of 1 or 89 for the given number.
 *
 * @param int $number
 * @return int
 */
function terminate(int $number): int
{
    /** @var int[] $TERMINATIONS */
    global $TERMINATIONS;

    if (in_array($number, [1, 89], true)) {
        return $number;
    }
    if (is_array($TERMINATIONS) && array_key_exists($number, $TERMINATIONS)) {
        return $TERMINATIONS[$number];
    }
    $TERMINATIONS[$number] = terminate(square_digits($number));

    return $TERMINATIONS[$number];
}

// assert(terminate(44) === 1);
// assert(terminate(85) === 89);
// assert(terminate(10000000) === 1);

$start = microtime(true);
$count = 0;
for ($i = 1; $i <= 10000; $i++) {
    if (terminate($i) === 89) {
        $count++;
    }
}
echo $count, PHP_EOL;
echo microtime(true) - $start, PHP_EOL;
echo memory_get_peak_usage(true), PHP_EOL;