Project Euler - solutions written in PHP

project-euler.php

<?php

declare(strict_types = 1);


final readonly class solution {
	public function __construct(
		public int $n,
		public string $info,
	) {}
};


$solvers = [
	1 => static function (): solution {
		$sum = 0;
		$ns = [];
		$l = 1000;

		for ($i = 1; $i < $l; $i++) {
			if ($i % 3 === 0 || $i % 5 === 0) {
				$sum += $i;
				$ns[] = $i;
			}
		}

		return new solution($sum, implode(' + ', array_slice($ns, -10)) . ' = ' . $sum);
	},

	2 => static function (): solution {
		$a = 1;
		$b = 2;
		$sum = 2;
		$ns = [];
		$l = 4_000_000;

		while ($b <= $l) {
			$_ = $b;
			$b = $a + $b;
			$a = $_;

			if ($b % 2 === 0) {
				$sum += $b;
				$ns[] = $b;
			}
		}

		return new solution($sum, implode(' + ', $ns) . ' = ' . $sum);
	},

	3 => static function (): solution {
		$n = 600_851_475_143;
		$ns = [];

		for ($d = 2; $d <= sqrt($n); $d++) {
			while ($n % $d === 0) {
				$n = (int) ($n / $d);
				$ns[] = $d;
			}
		}

		$ns[] = $n;

		return new solution($n, implode(' -> ', $ns));
	},

	4 => static function (): solution {
		$n = 0;
		$ns = [];

		for ($a = 999; $a >= 100; $a--) {
			for ($b = 999; $b >= 100; $b--) {
				$p = (string) ($a * $b);
				$len = strlen($p);

				for ($i = 0; $i < $len / 2; $i++) {
					if ($p[$i] !== $p[$len - $i - 1]) {
						continue 2;
					}
				}

				if ((int) $p > $n) {
					$n = (int) $p;
					$ns[] = $p;
				}
			}
		}

		return new solution($n, implode(' -> ', $ns));
	},

	5 => static function (): solution {
		$a = 1;
		$ns = [$a];

		for ($b = 2; $b <= 20; $b++) {
			$hcf = 0;
			$m = $a;
			$n = $b;

			while (true) {
				$rem = $n % $m;

				if ($rem === 0) {
					$hcf = $m;
					break;
				}

				$n = $m;
				$m = $rem;
			}

			$a = ($a * $b) / $hcf;
			$ns[] = $a;
		}

		return new solution($a, implode(' -> ', $ns));
	},

	6 => static function (): solution {
		$a = $b = 0;

		for ($i = 1; $i <= 100; $i++) {
			$a += $i ** 2;
			$b += $i;
		}

		$b2 = $b ** 2;
		$n = $b2 - $a;
		return new solution($n, sprintf('%d^2 - %d = %d - %d = %d', $b, $a, $b2, $a, $n));
	},

	7 => static function (): solution {
		$l = 10_001;
		$primes = [2];

		for ($n = 3; ; $n += 2) {
			$isPrime = true;

			foreach ($primes as $p) {
				if ($n % $p === 0) {
					$isPrime = false;
					break;
				}
			}

			if ($isPrime) {
				$primes[] = $n;
			}

			if (count($primes) === $l) {
				break;
			}
		}

		return new solution($n, '... ' . implode(', ', array_slice($primes, -10)));
	},

	8 => static function (): solution {
		$a = '7316717653133062491922511967442657474235534919493496983520312774506326239578318016984801869478851843858615607891129494954595017379583319528532088055111254069874715852386305071569329096329522744304355766896648950445244523161731856403098711121722383113622298934233803081353362766142828064444866452387493035890729629049156044077239071381051585930796086670172427121883998797908792274921901699720888093776657273330010533678812202354218097512545405947522435258490771167055601360483958644670632441572215539753697817977846174064955149290862569321978468622482839722413756570560574902614079729686524145351004748216637048440319989000889524345065854122758866688116427171479924442928230863465674813919123162824586178664583591245665294765456828489128831426076900422421902267105562632111110937054421750694165896040807198403850962455444362981230987879927244284909188845801561660979191338754992005240636899125607176060588611646710940507754100225698315520005593572972571636269561882670428252483600823257530420752963450';

		$n = 0;
		$l = 13;
		$ns = [];

		for ($i = 0; $i < strlen($a) - $l; $i++) {
			$p = $a[$i];
			$cns = [$p];

			for ($j = 1; $j < $l; $j++) {
				$p *= $a[$i + $j];
				$cns[] = $a[$i + $j];
			}

			if ($p > $n) {
				$n = $p;
				$ns = $cns;
			}
		}

		return new solution($n, implode(' * ', $ns) . ' = ' . $n);
	},

	9 => static function (): solution {
		$n = 0;
		for ($a = 3; $a <= 998; $a++) {
			for ($b = 4; $b <= 998; $b++) {
				$c = 1000 - $a - $b;

				if (($a ** 2 + $b ** 2) === $c ** 2) {
					$n = $a * $b * $c;
					break 2;
				}
			}
		}

		return new solution($n, sprintf('%d^2 + %d^2 = %d^2', $a, $b, $c));
	},

	10 => static function (): solution {
		$sum = 0;
		$primes = [];
		$l = 2_000_000;
		$processed = [];

		for ($n = 2; $n < $l; $n++) {
			if (isset($processed[$n])) {
				continue ;
			}

			$processed[$n] = true;
			$primes[] = $n;
			$sum += $n;

			for ($q = 2; ; $q++) {
				$m = $q * $n;

				if ($m >= $l) {
					break;
				}

				$processed[$m] = true;
			}
		}

		return new solution($sum, '... ' . implode(' + ', array_slice($primes, -10)) . ' = ' . $sum);
	},

	11 => static function (): solution {
		$g = '
			08 02 22 97 38 15 00 40 00 75 04 05 07 78 52 12 50 77 91 08
			49 49 99 40 17 81 18 57 60 87 17 40 98 43 69 48 04 56 62 00
			81 49 31 73 55 79 14 29 93 71 40 67 53 88 30 03 49 13 36 65
			52 70 95 23 04 60 11 42 69 24 68 56 01 32 56 71 37 02 36 91
			22 31 16 71 51 67 63 89 41 92 36 54 22 40 40 28 66 33 13 80
			24 47 32 60 99 03 45 02 44 75 33 53 78 36 84 20 35 17 12 50
			32 98 81 28 64 23 67 10 26 38 40 67 59 54 70 66 18 38 64 70
			67 26 20 68 02 62 12 20 95 63 94 39 63 08 40 91 66 49 94 21
			24 55 58 05 66 73 99 26 97 17 78 78 96 83 14 88 34 89 63 72
			21 36 23 09 75 00 76 44 20 45 35 14 00 61 33 97 34 31 33 95
			78 17 53 28 22 75 31 67 15 94 03 80 04 62 16 14 09 53 56 92
			16 39 05 42 96 35 31 47 55 58 88 24 00 17 54 24 36 29 85 57
			86 56 00 48 35 71 89 07 05 44 44 37 44 60 21 58 51 54 17 58
			19 80 81 68 05 94 47 69 28 73 92 13 86 52 17 77 04 89 55 40
			04 52 08 83 97 35 99 16 07 97 57 32 16 26 26 79 33 27 98 66
			88 36 68 87 57 62 20 72 03 46 33 67 46 55 12 32 63 93 53 69
			04 42 16 73 38 25 39 11 24 94 72 18 08 46 29 32 40 62 76 36
			20 69 36 41 72 30 23 88 34 62 99 69 82 67 59 85 74 04 36 16
			20 73 35 29 78 31 90 01 74 31 49 71 48 86 81 16 23 57 05 54
			01 70 54 71 83 51 54 69 16 92 33 48 61 43 52 01 89 19 67 48
		';

		$g = array_map(
			fn($s): array => array_map('intval', explode(' ', trim($s))),
			explode("\n", trim($g)),
		);

		$n = 0;
		$ns = [];
		$nsc = 4;
		$gs = count($g);
		$dirs = [[0, 1], [1, 0], [1, 1], [1, -1]];

		for ($i = 0; $i < $gs; $i++) {
			for ($j = 0; $j < $gs; $j++) {
				foreach ($dirs as $vc) {
					$m = $g[$i][$j];
					$cns = [$m];

					for ($k = 1; $k <= $nsc - 1; $k++) {
						$r = $i + $vc[0] * $k;
						$c = $j + $vc[1] * $k;

						if ($r <= 0 || $r >= $gs || $c <= 0 || $c >= $gs) {
							continue 2;
						}

						$nb = $g[$r][$c];

						$m *= $nb;
						$cns[] = $nb;
					}

					if ($m > $n) {
						$n = $m;
						$ns = $cns;
					}
				}
			}
		}

		return new solution($n, implode(' * ', $ns) . ' = ' . $n);
	},
];


$solutions = [
	1 => 233_168,
	2 => 4_613_732,
	3 => 6_857,
	4 => 906_609,
	5 => 232_792_560,
	6 => 25_164_150,
	7 => 104_743,
	8 => 23_514_624_000,
	9 => 31_875_000,
	10 => 142_913_828_922,
	11 => 70_600_674,
];


(static function () use ($solvers, $solutions): void {

	foreach ($solvers as $no => $solver) {
		$start = hrtime(true);
		$solution = $solver();
		$time = round((hrtime(true) - $start) / 1e6, 2);

		assert($solution->n === $solutions[$no]);

		echo '#', $no, ' ', $solution->n,
			' (', $time, 'ms)', "\n",
			$solution->info, "\n\n";
	}

})();