PHP solution to Project Euler problem # 11.

project-euler-11.php

<?php
/*
Largest product in a grid
Problem 11
In the 20×20 grid below, four numbers along a diagonal line have been marked in red.

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
The product of these numbers is 26 × 63 × 78 × 14 = 1788696.

What is the greatest product of four adjacent numbers in the same direction (up, down, left, right, or diagonally) in the 20×20 grid?
*/
$arr = array();
$arr[0] = explode(' ', '08 02 22 97 38 15 00 40 00 75 04 05 07 78 52 12 50 77 91 08');
$arr[1] = explode(' ', '49 49 99 40 17 81 18 57 60 87 17 40 98 43 69 48 04 56 62 00');
$arr[2] = explode(' ', '81 49 31 73 55 79 14 29 93 71 40 67 53 88 30 03 49 13 36 65');
$arr[3] = explode(' ', '52 70 95 23 04 60 11 42 69 24 68 56 01 32 56 71 37 02 36 91');
$arr[4] = explode(' ', '22 31 16 71 51 67 63 89 41 92 36 54 22 40 40 28 66 33 13 80');
$arr[5] = explode(' ', '24 47 32 60 99 03 45 02 44 75 33 53 78 36 84 20 35 17 12 50');
$arr[6] = explode(' ', '32 98 81 28 64 23 67 10 26 38 40 67 59 54 70 66 18 38 64 70');
$arr[7] = explode(' ', '67 26 20 68 02 62 12 20 95 63 94 39 63 08 40 91 66 49 94 21');
$arr[8] = explode(' ', '24 55 58 05 66 73 99 26 97 17 78 78 96 83 14 88 34 89 63 72');
$arr[9] = explode(' ', '21 36 23 09 75 00 76 44 20 45 35 14 00 61 33 97 34 31 33 95');
$arr[10] = explode(' ', '78 17 53 28 22 75 31 67 15 94 03 80 04 62 16 14 09 53 56 92');
$arr[11] = explode(' ', '16 39 05 42 96 35 31 47 55 58 88 24 00 17 54 24 36 29 85 57');
$arr[12] = explode(' ', '86 56 00 48 35 71 89 07 05 44 44 37 44 60 21 58 51 54 17 58');
$arr[13] = explode(' ', '19 80 81 68 05 94 47 69 28 73 92 13 86 52 17 77 04 89 55 40');
$arr[14] = explode(' ', '04 52 08 83 97 35 99 16 07 97 57 32 16 26 26 79 33 27 98 66');
$arr[15] = explode(' ', '88 36 68 87 57 62 20 72 03 46 33 67 46 55 12 32 63 93 53 69');
$arr[16] = explode(' ', '04 42 16 73 38 25 39 11 24 94 72 18 08 46 29 32 40 62 76 36');
$arr[17] = explode(' ', '20 69 36 41 72 30 23 88 34 62 99 69 82 67 59 85 74 04 36 16');
$arr[18] = explode(' ', '20 73 35 29 78 31 90 01 74 31 49 71 48 86 81 16 23 57 05 54');
$arr[19] = explode(' ', '01 70 54 71 83 51 54 69 16 92 33 48 61 43 52 01 89 19 67 48');

$arrUpperLimit = count($arr);
$arrInnerLimit = count($arr[0]);
$greatest = 0;

for($a=0; $a<$arrUpperLimit;$a++) {
	for($b=0; $b<$arrInnerLimit; $b++) {
		$left = normalize($a, $b) * normalize($a, $b-1) * normalize($a, $b-2) * normalize($a, $b-3);
		$down = normalize($a, $b) * normalize($a+1, $b) * normalize($a+2, $b) * normalize($a+3, $b);
		$up = normalize($a, $b) * normalize($a-1, $b) * normalize($a-2, $b) * normalize($a-3, $b);
		$right = normalize($a, $b) * normalize($a, $b+1) * normalize($a, $b+2) * normalize($a, $b+3);
		$left_up_diagonal = normalize($a, $b) * normalize($a-1, $b-1) * normalize($a-2, $b-2) * normalize($a-3, $b-3);
		$right_down_diagonal = normalize($a, $b) * normalize($a+1, $b+1) * normalize($a+2, $b+2) * normalize($a+3, $b+3);
		$right_up_diagonal = normalize($a, $b) * normalize($a-1, $b+1) * normalize($a-2, $b+2) * normalize($a-3, $b+3);
		$left_down_diagonal = normalize($a, $b) * normalize($a+1, $b-1) * normalize($a+2, $b-2) * normalize($a+3, $b-3);
		
		
		$max = max($up, $down, $left, $right, $left_up_diagonal, $right_down_diagonal, $right_up_diagonal, $left_down_diagonal);
		if($max > $greatest) { $greatest = $max; }
	}
}
echo "Greatest product of four adjacent numbers in the same direction = ", $greatest;

function normalize($a,$b) {
	global $arr;
	$retval = isset($arr[$a][$b])?(int)$arr[$a][$b]:1;
	return $retval;
}
?>