Problem11.php

<?php


/*
 * This function solves the problem 11 of the Project Euler.
 *
 * Problem description:
 * 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?

    Solution: 70600674
 */


function horizontalProduct($grid, $row, $col)
{
    $product = 1;
    for ($i = 0; $i < 4; $i++) {
        $product *= $grid[$row][$col + $i];
    }
    return $product;
}

function verticalProduct($grid, $row, $col)
{
    $product = 1;
    for ($i = 0; $i < 4; $i++) {
        $product *= $grid[$row + $i][$col];
    }
    return $product;
}

function diagonalRightProduct($grid, $row, $col)
{
    $product = 1;
    for ($i = 0; $i < 4; $i++) {
        $product *= $grid[$row + $i][$col + $i];
    }
    return $product;
}

function diagonalLeftProduct($grid, $row, $col)
{
    $product = 1;
    for ($i = 0; $i < 4; $i++) {
        $product *= $grid[$row + $i][$col - $i];
    }
    return $product;
}

function problem11()
{
    $grid = "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";

    //Transform the grid string to a matrix data type (nested arrays)
    $grid = explode(' ', $grid);
    $grid_matrix = [];
    $row = [];
    $i = 0;
    $matrix_size = 20;

    //Convert string $grid to a matrix
    foreach ($grid as $g) {
        $i++;
        $row[] = (int)trim($g);

        if ($i == $matrix_size) {
            $grid_matrix[] = $row;
            $row = [];
            $i = 0;
        }
    }
    $maxProduct = 0;

    for ($row = 0; $row < $matrix_size; $row++) {
        for ($col = 0; $col < $matrix_size; $col++) {
            // horizontal
            if ($col < $matrix_size - 3) {
                $product = horizontalProduct($grid_matrix, $row, $col);
                if ($product > $maxProduct) {
                    $maxProduct = $product;
                }
            }
            // vertical
            if ($row < $matrix_size - 3) {
                $product = verticalProduct($grid_matrix, $row, $col);
                if ($product > $maxProduct) {
                    $maxProduct = $product;
                }
            }
            // diagonal right
            if ($col < $matrix_size - 3 && $row < $matrix_size - 3) {
                $product = diagonalRightProduct($grid_matrix, $row, $col);
                if ($product > $maxProduct) {
                    $maxProduct = $product;
                }
            }
            // diagonal left
            if ($col > 2 && $row < $matrix_size - 3) {
                $product = diagonalLeftProduct($grid_matrix, $row, $col);
                if ($product > $maxProduct) {
                    $maxProduct = $product;
                }
            }
        }
    }

    return $maxProduct;
}