# Find the Largest Product in a Grid with Rust

Project Euler problem number 11 - Largest product in a grid - is stated as follows. In a defined 20x20 grid what is the greatest product of four adjacent numbers in the same direction (up, down, left, right, or diagonally)?

``````fn main() {
let lens_size: usize = 4;
let string: &str = "\
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";

// Convert the multiline string to a two dimensional array.
//  "01 02
//  "03 04" --> [[1, 2], [3, 4]]
let matrix = get_matrix_from_string(string);

// Get the greatest product of N (lens_size) adjacent numbers
// in the same direction (up, down, left, right, or diagonally) in the matrix.
let result = (0..matrix.len()-lens_size)
.map(|x| (0..matrix.len()-lens_size).map(|y| get_greatest_product_in_lens(&matrix, x,y, lens_size)).max())
.max()
.unwrap();

println!("{:?}", result);
}

fn get_greatest_product_in_lens(matrix: &[Vec<u32>], x:usize, y:usize, lens_size:usize) -> u32 {
// Get a sub set of the matrix based on lens size.
// Matrix   +   Lens    =   Result
// [            [           [
//   [1,2,3]     [0,0]        [1,2]
//   [4,5,6]     [1,1]        [3,4]
//   [7,8,9]    ]           ]
// ]
let submatrix = get_matrix_subset(&matrix, [[x, y], [x+lens_size-1, y+lens_size-1]]);

let array: [u32; 4] = [
get_largest_row_product(&submatrix),
get_largest_column_product(&submatrix),
get_lr_diagonal_product(&submatrix),
get_rl_diagonal_product(&submatrix)
];

*array.iter().max().unwrap_or(&0)
}

// Split a string into an int array.
// "01 02" --> [1,2]
fn string_to_intarray(string: &str) -> Vec<u32> {
// Split the string into a string array.
// "01 02" --> ["01", "02"]
string.split(' ')
// ["01", "02"] --> ["1", "2"]
.map(|s: &str| s.trim_left_matches('0'))
// Convert the strings into integers.
// ["1", "2"] --> [1,2]
.map(|s: &str| s.parse().unwrap_or(0))
// Transform the iterator into a collection.
.collect()
}

fn get_matrix_subset(matrix: &[Vec<u32>], lens: [[usize; 2]; 2]) -> Vec<Vec<u32>> {
// Remove rows.
matrix[lens[0][0]..lens[1][0] + 1]
.iter()
// Remove columns.
.map(|row| row[lens[0][1]..lens[1][1] + 1].to_owned())
// Transform the iterator into a collection.
.collect()
}

fn get_largest_row_product(matrix: &[Vec<u32>]) -> u32 {
(0..matrix.len())
.map(|x| (0..matrix[x].len()).fold(1, |sum, n| sum * matrix[x][n]))
.max()
.unwrap_or(0)
}

fn get_largest_column_product(matrix: &[Vec<u32>]) -> u32 {
(0..matrix.len())
.map(|x| (0..matrix[x].len()).fold(1, |sum, n| sum * matrix[n][x]))
.max()
.unwrap_or(0)
}

fn get_lr_diagonal_product(matrix: &[Vec<u32>]) -> u32 {
(0..matrix.len()).fold(1, |sum, n| sum * matrix[n][n])
}

fn get_rl_diagonal_product(matrix: &[Vec<u32>]) -> u32 {
(0..matrix.len()).fold(1, |sum, n| sum * matrix[n][matrix.len() - n - 1])
}

fn get_matrix_from_string(s: &str) -> Vec<Vec<u32>> {
// Convert the multiline string to a two dimensional array.
//  "01 02
//  "03 04" --> [[1, 2], [3, 4]]
s.split('\n')
// Creates rows by splitting the string on newline.
// ["01 02", "        03 04"]
.map(|x: &str| x.trim())