Problem 11: Largest Product in a Grid

Problem

• Link to the problem

Solution

See it on GitHub.

//* Problem 11: Largest Product in a Grid
//* 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?

//! time complexity: O(n^2)
//! where n is the size of the grid
use euler::prelude::*;

fn product<F>(selector: F) -> usize
where
    F: FnMut(usize) -> usize,
{
    (0..ADJACENT).map(selector).product()
}

fn solve() -> Solution {
    let mut max = 0usize;

    for row in 0..SIZE {
        for col in 0..SIZE {
            // right
            if col + ADJACENT <= SIZE {
                max = max.max(product(|i| GRID[row][col + i]));
            }

            // down
            if row + ADJACENT <= SIZE {
                max = max.max(product(|i| GRID[row + i][col]));
            }

            // diagonal down-right
            if row + ADJACENT <= SIZE && col + ADJACENT <= SIZE {
                max = max.max(product(|i| GRID[row + i][col + i]))
            }

            // diagonal down-left
            if row + ADJACENT <= SIZE && col >= ADJACENT - 1 {
                max = max.max(product(|i| GRID[row + i][col - i]))
            }
        }
    }

    solution!(max)
}

const SIZE: usize = 20;
const ADJACENT: usize = 4;

#[rustfmt::skip]
const GRID: [[usize; SIZE]; SIZE] = [
    [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],
];

problem!(
    11,
    solve,
    "9ded5bc849d33e477aa9c944138d34f0aacc485a372e84464e8a572712a5b7da"
);