Problem011.js

/*
 *
 * 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?
 */

export function largestProductInAGrid(arr) {
  let max = 0
  const k = 4

  const dx = [1, 0, 1, -1]
  const dy = [0, 1, 1, 1]

  for (let y = 0; y < arr.length; y++) {
    for (let x = 0; x < arr[y].length; x++) {
      for (let d = 0; d < 4; d++) {
        let p = 1
        for (let i = 0; i < k; i++) {
          p *= get(arr, y + i * dy[d], x + i * dx[d])
        }
        max = Math.max(p, max)
      }
    }
  }
  return max
}

function get(arr, y, x) {
  if (y >= 0 && y < arr.length && x >= 0 && x < arr[y].length) {
    return arr[y][x]
  }

  return 0
}