Project Euler Problem 11

problem11.scala

  /**
   * http://projecteuler.net/problem=11
   * http://odz.sakura.ne.jp/projecteuler/index.php?cmd=read&page=Problem%2011
   */

  val xs: List[List[Int]] = List(
           List(8, 2, 22, 97, 38, 15, 0, 40, 0, 75, 4, 5, 7, 78, 52, 12, 50, 77, 91, 8),
           List(49, 49, 99, 40, 17, 81, 18, 57, 60, 87, 17, 40, 98, 43, 69, 48, 4, 56, 62, 0),
           List(81, 49, 31, 73, 55, 79, 14, 29, 93, 71, 40, 67, 53, 88, 30, 3, 49, 13, 36, 65),
           List(52, 70, 95, 23, 4, 60, 11, 42, 69, 24, 68, 56, 1, 32, 56, 71, 37, 2, 36, 91),
           List(22, 31, 16, 71, 51, 67, 63, 89, 41, 92, 36, 54, 22, 40, 40, 28, 66, 33, 13, 80),
           List(24, 47, 32, 60, 99, 3, 45, 2, 44, 75, 33, 53, 78, 36, 84, 20, 35, 17, 12, 50),
           List(32, 98, 81, 28, 64, 23, 67, 10, 26, 38, 40, 67, 59, 54, 70, 66, 18, 38, 64, 70),
           List(67, 26, 20, 68, 2, 62, 12, 20, 95, 63, 94, 39, 63, 8, 40, 91, 66, 49, 94, 21),
           List(24, 55, 58, 5, 66, 73, 99, 26, 97, 17, 78, 78, 96, 83, 14, 88, 34, 89, 63, 72),
           List(21, 36, 23, 9, 75, 0, 76, 44, 20, 45, 35, 14, 0, 61, 33, 97, 34, 31, 33, 95),
           List(78, 17, 53, 28, 22, 75, 31, 67, 15, 94, 3, 80, 04, 62, 16, 14, 9, 53, 56, 92),
           List(16, 39, 05, 42, 96, 35, 31, 47, 55, 58, 88, 24, 0, 17, 54, 24, 36, 29, 85, 57),
           List(86, 56, 0, 48, 35, 71, 89, 7, 5, 44, 44, 37, 44, 60, 21, 58, 51, 54, 17, 58),
           List(19, 80, 81, 68, 5, 94, 47, 69, 28, 73, 92, 13, 86, 52, 17, 77, 4, 89, 55, 40),
           List(04, 52, 8, 83, 97, 35, 99, 16, 7, 97, 57, 32, 16, 26, 26, 79, 33, 27, 98, 66),
           List(88, 36, 68, 87, 57, 62, 20, 72, 3, 46, 33, 67, 46, 55, 12, 32, 63, 93, 53, 69),
           List(04, 42, 16, 73, 38, 25, 39, 11, 24, 94, 72, 18, 8, 46, 29, 32, 40, 62, 76, 36),
           List(20, 69, 36, 41, 72, 30, 23, 88, 34, 62, 99, 69, 82, 67, 59, 85, 74, 4, 36, 16),
           List(20, 73, 35, 29, 78, 31, 90, 1, 74, 31, 49, 71, 48, 86, 81, 16, 23, 57, 5, 54),
           List(1, 70, 54, 71, 83, 51, 54, 69, 16, 92, 33, 48, 61, 43, 52, 1, 89, 19, 67, 48)
          )

  val maxRow = 19
  val maxCol = 19

  lazy val horizontals = {
    def calc(xs: List[Int], ys: List[Int]): List[Int] = {
      xs match {
        case a :: b :: c :: d :: tail => calc(xs.tail, a * b * c * d :: ys)
        case _ => ys
      }
    }
    xs.map(calc(_, Nil))
  }.flatten

  lazy val verticals = {
    def calc(row: Int, col: Int, ys: List[Int]): List[Int] = {
      (row, col) match {
        case (r, c) if (r + 3 > maxRow && c == maxCol) => ys
        case (r, c) if (r + 3 > maxRow) => calc(0, c + 1, ys)
        case (r, c) => calc(r + 1, c, xs(r)(c) * xs(r + 1)(c) * xs(r + 2)(c) * xs(r + 3)(c) :: ys)
      }
    }
    calc(0, 0, Nil)
  }

  lazy val rightDiagonally = {
    def calc(row: Int, col: Int, ys: List[Int]): List[Int] = {
      (row, col) match {
        case (r, c) if (r + 3 > maxRow && c + 3 == maxCol) => ys
        case (r, c) if (r + 3 > maxRow) => calc(0, c + 1, ys)
        case (r, c) => calc(r + 1, c, xs(r)(c) * xs(r + 1)(c + 1) * xs(r + 2)(c + 2) * xs(r + 3)(c + 3) :: ys)
      }
    }
    calc(0, 0, Nil)
  }

  lazy val leftDiagonally = {
    def calc(row: Int, col: Int, ys: List[Int]): List[Int] = {
      (row, col) match {
        case (r, c) if (r + 3 > maxRow && c - 3 == 0) => ys
        case (r, c) if (r + 3 > maxRow) => calc(0, c - 1, ys)
        case (r, c) => calc(r + 1, c, xs(r)(c) * xs(r + 1)(c - 1) * xs(r + 2)(c - 2) * xs(r + 3)(c - 3) :: ys)
      }
    }
    calc(0, maxCol, Nil)
  }

  val ret = horizontals ++ verticals ++ rightDiagonally ++ leftDiagonally max

  println(ret)