Project Euler: Problem 11

Euler0011.scala

package euler.zerosum

object Euler0011 {

  def main(args: Array[String]) {
    val horizontal = take4ElemsEvery(1, given, Nil)
    val vertical = take4ElemsEvery(21, given, Nil)
    val diagonal = take4ElemsEvery(20, given, Nil) ::: take4ElemsEvery(22, given, Nil)

    val products = (horizontal ++ vertical ++ diagonal).map(_.product)

    println(products.max)
  }

  /**
   * @param n
   * @param src
   * @param dist
   * @return List[x]: { x: List(src(i), src(i+n), src(i+2n), src(i+3n)), i=[0, src.length) }
   */
  private def take4ElemsEvery(n: Int, src: List[Int], dist: List[List[Int]]): List[List[Int]] = {
    if(src.length == 0) {
      dist
    } else {
      val filtered = filterByIndex(src, _%n==0)
      take4ElemsEvery(n, src.tail, filtered.take(4) :: dist)
    }
  }

  /**
   * @param src
   * @param f
   * @return List[x]: { x = src(i), f(i) => true, i=[0, src.length) }
   */
  private def filterByIndex(src: List[Int], f: Int => Boolean): List[Int] = {
    src.zipWithIndex.filter(x => f(x._2)).unzip._1
  }

  /*
   * gridをListで表す。
   * Euler0011#take4ElemsEvery では、与えられたgridの右端と左端を跨いで数の組を作ることを許してしまう。
   * よってそのような数の組の積が最大値を取らないよう、右端に1列、下端に1行、0の行と列を入れた。
   */
  private val given = List(
     8,  2, 22, 97, 38, 15,  0, 40,  0, 75,  4,  5,  7, 78, 52, 12, 50, 77, 91,  8,   0,
    49, 49, 99, 40, 17, 81, 18, 57, 60, 87, 17, 40, 98, 43, 69, 48,  4, 56, 62,  0,   0,
    81, 49, 31, 73, 55, 79, 14, 29, 93, 71, 40, 67, 53, 88, 30,  3, 49, 13, 36, 65,   0,
    52, 70, 95, 23,  4, 60, 11, 42, 69, 24, 68, 56,  1, 32, 56, 71, 37,  2, 36, 91,   0,
    22, 31, 16, 71, 51, 67, 63, 89, 41, 92, 36, 54, 22, 40, 40, 28, 66, 33, 13, 80,   0,
    24, 47, 32, 60, 99,  3, 45,  2, 44, 75, 33, 53, 78, 36, 84, 20, 35, 17, 12, 50,   0,
    32, 98, 81, 28, 64, 23, 67, 10, 26, 38, 40, 67, 59, 54, 70, 66, 18, 38, 64, 70,   0,
    67, 26, 20, 68,  2, 62, 12, 20, 95, 63, 94, 39, 63,  8, 40, 91, 66, 49, 94, 21,   0,
    24, 55, 58,  5, 66, 73, 99, 26, 97, 17, 78, 78, 96, 83, 14, 88, 34, 89, 63, 72,   0,
    21, 36, 23,  9, 75,  0, 76, 44, 20, 45, 35, 14,  0, 61, 33, 97, 34, 31, 33, 95,   0,
    78, 17, 53, 28, 22, 75, 31, 67, 15, 94,  3, 80,  4, 62, 16, 14,  9, 53, 56, 92,   0,
    16, 39,  5, 42, 96, 35, 31, 47, 55, 58, 88, 24,  0, 17, 54, 24, 36, 29, 85, 57,   0,
    86, 56,  0, 48, 35, 71, 89,  7,  5, 44, 44, 37, 44, 60, 21, 58, 51, 54, 17, 58,   0,
    19, 80, 81, 68,  5, 94, 47, 69, 28, 73, 92, 13, 86, 52, 17, 77,  4, 89, 55, 40,   0,
     4, 52,  8, 83, 97, 35, 99, 16,  7, 97, 57, 32, 16, 26, 26, 79, 33, 27, 98, 66,   0,
    88, 36, 68, 87, 57, 62, 20, 72,  3, 46, 33, 67, 46, 55, 12, 32, 63, 93, 53, 69,   0,
     4, 42, 16, 73, 38, 25, 39, 11, 24, 94, 72, 18,  8, 46, 29, 32, 40, 62, 76, 36,   0,
    20, 69, 36, 41, 72, 30, 23, 88, 34, 62, 99, 69, 82, 67, 59, 85, 74,  4, 36, 16,   0,
    20, 73, 35, 29, 78, 31, 90,  1, 74, 31, 49, 71, 48, 86, 81, 16, 23, 57,  5, 54,   0,
     1, 70, 54, 71, 83, 51, 54, 69, 16, 92, 33, 48, 61, 43, 52,  1, 89, 19, 67, 48,   0,

     0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,   0)
}