Project Euler Problem 11

gistfile1.scala

/**
 * Project Euler Problem 11
 */
object P11 {

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

	def value(x:Int)(y:Int) = if(x < 0 || x > 19) 0 else if (y < 0 || y > 19) 0 else list(x + y * 20)

	def rightUp(x:Int)(y:Int)(n:Int) = (1 to n - 1).foldLeft(value(x)(y))((acc, n) => acc * value(x + n)(y - n))
	def right(x:Int)(y:Int)(n:Int) = (1 to n - 1).foldLeft(value(x)(y))((acc, n) => acc * value(x + n)(y))
	def rightDown(x:Int)(y:Int)(n:Int) = (1 to n - 1).foldLeft(value(x)(y))((acc, n) => acc * value(x + n)(y + n))
	def down(x:Int)(y:Int)(n:Int) = (1 to n - 1).foldLeft(value(x)(y))((acc, n) => acc * value(x)(y + n))

	def answer():Int = {
		val pattern = for(x <- 0 to 19; y <- 0 to 19) yield (x, y)
		val vals = pattern.flatMap(n =>
			List(rightUp(n._1)(n._2)(4), right(n._1)(n._2)(4), rightDown(n._1)(n._2)(4), down(n._1)(n._2)(4))
		)
		vals.max
	}
}