18 October, 2008

[Project Euler] Problem 11

Problem 11

表をArray[Array[Int]]に変換、4つの並びを(x,y)のTuple2のListとして表現し、全組み合わせ ( List[List[Tuple2[Int,Int]]]) から積が最大になるものを選択する。

object P011 {
val input:Array[String] = Array(
"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")
val table:Array[Array[Int]] = input.map{x => x.split(" ").map{_.toInt}}
def v(x:Int, y:Int):Int = table(y)(x)
val xscan:List[List[Tuple2[Int,Int]]] =
for(y <- List.range(0,20); x0 <- List.range(0,20-4)
) yield for(x <- List.range(x0, x0+4)) yield (x,y)
val yscan:List[List[Tuple2[Int,Int]]] =
for(x <- List.range(0,20); y0 <- List.range(0,20-4)
) yield for(y <- List.range(y0, y0+4)) yield (x,y)
val diagscan1 =
for(x0 <- List.range(0,20-4); y0 <- List.range(0,20-4)
) yield for(i <- List.range(0,4)) yield (x0+i, y0+i)
val diagscan2 =
for(x0 <- List.range(0,20-4); y0 <- List.range(0,20-4)
) yield for(i <- List.range(0,4)) yield (x0+3-i, y0+i)
def f(ps:List[Tuple2[Int,Int]]):Long = ps.foldLeft(1L){(a,t) => a * v(t._1,t._2)}
val result = (xscan ::: yscan ::: diagscan1 ::: diagscan2).sort{(a,b) => f(a)>f(b)}.head
def main(args:Array[String]) {
println(result)
println(result.map{t => v(t._1,t._2)})
println(f(result))
}
}

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