Problem 11 - regerege メモ帳

Problem 11
module Problem_0011

(*
【問題】
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
上の 20 × 20 の数字のなか、赤くマークされた数字の積は 26 × 63 × 78 × 14 = 1788696 となる。
上下左右斜めのいずれかの方向で連続する4つの数字の積のうち最大のものを求めよ。
A. ((17, 19), [89; 94; 97; 87], 70600674)
455 ms
*)

let text = @"
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
"
let north (x,y) = (x,y-1) // ↑
let northeast (x,y) = (x+1,y-1) // &#8599;
let east (x,y) = (x+1,y) // →
let southeast (x,y) = (x+1,y+1) // &#8600;
let south (x,y) = (x,y+1) // ↓
let southwest (x,y) = (x+1,y+1) // &#8601;
let west (x,y) = (x-1,y) // ←
let northwest (x,y) = (x-1,y-1)// &#8598;
let weys = seq {
    yield north
    yield northeast
    yield east
    yield southeast
    yield south
    yield southwest
    yield west
    yield northwest
}

let find () =
    // 探索対象の文字列を1次元配列シーケンスとする。
    let t = text.Replace("\r\n", " ").Trim()
    let cells = seq { for p in 0..3..t.Length -> int t.[p..p+1] }
    // 各方位の計算
    let rec findCells inc (x,y) (l : int list) =
        match (inc (x,y)) with
        | (0,_) | (_,0) | (21,_) | (_,21) -> ((x,y), [], -1)
        | (x,y) ->
            match l with
            | [_;_;_;_;] ->
                let num = List.reduce((*)) l
                ((x,y), l, num)
            | _ ->
                let cell = Seq.nth (x*y-1) cells
                findCells inc (x,y) (l@[cell])
    // 探索
    seq {
        for x in 1..20 do
            for y in 1..20 do
                for f in weys ->
                    findCells f (x,y) []
    }
    |> Seq.maxBy (fun (state, f, num) -> num)

let run() =
    find()