おまけ

Project Eular Problem 15
分割統治法、再帰と動的計画法、メモ化の組み合わせのパターン

let mutable maxMemo = 256   // 257*257*sizeof(bigint) bigintは可変長
let routeMemo = Array2D.create (maxMemo + 1) (maxMemo + 1) 0I

let rec route x y =
    let a = routeMemo.[x, y]
    match a = 0I with
        | false -> a
        | true  ->
            let ans =
                match x > 0 with
                    | true ->
                        match y > 0 with
                            | true  -> route (x - 1) y + route x (y - 1)
                            | false -> route (x - 1) 0  // 1に決まってるけどｗ
                    | false ->
                        match y > 0 with
                            | true  -> route (y - 1) 0   // まあ1
                            | false -> 1I
            routeMemo.[x, y] <- ans
            ans

let solve px py =
    route px py

let run () =
    solve 20 20