用F#计算8皇后问题

代码如下：

let queen n = 
    let isValid arr x i =
        seq {0..i - 1}
        |> Seq.exists (fun j -> x = Array.item j arr || abs (i - j) = abs (x - Array.item j arr))
        |> not
    let rec search i arr n =
        match i >= n with
        | true -> 1
        | false ->
            seq {0..n - 1}
            |> Seq.map (fun x -> 
                match isValid arr x i with
                | true -> arr[i] <- x; search (i+1) arr n
                | false -> 0)
            |> Seq.sum
    search 0 (Array.create n 0) n

printfn "%d" (queen 8)

稍微修改一下，利用活动模式：

let queen n = 
    let (|Valid|_|) (arr:int[]) (i, x) =
        let isNotValid =
            seq {0 .. (i - 1)}
            |> Seq.exists (fun j -> x = arr.[j] || abs (i - j) = abs (x - arr.[j]))
        if isNotValid then None else Some Valid
    let rec search i arr n =
        if i >= n then 1
        else
            seq {0 .. (n - 1)}
            |> Seq.map (fun x -> 
                match (i, x) with
                | Valid arr -> arr[i] <- x; search (i+1) arr n
                | _ -> 0)
            |> Seq.sum
    search 0 [|for _ in 0..n -> 0|] n
printfn "%d" (queen 8)