如何在出现函数最大值的列表中查找值 [英] How to find the value in a list at which a maximum value of a function occurs

问题描述

我不仅要查找应用于列表的函数的最大值(我将仅使用List.maxBy)，还要找到出现在列表中的值.感觉这是一个相当普通的操作，并且考虑到F#库的丰富程度，总的来说我发现它实际上已经可用并不会感到惊讶，但是如果有的话，我似乎找不到它！

I want to find not just the maximum value of a function applied to a list (for which I would just use List.maxBy) but also the value in the list this occurred at. This feels like a fairly common operation and given the richness of the F# libraries in general I wouldn't be at all surprised to discover it was actually already available but I cannot seem to find it if it is!

为了举例说明，我希望能够映射列表domain和函数f

To illustrate with an example, I want to be able to map a list domain and a function f

let domain = [0 .. 5]
let f x = -x * (x - 2)

到(1, 1)(因为应用于列表其他元素的函数小于1).

to (1, 1) (since the function applied to an other element of the list is less than 1).

我首先尝试过:

let findMaximum domain f =
    let candidates = [ for x in domain do
                        yield x, f x ]
    let rec findMaximumHelper domain f currentMax =
        match domain with
        | [] -> currentMax
        | head::tail -> 
            let cand = f head
            match currentMax with
            | None ->
                let newMax = Some(head, cand)
                findMaximumHelper tail f newMax
            | Some(maxAt, possMax) ->
                let newMax =
                    if cand > possMax then Some(head, cand)
                    else Some(maxAt, possMax)
                findMaximumHelper tail f newMax
    findMaximumHelper domain f None

let answer = findMaximum domain f

这时我意识到这与 fold 操作非常接近，并将其放在一起

at which point I realised this is very close to a fold operation, and put together

let findMaximum2 domain f =
    let findMaximumHelper f acc x =
        let cand = f x
        match acc with
        | None -> Some(x, cand)
        | Some(maxAt, possMax) ->
            if cand > possMax then Some(x, cand)
            else Some(maxAt, possMax)
    List.fold (findMaximumHelper f) None domain

let answer2 = findMaximum2 domain f

相反.

我的问题是，这些惯用的F#方法是否可以解决此问题，或者确实有更好的方法来解决此问题?

My question is, are these idiomatic F# ways of solving this problem, or indeed, is there a better way of solving this?

推荐答案

实际上，F#库提供了所有必要的高阶函数来简洁地表达这一点:

Indeed, the F# library provides all the necessary higher order functions to express this succinctly:

domain
|> Seq.map (fun x -> x, f x)
|> Seq.maxBy snd

注意:已更新为使用Seq.map和Seq.maxBy而不是List.map和List.maxBy来解决@ildjarn关于创建不必要的中间列表的担忧.

Note: updated to use Seq.map and Seq.maxBy instead of List.map and List.maxBy to address @ildjarn's concern about creating an unnecessary intermediate list.

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