F# replace ref variable with something fun

Question

I have the following F# function which makes use of a ref variable to seed and keep track of a running total, something tells me this isn't in the spirit of fp or even particular clear on its own. I'd like some direction on the clearest (possible fp, but if an imperative approach is clearer I'd be open to that) way to express this in F#. Note that selectItem implements a random weighted selection algorithm.

type WeightedItem(id: int, weight: int) =
    member self.id = id
    member self.weight = weight

let selectItem (items: WeightedItem list) (rand:System.Random) =
    let totalWeight = List.sumBy (fun (item: WeightedItem) -> item.weight) items
    let selection = rand.Next(totalWeight) + 1
    let runningWeight = ref 0
    List.find 
        (fun (item: WeightedItem) ->
            runningWeight := !runningWeight + item.weight
            !runningWeight >= selection)
        items

let items = [new WeightedItem(1,100); new WeightedItem(2,50); new WeightedItem(3,25)]
let selection = selectItem items (new System.Random())

Answer 1

Hm, here's one way to do it with a fold, but it feels inelegant and always traverses the whole list...

type WeightedItem(id: int, weight: int) = 
    member self.id = id 
    member self.weight = weight 

let selectItem (items: WeightedItem list) (rand:System.Random) = 
    let totalWeight = List.sumBy (fun (item: WeightedItem) -> item.weight) items 
    let selection = rand.Next(totalWeight) + 1 
    List.fold 
        (fun (runningWeight,found) (item: WeightedItem) -> 
            if not found then
                let newRunningWeight = runningWeight + item.weight 
                newRunningWeight, newRunningWeight >= selection
            else
                (runningWeight,found)) 
        (0,false)
        items 
    |> fst

let items = [new WeightedItem(1,100)
             new WeightedItem(2,50)
             new WeightedItem(3,25)] 
let selection = selectItem items (new System.Random()) 

Answer 2

Hm, here's one with Seq.scan, but it also feels very ugly...

type WeightedItem(id: int, weight: int) = 
    member self.id = id 
    member self.weight = weight 

let selectItem (items: WeightedItem list) (rand:System.Random) = 
    let totalWeight = List.sumBy (fun (item: WeightedItem) -> item.weight) items 
    let selection = rand.Next(totalWeight) + 1 
    Seq.scan 
        (fun (runningWeight,found,itemO) (item: WeightedItem) -> 
            if not found then
                let newRunningWeight = runningWeight + item.weight 
                newRunningWeight, newRunningWeight >= selection, Some(item)
            else
                (runningWeight,found,itemO)) 
        (0,false,None)
        items 
    |> Seq.find (fun (rw,f,i) -> f)
    |> (fun (rw,f,i) -> i.Value)

let items = [new WeightedItem(1,100)
             new WeightedItem(2,50)
             new WeightedItem(3,25)] 
let selection = selectItem items (new System.Random()) 

Answer 3

Hm, here's some mutables and a loop; still traverses the whole list though...

type WeightedItem(id: int, weight: int) = 
    member self.id = id 
    member self.weight = weight 

let selectItem (items: WeightedItem list) (rand:System.Random) = 
    let totalWeight = List.sumBy (fun (item: WeightedItem) -> item.weight) items 
    let selection = rand.Next(totalWeight) + 1 
    let mutable runningWeight = 0
    let mutable found = None
    for item in items do
        match found with
        | None ->
            runningWeight <- runningWeight + item.weight 
            if runningWeight >= selection then
                found <- Some(item)
        | _ -> ()
    found.Value

let items = [new WeightedItem(1,100)
             new WeightedItem(2,50)
             new WeightedItem(3,25)] 
let selection = selectItem items (new System.Random()) 

This is my favorite of the three. I look forward to the day that F# adds break. Of course you can call GetEnumerator and take full control, but that is ugly too.

Answer 4

Here is a version of the search algorithm using a recursive function. My F# is very rusty and I don't know what to return when we can't find anything:

let rec find list item total =
    match list with
    | h::t -> if h > total then h else find t item total+h
    | [] -> 0 //<-- return some sort of default to say can't find the item

EDIT

Full code:

type WeightedItem(id: int, weight: int) = 
    member self.id = id 
    member self.weight = weight 

let selectItem (items: WeightedItem list) (rand:System.Random) = 
    let totalWeight = List.sumBy (fun (item: WeightedItem) -> item.weight) items 
    let selection = rand.Next(totalWeight) + 1 
    let rec find runningWeight ((h:WeightedItem)::t) =
        let newRunningWeight = runningWeight + h.weight
        if newRunningWeight >= selection then
            h
        else
            find newRunningWeight t
    find 0 items

let items = [new WeightedItem(1,100)
             new WeightedItem(2,50)
             new WeightedItem(3,25)] 
let selection = selectItem items (new System.Random()) 

Answer 5

Igor's answer is probably the best one for items stored in a list in terms of efficiency, but since Brian's scan approach is representative of a recurrent sequence manipulation pattern, I suggest a slightly more compact variation :

let selectItem (items: WeightedItem list) (rand:System.Random) =
    let totalWeight = List.sumBy (fun (item: WeightedItem) -> item.weight) items
    let selection = rand.Next(totalWeight) + 1
    items
    |> Seq.scan (fun acc (item : WeightedItem) -> acc + item.weight) 0
    |> Seq.skip 1 |> Seq.zip items
    |> Seq.find (fun (i, rw) -> rw >= selection) |> fst

Answer 6

Use Seq.unfold to build an on-demand sequence that accumulates runningWeight and then search it for the first element that had a sufficiently large runningWeight using Seq.pick:

let gen = function
  | _, [] -> None
  | runningWeight, item::items ->
      let runningWeight = runningWeight + item.weight
      Some((if runningWeight >= selection then Some item else None), (runningWeight, items))
Seq.unfold gen (0, xs) |> Seq.pick id