recursionf#treenested-sets

F# How create tree from nested sets?


I have nested sets data from my db and need transform this to tree data structure:

type Item = {
    Id: int
    Left: int
    Right: int
    Level: int
}
type Items = Item list
type Tree = {Parent: Item; Childrens: Tree list}

My my failed attempt:

  1. Get childrens items for root item and create root of tree
  2. Search childrens for each child from step 1, build new tree
  3. Repeat step 2 until transform all items (nested sets) to tree
let predicate p c = (c.Level = p.Level + 1) && (c.Left > p.Left) && (c.Right < p.Right)
let initLeaf item = {Parent = item; Childrens = []}
let initLeafs = List.map (fun x -> initLeaf x)
let getChildrens parent = List.filter (fun x -> predicate parent x)

let build (initList: Item list) =
    let sortedList = initList |> List.sortBy (fun x -> x.Left)
    let getChildrens2 parent = 
        let items = sortedList |> getChildrens parent
        if not (List.isEmpty items) then items |> initLeafs else []
    let root = initLeaf sortedList.Head
    
    let rec loop (tree: Tree) =
        let childrens =
            match tree.Childrens with
                | [] -> 
                    getChildrens2 tree.Parent
                | x ->
                    x |> List.collect (fun y -> loop y)
        loop {tree with Childrens = childrens}
    loop root
let res = build items

Solution

  • Here's my attempt at this. The example is taken from Wikipedia. I changed the type of Item.Id to string for better output readability, but the method is still applicable.

    [<StructuredFormatDisplay("'{Id}'(L:{Left} R:{Right})")>]
    type Item = {Id: string; Left: int; Right: int; Level: int}
    type Tree = {Node: Item; Children: Tree list}
    
    let lst : Item list = [
      { Id="Clothing"; Left=1; Right=22; Level=0 }
      { Id="Men's"; Left=2; Right=9; Level=1 }
      { Id="Women's"; Left=10; Right=21; Level=1 }
      { Id="Suits"; Left=3; Right=8; Level=2 }
      { Id="Slacks"; Left=4; Right=5; Level=3 }
      { Id="Jackets"; Left=6; Right=7; Level=3 }
      { Id="Dresses"; Left=11; Right=16; Level=2 }
      { Id="Skirts"; Left=17; Right=18; Level=2 }
      { Id="Blouses"; Left=19; Right=20; Level=2 }
      { Id="Evening Gowns"; Left=12; Right=13; Level=3 }
      { Id="Sun Dresses"; Left=14; Right=15; Level=3 }
    ]
    
    let sorted = lst |> List.sortBy (fun x -> x.Left)
    let rootItem :: unassinged = sorted
    
    let isParentOf p c = (c.Level = p.Level + 1) && (c.Left > p.Left) && (c.Right < p.Right)
    
    let rec buildTree (xs : Item list) (item : Item) : Tree * Item list =
      let children, rest = List.partition (isParentOf item) xs
      let subtrees, rest = List.mapFold buildTree rest children
      let tree = {Node = item; Children = subtrees}
      tree, rest
    
    let tree, _ = buildTree unassinged rootItem
    

    Output (truncated):

    val tree : Tree =
      { Node = 'Clothing'(L:1 R:22)
        Children =
                  [{ Node = 'Men's'(L:2 R:9)
                     Children =
                               [{ Node = 'Suits'(L:3 R:8)
                                  Children =
                                            [{ Node = 'Jackets'(L:6 R:7)
                                               Children = [] };
                                             { Node = 'Slacks'(L:4 R:5)
                                               Children = [] }] }] };
                   { Node = 'Women's'(L:10 R:21)
    ...
    

    Edit: this is the shortest tail-recursive version I could come up with.

    let buildTree1 (root : Item) : Tree =
      let rec go (pending : Item list) (m: Map<Item, Tree>) : Map<Item, Tree> =
        match pending with
        | [] -> m
        | x :: xs ->
          let children = List.filter (isParentOf x) unassinged
          if List.isEmpty children then
            let mUpd = Map.add x {Node=x; Children = []} m
            go xs mUpd
          else
            let pendingChildren = List.filter (fun y -> not <| Map.containsKey y m) children
            match pendingChildren with
            | [] ->
              let subtrees = List.map (fun x -> m.[x]) children
              let mUpd = Map.add x {Node=x; Children = subtrees} m
              go xs mUpd
            | ps -> go (ps @ (x :: xs)) m
      go [root] Map.empty |> Map.find root
    
    let tree = buildTree1 rootItem
    

    Maybe it could be improved using the continuation-passing style.