How to partition a list with a given group size?

Question

I'm looking for the best way to partition a list (or seq) so that groups have a given size. for ex. let's say I want to group with size 2 (this could be any other number though):

let xs = [(a,b,c); (a,b,d); (y,z,y); (w,y,z); (n,y,z)]
let grouped = partitionBySize 2 input
// => [[(a,b,c);(a,b,d)]; [(y,z,y);(w,y,z)]; [(n,y,z)]]

The obvious way to implement partitionBySize would be by adding the position to every tuple in the input list so that it becomes

[(0,a,b,c), (1,a,b,d), (2,y,z,y), (3,w,y,z), (4,n,y,z)]

and then use GroupBy with

xs |> Seq.ofList |> Seq.GroupBy (function | (i,_,_,_) -> i - (i % n))

However this solution doesn't look very elegant to me. Is there a better way to implement this function (maybe with a built-in function)?

Answer 1

This seems to be a repeating pattern that's not captured by any function in the F# core library. When solving similar problems earlier, I defined a function Seq.groupWhen (see F# snippets) that turns a sequence into groups. A new group is started when the predicate holds.

You could solve the problem using Seq.groupWhen similarly to Seq.group (by starting a new group at even index). Unlike with Seq.group, this is efficient, because Seq.groupWhen iterates over the input sequence just once:

[3;3;2;4;1;2;8] 
|> Seq.mapi (fun i v -> i, v) // Add indices to the values (as first tuple element)
|> Seq.groupWhen (fun (i, v) -> i%2 = 0) // Start new group after every 2nd element
|> Seq.map (Seq.map snd) // Remove indices from the values

Implementing the function directly using recursion is probably easier - the solution from John does exactly what you need - but if you wanted to see a more general approach then Seq.groupWhen may be interesting.

Answer 2

List.chunkBySize (hat tip: Scott Wlaschin) is now available and does exactly what you're talking about. It appears to be new with F# 4.0.

let grouped = [1..10] |> List.chunkBySize 3
// val grouped : int list list = 
//   [[1; 2; 3]; [4; 5; 6]; [7; 8; 9]; [10]]

Seq.chunkBySize and Array.chunkBySize are also now available.

Answer 3

Here's a tail-recursive function that traverses the list once.

let chunksOf n items =
  let rec loop i acc items = 
    seq {
      match i, items, acc with
      //exit if chunk size is zero or input list is empty
      | _, [], [] | 0, _, [] -> ()
      //counter=0 so yield group and continue looping
      | 0, _, _::_ -> yield List.rev acc; yield! loop n [] items 
      //decrement counter, add head to group, and loop through tail
      | _, h::t, _ -> yield! loop (i-1) (h::acc) t
      //reached the end of input list, yield accumulated elements
      //handles items.Length % n <> 0
      | _, [], _ -> yield List.rev acc
    }
  loop n [] items

Usage

[1; 2; 3; 4; 5]
|> chunksOf 2 
|> Seq.toList //[[1; 2]; [3; 4]; [5]]

I like the elegance of Tomas' approach, but I benchmarked both our functions using an input list of 10 million elements. This one clocked in at 9 secs vs 22 for his. Of course, as he admitted, the most efficient method would probably involve arrays/loops.

Answer 4

What about a recursive approach? - only requires a single pass

let rec partitionBySize length inp dummy = 
    match inp with
    |h::t ->
        if dummy |> List.length < length then
            partitionBySize length t (h::dummy)
        else dummy::(partitionBySize length t (h::[]))
    |[] -> dummy::[]

Then invoke it with partitionBySize 2 xs []

Answer 5

let partitionBySize size xs =
  let sq = ref (seq xs)
  seq {
    while (Seq.length !sq >= size) do
      yield Seq.take size !sq
      sq := Seq.skip size !sq
    if not (Seq.isEmpty !sq) then yield !sq
  }
  // result to list, if you want
  |> Seq.map (Seq.toList)
  |> Seq.toList

UPDATE

let partitionBySize size (sq:seq<_>) =
  seq {
    let e = sq.GetEnumerator()
    let empty = ref true;
    while !empty do
      yield seq { for i = 1 to size do
                    empty := e.MoveNext()
                    if !empty then yield e.Current
            }
  }

array slice version:

let partitionBySize size xs =
  let xa = Array.ofList xs
  let len = xa.Length
  [
    for i in 0..size..(len-1) do
      yield ( if i + size >= len then xa.[i..] else xa.[i..(i+size-1)] ) |> Array.toList 
  ]

Answer 6

Well, I was late for the party. The code below is a tail-recursive version using high-order functions on List:

let partitionBySize size xs =
    let i = size - (List.length xs - 1) % size
    let xss, _, _ =
        List.foldBack( fun x (acc, ls, j) -> 
                                          if j = size then ((x::ls)::acc, [], 1) 
                                          else (acc, x::ls, j+1)
                       ) xs ([], [], i)
    xss

I did the same benchmark as Daniel did. This function is efficient while it is 2x faster than his approach on my machine. I also compared it with an array/loop version, they are comparable in terms of performance.

Moreover, unlike John's answer, this version preserves order of elements in inner lists.