How can I Implement my own List.partition using tail
I'm trying to write my own List.partition function for F# practice. Here's my first (naive) attempt:
let rec mypartition_naive func list =
match list with
| [] -> ([],[])
| head::tail ->
let (h1,h2) = mypartition_naive func tail
if func head
then (head::h1,h2)
else (h1,head::h2)
This works, but it's not tail-recursive. I put together a second attempt that uses an accumulator to become tail-recursive:
let mypartition_accumulator func list =
let rec helper acc listinner =
match listinner with
| head::tail ->
let a,b = acc
let newacc = if func head then (head::a,b) else (a,head::b)
helper newacc tail
| _ -> acc
helper ([],[]) list
Strictly speaking, this works: it partitions the list. The problem is that this reverses the order of the lists. I get this:
let mylist = [1;2;3;4;5;6;7;8]
let partitioned = mypartition_accumulator (fun x -> x % 2 = 0) mynums
//partitioned is now ([8; 6; 4; 2], [7; 5; 3; 1])
//I want partitioned to be ([2; 4; 6; 8], [1; 3; 5; 7])
I think that I can use continuation passing to write a tail-recursive partition function that doesn't reverse the list elements, but I don't really understand continuation passing (and I've read a lot about it). How can I write partition using tail-recursive and keeping the list elements in order?
这是一个CPS版本，但List.rev是要走的路（参见这个相关答案）。
let partition f list =
let rec aux k = function
| h::t -> aux (fun (a, b) ->
k (if f h then h::a, b else a, h::b)) t
| [] -> k ([], [])
aux id list
Although already answered, this question deserves an attempt at an explanation. The accumulator-based, tail-recursive version is basically fold , left-to-right and hence in need of reversal.
let fold folder state list : 'State =
let rec aux state = function
| [] -> state
| h:'T::t -> aux (folder state h) t
aux state list
// val fold : folder:('State -> 'T -> 'State) -> state:'State -> list:'T list -> 'State
let partitionFold p =
fold (fun (a, b) h -> if p h then h::a, b else a, h::b) ([], [])
>> fun (a, b) -> List.rev a, List.rev b
partitionFold (fun x -> x % 2 = 0) [0..10]
// val it : int list * int list = ([0; 2; 4; 6; 8; 10], [1; 3; 5; 7; 9])
The signature and functionality of fold is now exactly that of List.fold from the standard library.
In contrast, the version in continuation-passing style is equivalent to foldBack (cf. List.foldBack ). It iterates recursively from right-to-left (last element first), and thus obtains the desired order right away.
let foldBack folder list state : 'State =
let rec aux k = function
| [] -> k state
| h:'T::t -> aux (folder h >> k) t
aux id list
// val foldBack :
// folder:('T -> 'State -> 'State) -> list:'T list -> state:'State -> 'State
let partitionFoldBack p list =
foldBack (fun h (a, b) -> if p h then h::a, b else a, h::b) list ([], [])
partitionFoldBack (fun x -> x % 2 = 0) [0..10]
// val it : int list * int list = ([0; 2; 4; 6; 8; 10], [1; 3; 5; 7; 9])
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