I have a list of integers named t that has an even length n = List.length t. I want to get two lists, the partition of t from index 0 to (n / 2 - 1), and the partition of t from index (n / 2) to (n-1). In other words, I want to split the list t in two parts, but I cannot find anything that does that in the List module (there is List.filter, but it does not filter by index, it takes a function instead).
An example of what I want to do:
let t = [8 ; 66 ; 4 ; 1 ; -2 ; 6 ; 4 ; 1] in
(* Split it to get t1 = [ 8 ; 66 ; 4 ; 1] and t2 = [-2 ; 6 ; 4 ; 1] *)
For now,I have something like this
let rec split t1 t2 n =
match t1 with
| hd :: tl when (List.length tl > n) -> split tl (hd :: t2) n;
| hd :: tl when (List.length tl = n) -> (t1,t2);
| _ -> raise (Failure "Unexpected error");;
let a = [1;2;3;4;7;8];;
let b,c = split a [] (List.length a / 2 - 1);;
List.iter (fun x -> print_int x) b;
print_char '|';
List.iter (fun x -> print_int x) c;
Output is:
478|321, the order has been reversed!
Calculating the length of the list requires walking the list, so it takes time that's linear in the length of the list. Your attempt calculates the length of the remaining list at each step, which makes the total running time quadratic. But you actually don't need to do that! First you calculate the total length of the list. After that, the place to cut is halfway from the beginning, which you can locate by incrementing a counter as you go through the list.
As for the reversal, let's look at what happens to the first element of the list. In the first call to split, the accumulator t2 is the empty list, so h gets put at the end of the list. The next element will be placed before that, and so on. You need to put the first element at the head of the list, so prepend it to the list built by the recursive call.
let rec split_at1 n l =
if n = 0 then ([], l) else
match l with
| [] -> ([], []) (*or raise an exception, as you wish*)
| h :: t -> let (l1, l2) = split_at1 (n-1) t in (h :: l1, l2);;
let split_half1 l = split_at1 (List.length l / 2) l;;
This operates in linear time. A potential downside of this implementation is that the recursive call it makes is not a tail call, so it will consume a large amount of stack on large lists. You can fix this by building the first half as an accumulator that's passed to the function. As we saw above, this creates a list in reverse order. So reverse it at the end. This is a common idiom when working with lists.
let rec split_at2 n acc l =
if n = 0 then (List.rev acc, l) else
match l with
| [] -> (List.rev acc, [])
| h :: t -> split_at2 (n-1) (h :: acc) t;;
let split_half2 l = split_at2 (List.length l / 2) [] l;;
Related
So consider getting a list of [1; 2; 3; 4; 5; 6; 7; 8; 9] and reshape it into [[1; 2; 3]; [4; 5; 6]; [7; 8; 9]]. How would you do that in OCaml? I want a simple function or something from the standard library.
Turns out, it can be easily done with 3 lines of code, considering that the length of the list is divisible by 3.
let rec re_shape = function
| x :: xs :: xz :: xt -> [x; xs; xz] :: re_shape xt
| _ -> []
How this works is that for each iteration it cons a list of 3 to the rest of the function, till it reaches the end. The last line is added for safety.
As you have shown an effort to solve this, for your consideration, see a strategy below for generalizing this to allow for any length.
The partition function will allow us to get the first n elements from the list and the remainder, raising Invalid_argument if there aren't n elements in the list.
The chunks function applies this recursively to the remainder to build a list of lists.
let partition n lst =
let rec partition' n (first, rest) =
match n, rest with
| 0, _ -> (List.rev first, rest)
| _, [] -> raise (Invalid_argument "List not long enough")
| _, x::xs -> partition' (n-1) (x :: first, xs)
in
partition' n ([], lst)
let rec chunks n lst =
match partition n lst with
| first, [] -> [first]
| first, rest -> first :: chunks n rest
| exception (Invalid_argument _) ->
raise (Invalid_argument (Format.sprintf "List length not evenly divisible by %d" n))
This second function is not tail-recursive, though that can readily be addressed in OCaml 4.14 and later with:
let[#tail_mod_cons] rec chunks n lst =
...
I am new to F# & tuples and I am trying to split a list into three lists of tuples using recursion and matching.
For example, a list of [1; 2; 3] would return:
l1 = [1]
l2 = [2]
l3 = [3]
or
[1;2;3;4;5;6;7]:
l1 = [1;2;3]
l2 = [4; 5]
l3 = [6; 7]
So far my code starts out as
let rec split x =
match x with
| _ -> [], [], []
I'm not sure where to start when inserting elements into each list.
The most basic approach would be to walk over the list, process the rest of it recursively and then append the current element to one of the three returned lists. You will need to add an extra parameters i to the function to keep track of how far in the list you are (and then use this to determine where should the current elemnt go). The general structure in the most basic form is:
let split l =
let length = List.length l
let rec loop i l =
match l with
| [] ->
// Empty list just becomes a triple of empty lists
[], [], []
| x::xs ->
// Process the rest of the list recursively. This
// gives us three lists containing the values from 'xs'
let l1, l2, l3 = loop (i + 1) xs
// Now comes the tricky bit. Here you need to figure out
// whether 'x' should go into 'l1', 'l2' or 'l3'.
// Then you can append it to one of them using something like:
l1, x::l2, l3
// Walk over the list, starting with index 'i=0'
loop 0 l
What to do about the tricky bit? I do not have a solution that works exactly as you wanted, but the following is close - it simply looks whether i is greater than 1/3 of the length or 2/3 of the length:
let split l =
let length = List.length l
let rec loop i l =
match l with
| [] -> [], [], []
| x::xs ->
let l1, l2, l3 = loop (i + 1) xs
if i >= length / 3 * 2 then l1, l2, x::l3
elif i >= length / 3 then l1, x::l2, l3
else x::l1, l2, l3
loop 0 l
This will always create groups of length / 3 and put remaining elements in the last list:
split [1..3] // [1], [2], [3]
split [1..4] // [1], [2], [3; 4]
split [1..5] // [1], [2], [3; 4; 5]
split [1..6] // [1; 2], [3; 4], [5; 6]
You should be able to adapt this to the behaviour you need - there is some fiddly calculation that you need to do to figure out exactly where the cut-off points are, but that's a matter of getting the +/-1s right!
There is a function for that in the List module.
You can test it easily in F# interactive (fsi).
let input = [1;2;3];;
let output = List.splitInto 3 input;;
output;;
val it : int list list = [[1]; [2]; [3]]
So it returns a list of lists.
If you want to do it by hand, you can still use other list functions (which might be good exercise in itself):
let manualSplitInto count list =
let l = List.length list
let n = l / count
let r = l % count
List.append
[(List.take (n+r) list)]
(List.unfold (fun rest ->
match rest with
| [] -> None
| _ -> let taken = min n (List.length rest)
Some (List.take taken rest, List.skip taken rest))
(List.skip (n+r) list))
Here, List.unfold does the iteration (recursing) part for you.
So, if you really want to train working with recursive functions, you will end up writing your own List.unfold replacement or something more tailored to your concrete use case.
let pedestrianSplitInto count list =
let l = List.length list
let n = l / count
let r = l % count
let rec step rest acc =
match rest with
| [] -> acc
| _ ->
let taken = min n (List.length rest)
step (List.skip taken rest) ((List.take taken rest) :: acc)
List.rev (step (List.skip (n+r) list) [List.take (n+r) list])
Please observe how similar the implementation of function step is to the lambda given to List.unfold in manualSplitInto.
If you also do not want to use functions like List.take or List.skip, you will have to go even lower level and do element wise operations, such as:
let rec splitAtIndex index front rear =
match index with
| 0 -> (List.rev front, rear)
| _ -> splitAtIndex (index - 1) ((List.head rear) :: front) (List.tail rear)
let stillLivingOnTreesSplitInto count list =
let l = List.length list
let n = l / count
let r = l % count
let rec collect result (front,rear) =
match rear with
| [] -> (front :: result)
| _ -> collect (front :: result) (splitAtIndex n [] rear)
let x = splitAtIndex (n+r) [] list
collect [] x |> List.rev
If you know it will always be triplets then this should work.
let xs = [1..7]
let n = List.length xs
let y = List.mapi (fun i x -> (x, 3 * i / n)) xs
List.foldBack (fun (x, i) (a,b,c) -> match i with 0 -> (x::a,b,c) | 1 -> (a,x::b,c) | 2 -> (a,b,x::c)) y (([],[],[]))
How do you write a f# recursive function that accepts a positive integer n and a list xs as input, and returns a list containing only the first n elements in xs.
let rec something n xs =
..
something 3 [1..10] = [1;2;3]
The short answer is: Don't, just use Seq.take.
A simple version would be something like:
let rec take n list =
match n with
| 0 -> []
| _ -> List.head list :: take (n - 1) (List.tail list)
A tail-recursive could look like:
let rec take n list =
let rec innertake m innerlist acc =
match m with
| 0 -> List.rev acc
| _ -> innertake (m - 1) (List.tail innerlist) ((List.head innerlist) :: acc)
innertake n list []
Note that neither of these does anything to handle the case that the input list is shorter than the requested number of items.
I am new to ocaml and trying to write some code to generate all lists of number between two value.
For example, if I call this function generate, I want to obtain something like this :
let generate ~min ~max ~length (* Maybe other arguments *) =
(* The code *)
;;
generate ~min:0 ~max:3 ~length:4;;
Should return
[
[0;0;0];
[1;0;0];
[2;0;0];
[3;0;0];
[0;1;0];
And so on, to
[3;2;3];
[0;3;3];
[1;3;3];
[2;3;3];
[3;3;3];
]
I already tried code like this :
open Core.Std;;
type next_list =
| Complete of int list
| Partial of int list
| Result of (int array) list
;;
let rec next ~r ~min ~max ~l =
let detox = function | Partial a -> a | _ -> assert false in
match l with
| Partial (hd :: tl) when hd <= max -> Partial (hd + 1 :: tl)
| Partial (hd :: tl) when hd = max + 1 -> next ~r ~min ~max
~l:(Partial (min :: (detox (next ~r ~min ~max ~l:(Partial tl))) ))
| Complete (hd :: tl) when hd <= max -> next ~r:([l] :: r) ~min ~max
~l:(Complete (hd + 1 :: tl))
| Complete (hd :: tl) when hd = max + 1 -> next ~r ~min ~max
~l:(Complete (min :: (detox (next ~r ~min ~max ~l:(Partial tl)))))
(*| Partial [] -> next ~r ~min ~max ~l:(Result r)*)
| Result a -> Result a
It may be spread around several functions if necessary, that is not a problem.
I am also interested by non ocaml code or idea.
Thanks for your help.
This is my first question on Stackoverflow, do not hesitate to say if my question is unclear.
here some solution :
First, let's define that takes 2 lists l1 & l2 as input and that produces a list of list, where each element is l2 augmented by 1 element of l1 :
let enumerate l ll = List.fold ~init:[] ~f:(fun op x -> (x::ll)::op) l;;
enumerate [0;1;2;3] [4;5;6];;
- : int list list = [[3; 4; 5; 6]; [2; 4; 5; 6]; [1; 4; 5; 6]; [0; 4; 5; 6]]
Now generate :
let rec generate length ll =
if length=1 then List.fold ~init:[] ~f:(fun op x -> [x]::op) ll
else
let result = generate (length-1) ll in
List.fold ~init:[] ~f:(fun op x -> (enumerate ll x)#op) result;;
and usage is as follows :
generate 2 [1;2;3];; (* instead of generate ~min:1 ~max:3 ~length:2 *)
Some explanation :
List.fold ~init:[] ~f:(fun op x -> [x]::op) ll
=> this creates the initial list of list (singleton)
And the second : takes each of the list of length -1 and performs the enumeration.
Here's a hint:
let count_prefix low high lists =
???
let generate min max length =
let rec recur low high len =
if len = 0 then []
else count_prefix low high (recur low high (len - 1)) in
recur min max length
count_prefix should return a list that is the elements of lists prefixed with the numbers low to high. If lists is empty, it should return a list of lists containing the numbers low to high. That is:
count_prefix 0 3 [] => [[0]; [1]; [2]]
count_prefix 0 3 [[10];[20]] => [[0; 10]; [0; 20]; [1; 10]; [1; 20]; [2; 10]; [2; 20]]
Fill in the definition of count_prefix.
I would like to implement a function that takes as input a size n and a list. This function will cut the list into two lists, one of size n and the rest in another list. I am new to this language and have a hard time learning the syntax.
The main problem I have is that is finding a way to express a size of the list without using any loops or mutable variables.
Can anyone give a me some pointers?
Let's start with the function's type signature. Since it gets n and a list as arguments and returns a pair of lists, you have a function split:
val split : int -> 'a list -> 'a list * 'a list
Here is one approach to implement this function:
let split n xs =
let rec splitUtil n xs acc =
match xs with
| [] -> List.rev acc, []
| _ when n = 0 -> List.rev acc, xs
| x::xs' -> splitUtil (n-1) xs' (x::acc)
splitUtil n xs []
The idea is using an accumulator acc to hold elements you have traversed and decreasing n a long the way. Because elements are prepended to acc, in the end you have to reverse it to get the correct order.
The function has two base cases to terminate:
There's no element left to traverse (xs = [] at that point).
You have gone through the first n elements of the list (n decreases to 0 at that time).
Here is a short illustration of how split computes the result:
split 2 [1; 2; 3] // call the auxiliary function splitUtil
~> splitUtil 2 [1; 2; 3] [] // match the 3rd case of x::xs'
~> splitUtil 1 [2; 3] [1] // match the 3rd case of x::xs'
~> splitUtil 0 [3] [2; 1] // match the 2nd case of n = 0 (base case)
~> List.rev [2; 1], [3] // call List.rev on acc
~> [1; 2], [3]
let split n list =
let rec not_a_loop xs = function
| (0, ys) | (_, ([] as ys)) -> (List.rev xs), ys
| (n, x::ys) -> not_a_loop (x::xs) (n-1, ys)
not_a_loop [] (n, list)
New solution - splitAt is now built into List and Array. See commit around 2014 on github. I noticed this today while using F# in VS.2015
Now you can simply do this...
let splitList n list =
List.splitAt n list
And as you might expect the signature is...
n: int -> list: 'a list -> 'a list * 'a list
Example usage:
let (firstThree, remainder) = [1;2;3;4;5] |> (splitList 3)
printfn "firstThree %A" firstThree
printfn "remainder %A" remainder
Output:
firstThree [1; 2; 3]
remainder [4; 5]
Github for those interested: https://github.com/dsyme/visualfsharp/commit/1fc647986f79d20f58978b3980e2da5a1e9b8a7d
One more way, using fold:
let biApply f (a, b) = (f a, f b)
let splitAt n list =
let splitter ((xs, ys), n') c =
if n' < n then
((c :: xs, ys), n' + 1)
else
((xs, c :: ys), n' + 1)
List.fold splitter (([], []), 0) list
|> fst
|> biApply List.rev
Here is a great series on folds than you can follow to learn more on the topic.