I have to write a function that, given two lists, it returns a list of the elements of the first one whose square is present in the second one (sry for my english). I can't do it recursively and i can't use List.filter.
this is what i did:
let lst1= [1;2;3;4;5];;
let lst2= [9;25;10;4];;
let filquadi lst1 lst2 =
let aux = [] in
List.map(fun x -> if List.mem (x*x) lst2 then x::aux else []) lst1;;
It works but it also prints [] when the number doesn't satisfy the if statement:
filquadi lst1 lst2 ;;
- : int list list = [[]; [2]; [3]; []; [5]]
how can I return a list of numbers instead of a list of a list of numbers?
- : int list = [2;3;5]
You can use List.concat to put things together at the end:
List.concat (List.map ...)
As a side comment, aux isn't doing anything useful in your code. It's just a name for the empty list (since OCaml variables are immutable). It would probably be clearer just to use [x] instead of x :: aux.
As another side comment, this is a strange sounding assignment. Normally the reason to forbid use of functions from the List module is to encourage you to write your own recursive solution (which indeed is educational). I can't see offhand a reason to forbid the use of recursion, but it's interesting to combine functions from List in different ways.
Your criteria don't say you can't use List.fold_left or List.rev, so...
let filter lst1 lst2 =
List.fold_left
(fun init x ->
if List.mem (x * x) lst2 then x::init
else init)
[] lst1
|> List.rev
We start with an empty list, and as we fold over the first list, add the current element only if that element appears in the second list. Because this results in a list that's reversed from its original order, we then reverse that.
If you're not supposed to use recursion, this is technically cheating, because List.fold_left works recursively, but then so does basically anything working with lists. Reimplementing the List module's functions is going to involve a lot of recursion, as can be seen from reimplementing fold_left and filter.
let rec fold_left f init lst =
match lst with
| [] -> init
| x::xs -> fold_left f (f init x) xs
let rec filter f lst =
match lst with
| [] -> []
| x::xs when f x -> x :: filter f xs
| _::xs -> filter f xs
Related
I'm trying to make a function which returns a list of the first element of each sub-list, including empty lists being returned as [].
let firstCol (lst: 'a list list) =
List.map List.head lst
This works as long as there are no empty lists, but I get the following error message when my input includes an empty list:
System.ArgumentException: The input list was empty.
How do I go about this? Thanks in advance.
You can use List.tryHead or write your own function from the ground, or with helpers like List.fold/List.foldBack.
If you do List.tryHead you get an option as a result, either Some element, or None if the list is empty. So you must think what happens in the None case. You cannot return an empty list for a sub-list, because a list must have the same type. But you could for example skip empty lists. Or just keep the Option. As it indicates when a list was empty.
let xs = [[1;2;3];[];[4;5;6];[];[7;8;9]]
printfn "%A" (List.map List.tryHead xs)
returning
[Some 1; None; Some 4; None; Some 7]
You could skip the empty sub-lists
printfn "%A" (List.choose List.tryHead xs)
so you get
[1;4;7]
or do it on your own, with List.foldBack
let firstCol xs =
let folder xs acc =
match List.tryHead xs with
| Some x -> x :: acc
| None -> acc
List.foldBack folder xs []
Or even more basic
let rec firstCol xs =
match xs with
| [] -> []
| []::xss -> firstCol xss
| (x::xs)::xss -> x :: firstCol (xss)
The last version is not tail-recursive, but anyway, you should try and train to understand such a recursive definition. And be able to turn such a function into an tail-recursive on your own.
What you're asking for can't be done with the signature you currently have. Consider this input:
[
[1; 2]
[]
[3; 4]
]
It looks like you're asking for the following output:
[
1
[]
3
]
However, that isn't a legal list in F# because its elements don't have the same type.
I think your best bet is just to use tryHead instead, as suggested in the other answers.
I have this list of tuples
[(4,'a'), (1,'b'), (2,'c'), (2,'a'), (1,'d'), (4,'e')]
I want to get the first elements of every tuple then replicate it to make the following: "aaaabccaadeeee"
I came up with this code, but it only gives me the replicate of the first tuple.
replicate (fst ( head [(4,'a'), (1,'b')])) ( snd ( head [(4,'a'), (1,'b')]))
--output is: "aaaa"
I was thinking to use map for to get the replicate of every tuple, but I didn't succeed.
Since you already know how to find the correct answer for a single element, all you need is a little recursion
func :: [(Int, a)] -> [a]
func [] = []
func ((n, elem):rest) = (replicate n elem) ++ (func rest)
Mapping the values should also work. You just need to concatenate the resulting strings into one.
func :: [(Int, a)] -> [a]
func xs = concat $ map func2 xs where
func2 (n, elem) = replicate n elem
Or, if you are familiar with currying:
func :: [(Int, a)] -> [a]
func xs = concat $ map (uncurry replicate) xs
Finally, if you are comfortable using function composition, the definition becomes:
func :: [(Int, a)] -> [a]
func = concat . map (uncurry replicate)
Using concat and map is so common, there is a function to do just that. It's concatMap.
func :: [(Int, a)] -> [a]
func = concatMap (uncurry replicate)
Let
ls = [(4,'a'), (1,'b'), (2,'c'), (2,'a'), (1,'d'), (4,'e')]
in
concat [replicate i x | (i, x) <- ls]
will give
"aaaabccaadeeee"
The point-free version
concat . map (uncurry replicate)
You are correct about trying to use map. But first lets see why your code did not work
replicate (fst ( head [(4,'a'), (1,'b')])) ( snd ( head [(4,'a'), (1,'b')]))
Your first parameter to replicate is the head of your list which is (4, 'a'). Then you are calling fst on this, thus the first parameter is 4. Same things happens with second parameter and you get 'a'. The result of which you see.
Before using map lets try to do this with recursion. You want to take one element of list and apply replicate to it and then combine it with the result of applying replicate on the second element.
generate [] = []
generate (x:xs) = replicate (fst x) (snd x) ++ generate xs
Do note I am using pattern matching to get the first element of list. You can us the pattern matching to get the element inside the tuple as well, and then you would not need to use the fst/snd functions. Also note I am using pattern matching to define the base case of empty list.
generate [] = []
generate ((x,y):xs) = replicate x y ++ generate xs
Now coming to map, so map will apply your function to every element of the list, here's the first try
generate (x,y) = replicate x y
map generate xs
The result of the above will be slightly different from recursion. Think about it, map is going to apply generate to every element and store the result in a list. generate creates a list. So when you apply map you are creating a list of list. You can use concat to flatten it if you want, which will give you the same result as recursion.
Last thing, if you can use recursion, then you can use fold as well. Fold will just apply a function to every element of the list and return the accumulated results (broadly speaking).
--first parameter is the function to apply, second is the accumulator, third is your list
foldr step [] xs
where step (x,y) acc =
(replicate x y) ++ acc
Again here I have used pattern matching in the function step to extract the elements of the tuple out.
So this is one way to append two lists:
let rec append l1 l2 =
match l1 with
| h :: t -> h :: append t l2
| [] -> l2
But I am trying to write a tail-recursive version of append. (solve the problem before calling the recursive function).
This is my code so far, but when I try to add append in the first if statement the code becomes faulty for weird reasons.
let list1 = [1;2;3;4]
let list2 = [5;6;7;8]
let rec append lista listb =
match listb with
| h :: taillist -> if taillist != [] then
begin
lista # [h];
(* I cant put an append recursive call here because it causes error*)
end else
append lista taillist;
| [] -> lista;;
append list1 list2;;
The easiest way to transform a non tail-recursive list algorithm into a tail-recursive one, is to use an accumulator. Consider rewriting your code using a third list, that will accumulate the result. Use cons (i.e., ::) to prepend new elements to the third list, finally you will have a result of concatenation. Next, you need just to reverse it with List.rev et voila.
For the sake of completeness, there is a tail-recursive append:
let append l1 l2 =
let rec loop acc l1 l2 =
match l1, l2 with
| [], [] -> List.rev acc
| [], h :: t -> loop (h :: acc) [] t
| h :: t, l -> loop (h :: acc) t l
in
loop [] l1 l2
I would recommend to solve 99 problems to learn this idiom.
A couple of comments on your code:
It seems like cheating to define a list append function using #, since this is already a function that appends two lists :-)
Your code is written as if OCaml were an imperative language; i.e., you seem to expect the expression lista # [h] to modify the value of lista. But OCaml doesn't work that way. Lists in OCaml are immutable, and lista # [h] just calculates a new value without changing any previous values. You would need to pass this new value in your recursive call.
As #ivg says, the most straightforward way to solve your problem is using an accumulator, with a list reversal at the end. This is a common idiom in a language with immutable lists.
A version using constant stack space, implemented with a couple of standard functions (you'll get a tail-recursive solution after unfolding the definitions):
let append xs ys = List.rev_append (List.rev xs) ys
Incidentally, some OCaml libraries implement the append function in a pretty sophisticated way:
(1) see core_list0.ml in the Core_kernel library: search for "slow_append" and "count_append"
(2) or batList.mlv in the Batteries library.
An alternative tail-recursive solution (F#) leveraging continuations :
let concat x =
let rec concat f = function
| ([], x) -> f x
| (x1::x2, x3) -> concat (fun x4 -> f (x1::x4)) (x2, x3)
concat id x
I think the best way to go about it, like some have said would be to reverse the first list, then recursively add the head to the front of list2, but the top comment with code uses an accumulator, when you can get the same result without it by :: to the second list instead of an accumulator
let reverse list =
let rec reverse_helper acc list =
match list with
| [] -> acc
| h::t -> reverse_helper (h::acc) t in
reverse_helper [] lst;;
let append list1 list2 =
let rec append_helper list1_rev list2 =
match list1_rev with
| [] -> list2
| h :: t -> append_helper t (h::lst2) in
append_helper (reverse lst1) lst2;;
A possible answer to your question could be the following code :
let append list1 list2 =
let rec aux acc list1 list2 = match list1, list2 with
| [], [] -> List.rev(acc)
| head :: tail, [] -> aux (head :: acc) tail []
| [], head :: tail -> aux (head :: acc) [] tail
| head :: tail, head' :: tail' -> aux (head :: acc) tail (head' :: tail')
in aux [] list1 list2;
It's pretty similar to the code given by another one of the commenters on your post, but this one is more exhaustive, as I added a case for if list2 is empty from the beginning and list1 isn't
Here is a simpler solution:
let rec apptr l k =
let ln = List.rev l in
let rec app ln k acc = match ln with
| [] -> acc
| h::t -> app t k (h::acc) in
app ln k k
;;
let rec append (mylist: 'a list) (myotherlist : 'a list ): 'a list =
match mylist with
| [] -> myotherlist
| a :: rest -> a :: append rest myotherlist
With a list of integers such as:
[1;2;3;4;5;6;7;8;9]
How can I create a list of list of ints from the above, with all new lists the same specified length?
For example, I need to go from:
[1;2;3;4;5;6;7;8;9] to [[1;2;3];[4;5;6];[7;8;9]]
with the number to split being 3?
Thanks for your time.
So what you actually want is a function of type
val split : int list -> int -> int list list
that takes a list of integers and a sub-list-size. How about one that is even more general?
val split : 'a list -> int -> 'a list list
Here comes the implementation:
let split xs size =
let (_, r, rs) =
(* fold over the list, keeping track of how many elements are still
missing in the current list (csize), the current list (ys) and
the result list (zss) *)
List.fold_left (fun (csize, ys, zss) elt ->
(* if target size is 0, add the current list to the target list and
start a new empty current list of target-size size *)
if csize = 0 then (size - 1, [elt], zss # [ys])
(* otherwise decrement the target size and append the current element
elt to the current list ys *)
else (csize - 1, ys # [elt], zss))
(* start the accumulator with target-size=size, an empty current list and
an empty target-list *)
(size, [], []) xs
in
(* add the "left-overs" to the back of the target-list *)
rs # [r]
Please let me know if you get extra points for this! ;)
The code you give is a way to remove a given number of elements from the front of a list. One way to proceed might be to leave this function as it is (maybe clean it up a little) and use an outer function to process the whole list. For this to work easily, your function might also want to return the remainder of the list (so the outer function can easily tell what still needs to be segmented).
It seems, though, that you want to solve the problem with a single function. If so, the main thing I see that's missing is an accumulator for the pieces you've already snipped off. And you also can't quit when you reach your count, you have to remember the piece you just snipped off, and then process the rest of the list the same way.
If I were solving this myself, I'd try to generalize the problem so that the recursive call could help out in all cases. Something that might work is to allow the first piece to be shorter than the rest. That way you can write it as a single function, with no accumulators
(just recursive calls).
I would probably do it this way:
let split lst n =
let rec parti n acc xs =
match xs with
| [] -> (List.rev acc, [])
| _::_ when n = 0 -> (List.rev acc, xs)
| x::xs -> parti (pred n) (x::acc) xs
in let rec concat acc = function
| [] -> List.rev acc
| xs -> let (part, rest) = parti n [] xs in concat (part::acc) rest
in concat [] lst
Note that we are being lenient if n doesn't divide List.length lst evenly.
Example:
split [1;2;3;4;5] 2 gives [[1;2];[3;4];[5]]
Final note: the code is very verbose because the OCaml standard lib is very bare bones :/ With a different lib I'm sure this could be made much more concise.
let rec split n xs =
let rec take k xs ys = match k, xs with
| 0, _ -> List.rev ys :: split n xs
| _, [] -> if ys = [] then [] else [ys]
| _, x::xs' -> take (k - 1) xs' (x::ys)
in take n xs []
I'm working with a list of lists in OCaml, and I'm trying to write a function that combines all of the lists that share the same head. This is what I have so far, and I make use of the List.hd built-in function, but not surprisingly, I'm getting the failure "hd" error:
let rec combineSameHead list nlist = match list with
| [] -> []#nlist
| h::t -> if List.hd h = List.hd (List.hd t)
then combineSameHead t nlist#uniq(h#(List.hd t))
else combineSameHead t nlist#h;;
So for example, if I have this list:
[[Sentence; Quiet]; [Sentence; Grunt]; [Sentence; Shout]]
I want to combine it into:
[[Sentence; Quiet; Grunt; Shout]]
The function uniq I wrote just removes all duplicates within a list. Please let me know how I would go about completing this. Thanks in advance!
For one thing, I generally avoid functions like List.hd, as pattern maching is usually clearer and less error-prone. In this case, your if can be replaced with guarded patterns (a when clause after the pattern). I think what is happening to cause your error is that your code fails when t is []; guarded patterns help avoid this by making the cases more explicit. So, you can do (x::xs)::(y::ys)::t when x = y as a clause in your match expression to check that the heads of the first two elements of the list are the same. It's not uncommon in OCaml to have several successive patterns which are identical except for guards.
Further things: you don't need []#nlist - it's the same as just writing nlist.
Also, it looks like your nlist#h and similar expressions are trying to concatenate lists before passing them to the recursive call; in OCaml, however, function application binds more tightly than any operator, so it actually appends the result of the recursive call to h.
I don't, off-hand, have a correct version of the function. But I would start by writing it with guarded patterns, and then see how far that gets you in working it out.
Your intended operation has a simple recursive description: recursively process the tail of your list, then perform an "insert" operation with the head which looks for a list that begins with the same head and, if found, inserts all elements but the head, and otherwise appends it at the end. You can then reverse the result to get your intended list of list.
In OCaml, this algorithm would look like this:
let process list =
let rec insert (head,tail) = function
| [] -> head :: tail
| h :: t ->
match h with
| hh :: tt when hh = head -> (hh :: (tail # t)) :: t
| _ -> h :: insert (head,tail) t
in
let rec aux = function
| [] -> []
| [] :: t -> aux t
| (head :: tail) :: t -> insert (head,tail) (aux t)
in
List.rev (aux list)
Consider using a Map or a hash table to keep track of the heads and the elements found for each head. The nlist auxiliary list isn't very helpful if lists with the same heads aren't adjacent, as in this example:
# combineSameHead [["A"; "a0"; "a1"]; ["B"; "b0"]; ["A"; "a2"]]
- : list (list string) = [["A"; "a0"; "a1"; "a2"]; ["B"; "b0"]]
I probably would have done something along the lines of what antonakos suggested. It would totally avoid the O(n) cost of searching in a list. You may also find that using a StringSet.t StringMap.t be easier on further processing. Of course, readability is paramount, and I still find this hold under that criteria.
module OrderedString =
struct
type t = string
let compare = Pervasives.compare
end
module StringMap = Map.Make (OrderedString)
module StringSet = Set.Make (OrderedString)
let merge_same_heads lsts =
let add_single map = function
| hd::tl when StringMap.mem hd map ->
let set = StringMap.find hd map in
let set = List.fold_right StringSet.add tl set in
StringMap.add hd set map
| hd::tl ->
let set = List.fold_right StringSet.add tl StringSet.empty in
StringMap.add hd set map
| [] ->
map
in
let map = List.fold_left add_single StringMap.empty lsts in
StringMap.fold (fun k v acc-> (k::(StringSet.elements v))::acc) map []
You can do a lot just using the standard library:
(* compares the head of a list to a supplied value. Used to partition a lists of lists *)
let partPred x = function h::_ -> h = x
| _ -> false
let rec combineHeads = function [] -> []
| []::t -> combineHeads t (* skip empty lists *)
| (hh::_ as h)::t -> let r, l = List.partition (partPred hh) t in (* split into lists with the same head as the first, and lists with different heads *)
(List.fold_left (fun x y -> x # (List.tl y)) h r)::(combineHeads l) (* combine all the lists with the same head, then recurse on the remaining lists *)
combineHeads [[1;2;3];[1;4;5;];[2;3;4];[1];[1;5;7];[2;5];[3;4;6]];;
- : int list list = [[1; 2; 3; 4; 5; 5; 7]; [2; 3; 4; 5]; [3; 4; 6]]
This won't be fast (partition, fold_left and concat are all O(n)) however.