I'm trying to write a function that finds the longest running sub-list of increasing integers in a list.
This is what I have so far (very long variable names to help me understand it better):
let increasing list =
let rec aux inputList currentLongestList currentHighestList lastInsertedElement =
match inputList with
| [] ->
if List.length currentLongestList > List.length currentHighestList then currentLongestList
else currentLongestList
| hd :: tl ->
if hd > lastInsertedElement then aux tl (currentLongestList # hd) currentHighestList hd
else aux tl currentLongestList currentHighestList lastInsertedElement
in
aux list [] [] [min_int]
;;
My issue is that when this is entered, it says val increasing : int list list -> int list = <fun> implying 2 lists need to be passed where I only want one in the function? What am I doing wrong? Also, the function doesn't work if I take away the square brackets from min_int, even though I don't see why they're needed - what would I have to do to get rid of them?
The inferred type informs you that the argument named list is a list of lists of integers. Let us understand why, step by step.
First, the type checker has unified the type list with the type of inputList because of your call to aux at the end of the function increasing.
Second, the head of the aux argument named inputList is compared with lastInsertedElement in the second case of aux pattern-matching. Since lastInsertedElement is of type int list because of your initial call to aux, the type induces that inputList has type int list list.
For your second question, "why the brackets seem needed around min_int?". Look at the expression "... # hd". It implies that "hd" must be a list...
Related
I have the following function in OCaml:
let get_all_parents lst =
List.map (fun (name,opt) -> opt) lst
That maps my big list with (name, opt) to just a list of opt. An option can contain of either None or Some value which in this case is a string. I want a list of strings with all my values.
I am a beginner learning OCaml.
I don't think filter and map used together is a good solution to this problem. This is because when you apply map to convert your string option to string, you will have the None case to deal with. Even if you know that you won't have any Nones because you filtered them away, the type checker doesn't, and can't help you. If you have non-exhaustive pattern match warnings enabled, you will get them, or you will have to supply some kind of dummy string for the None case. And, you will have to hope you don't introduce errors when refactoring later, or else write test cases or do more code review.
Instead, you need a function filter_map : ('a -> 'b option) -> 'a list -> 'b list. The idea is that this works like map, except filter_map f lst drops each element of lst for which f evaluates to None. If f evaluates to Some v, the result list will have v. You could then use filter_map like so:
filter_map (fun (_, opt) -> opt) lst
You could also write that as
filter_map snd lst
A more general example would be:
filter_map (fun (_, opt) ->
match opt with
| Some s -> Some (s ^ "\n")
| None -> None)
lst
filter_map can be implemented like this:
let filter_map f lst =
let rec loop acc = function
| [] -> List.rev acc
| v::lst' ->
match f v with
| None -> loop acc lst'
| Some v' -> loop (v'::acc) lst'
in
loop [] lst
EDIT For greater completeness, you could also do
let filter_map f lst =
List.fold_left (fun acc v ->
match f v with
| Some v' -> v'::acc
| None -> acc) [] lst
|> List.rev
It's a shame that this kind of function isn't in the standard library. It's present in both Batteries Included and Jane Street Core.
I'm going to expand on #Carsten's answer. He is pointing you the right direction.
It's not clear what question you're asking. For example, I'm not sure why you're telling us about your function get_all_parents. Possibly this function was your attempt to get the answer you want, and that it's not quite working for you. Or maybe you're happy with this function, but you want to do some further processing on its results?
Either way, List.map can't do the whole job because it always returns a list of the same length as its input. But you need a list that can be different lengths, depending on how many None values there are in the big list.
So you need a function that can extract only the parts of a list that you're interested in. As #Carsten says, the key function for this is List.filter.
Some combination of map and filter will definitely do what you want. Or you can just use fold, which has the power of both map and filter. Or you can write your own recursive function that does all the work.
Update
Maybe your problem is in extracting the string from a string option. The "nice" way to do this is to provide a default value to use when the option is None:
let get default xo =
match xo with
| None -> default
| Some x -> x
# get "none" (Some "abc");;
- : string = "abc"
# get "none" None;;
- : string = "none"
#
type opt = Some of string | None
List.fold_left (fun lres -> function
(name,Some value) -> value::lres
| (name,None) -> lres
) [] [("s1",None);("s2",Some "s2bis")]
result:
- : string list = ["s2bis"]
I want to print out the column of a matrix but i keep getting an error.
Error: This expression has type 'a list but an expression was expected of type int
let rec get_column2 mat x = match mat with
| [] -> raise (Failure "empty list")
| h::t -> if x = 1 then h else get_column2 t (x-1);;
let rec get_column mat x= match mat with
| [] -> raise (Failure "empty list")
| []::tv -> get_column tv x
| hv::tv -> get_column2 hv x::get_column tv x;;
Matrix example [[2;5;6];[3;5;3][3;6;8]]
The first part works fine on type int list so I added the second part to go through the int list list and cut them into int list's and then tryed to get the columns of each separately.
I also tryed it this way:
let rec get_column mat x =
let rec column matr y =
if matr = [] then raise (Failure "empty list") else
if y = 1 then List.hd matr else
column (List.tl matr) y-1;
in column (List.hd mat) x :: get_column (List.tl mat) x;;
The second example translates fine but then doesn't work. I get an Exception "tl". (I'm not sure the function nesting is done right since I'm just learning Ocaml).
get_column2 - your first function, works as it should. That is it will fetch the value of each row in the matrix. It's a good helper function for you to extract the value from a list.
Your second function get_column gets all the types right, and you're accumulating everything, except that instead of stopping when you have an empty list [] you end up throwing an exception. That is your matrix example will go through just nicely, until it has no more lists to go through, then it will always throw the exception. (because the recursion keeps going till it's an empty list, and Ocaml will do as you told it too, fail when it gets an empty list.
The only thing you were missing was the exception, instead of throwing an exception, just return an empty list. That way your recursion will go all the way and accumulate till it's an empty list, and at the final step where the matrix is empty, it will append the empty list to the result, and you're golden.
So your code should be:
let rec get_column2 mat x = match mat with
| [] -> raise (Failure "empty list")
| h::t -> if x = 1 then h else get_column2 t (x-1)
let rec get_column mat x= match mat with
| [] -> [] (*doesn't throw an exception here*)
| []::tv -> get_column tv x
| hv::tv -> (get_column2 hv x)::get_column tv x
Instead of throwing the exception when it's an empty list, maybe you could check if the value of x is more than the length of the inner list.
Also, here's my implementation of doing it. It's still fairly basic as it doesn't use List.iter which everyone loves, but it doesn't rely on any additional packages. It makes use of nested functions so you don't expose them everywhere and pollute the namespace.
(*mat is a list of int list*)
let get_col mat x =
let rec helper rows x = (*helper function that gets the value at x*)
match rows with
| [] -> raise (Failure "empty list")
| h::t -> if x = 1 then h else helper t (x-1)
in
let rec wrapper mat= (*function that walks through all the rows*)
match mat with
| [] -> []
| rows::tl -> (helper rows x)::(wrapper tl) (*keep accumulating value*)
in wrapper mat
How you can visualize the [] -> [] part is that when the recursion is at it's final stage (mat is reduced to an empty list), the wrapper function returns the empty list, which will be appended to the recursion stack (since we are accumulating the values in a list as per (helper rows x)::(wrapper tl)), and the recursion will complete.
You don't hit this error with your get_column2 as you tell ocaml to stop recursing and return a value when x=1.
Edit, Additional:
As Jeffrey mentioned, a much more elegant way of handling the error is adding the case for [row], where row is the last row in the matrix. You just return (helper row x) there. And you could have the empty matrix as a failure.
Example using your code:
let rec get_column mat x= match mat with
| [] -> raise (Failure "empty list") (*fail here, as we don't want to compute a matrix with no rows.*)
| [tv] -> get_column tv x (*just return the value*)
| hv::tv -> (get_column2 hv x)::get_column tv x
When I try your first example, I don't get a type error. When I run it, I get the "empty list" failure. So your description of your problem seems wrong.
If you want to treat an empty matrix as an error, you must be very careful to handle a 1 x n matrix as your base case. I don't see that in your code.
I am working on a OCaml motion detection program. It analyzes two images and detects if there was motion. One part requires me summing a row of values and then also summing an entire image. This is what I have currenly:
let rec sumImRow(maskedrow) =
match maskedrow with
| [] -> 0
| mskRhd::mskRtl -> mskRhd + (sumImRow mskRtl)
;;
let rec sumImage(maskedimage) =
match maskedimage with
| mskRhd::mskRtl -> (sumImRow mskRhd)::(sumImage mskRtl)
| _ -> []
;;
and the given value is int list list -> int list = <fun>.
I don't quite understand why this is giving me int list.
tl;dr: You construct a new list instead of summing the integers.
Well, we can agree that sumImRow has type int list -> int as it takes elements from the list and then return their sum.
sumImage will have a list argument as it deconstructs it in the pattern matching. It then returns the list of result of sumImRow, meaning sumImage gets as argument a list of what sumImRow takes and returns a list of results. So we indeed have int list list -> int list.
You can avoid that by replacing :: with + and [] with 0 in sumImage's matching result.
You can also make a more improved code by using List.fold_left:
let sumImRow l = List.fold_left (+) 0 l;;
let sumImage l = List.fold_left (List.fold_left (+)) 0 l;;
The two return values of sumImage are both lists. So naturally its return type is a list.
(Most likely you should be using + rather than :: in sumImage. And the base case should be 0 rather than [].)
I am trying to produce the solution for an intersection of two sets using tail recursion and an empty list [] as an accu:
let rec setintersect list list =
let rec setintersect2 a b c =
match a with
| [] -> (match b with [] -> (setsimplify c) | h::t -> (setsimplify c))
| h1::t1 -> (match b with [] -> (setsimplify c) |h2::t2 -> (if (elementof h1 b) then (setintersect2 t1 b (c#[h1])) else (setintersect2 t1 b c))) in
setintersect2 list list [];;
Elementof takes takes "an int and a list" and is correctly working to give true if x is an element of the list, false otherwise..
Here is the problem:
# setintersect [5;2;1] [2;6;9];;
- : int list = [2; 6; 9]
and it should give [2].
What am I doing wrong?
I feel like there's something really simple that I am misunderstanding!
Edit:
Thanks for the responses so far.
setsimplify just removes the duplicates.
so [2,2,3,5,6,6] becomes [2,3,5,6]. Tested and made sure it is working properly.
I am not supposed to use anything from the List library either. Also, I must use "tail recursion" with the accumulator being a list that I build as I go.
Here is the thought:
Check the head element in list1, IF it exists in list2, THEN recurse with the "tail of list1, list2, and list c with that element added to it". ELSE, then recurse with "tail of list1, list2 and list c(as it is)".
end conditions are either list1 or list2 are empty or both together are empty, return list c (as it is).
let rec setintersect list list = is wrong: the two arguments should be named differently (you should of course update the call to setintersect2 accordingly), otherwise the second will shadow the first. I would have thought that OCaml would have at least warned you about this fact, but it appears that it is not the case.
Apart from that, the code seems to do the trick. There are a couple of things that could be improved though:
setintersect itself is not recursive (only setintersect2 is), you thus don't need the rec
you should find a different name for the argument of setintersect2. In particular, it is not obvious which is the accumulator (acc or accu will be understood by most OCaml programmers in these circumstances).
c#[h1] is inefficient: you will traverse c completely each time you append an element. It's better to do h1::c and reverse the result at the end
As a bonus point, if you append element at the beginning of c, and assume that a is ordered, you don't have to call setsimplify at the end of the call: just check whether c is empty, and if this is not the case, append h1 only if it is not equal to the head of c.
First, You didn't list out your setsimplify function.
To write an ocaml function, try to split it first, and then combine if possible.
To solve this task, you just go through all elements in l1, and for every element, you check whether it is in l2 or not, right?
So definitely you need a function to check whether an element is in a list or not, right?
let make one:
let rec mem x = function
| [] -> false
| hd::tl -> hd = x || mem x tl
Then you can do your intersection:
let rec inter l1 l2 =
match l1 with
| [] -> []
| hd::tl -> if mem hd l2 then hd::(inter tl l2) else inter tl l2
Note that the above function is not tail-recursive, I guess you can change it to tail-recursive as an excise.
If you use std library, then it is simple:
let intersection l1 l2 = List.filter (fun x -> List.mem x l2) l1
I recently started with F# and implemented a very basic recursive function that represents the Sieve of Eratosthenes. I came up with the following, working code:
static member internal SieveOfEratosthenesRecursive sequence accumulator =
match sequence with
| [] -> accumulator
| head::tail -> let rest = tail |> List.filter(fun number -> number % head <> 0L)
let newAccumulator = head::accumulator
Prime.SieveOfEratosthenesRecursive rest newAccumulator
This function is not really memory efficient so I tried to eliminate the variables "rest" and "newAccumulator". I came up with the following code
static member internal SieveOfEratosthenesRecursive sequence accumulator =
match sequence with
| [] -> accumulator
| head::tail -> tail |> List.filter(fun number -> number % head <> 0L)
|> Prime.SieveOfEratosthenesRecursive (head::accumulator)
As far as I understand the tutorials I've read Prime.SieveOfEratosthenesRecursive will be called with the filtered tail as first parameter and a list consisting of head::accumulator as second one. However when I try to run the code with the reduced variable usage, the program gets trappen in an infinite loop. Why is this happening and what did I do wrong?
As far as I understand the tutorials I've read Prime.SieveOfEratosthenesRecursive will be called with the filtered tail as first parameter and a list consisting of head::accumulator as second one.
You have this backwards.
In the first version, you're passing rest then newAccumulator; in the second version, you're effectively passing newAccumulator then rest. I.e., you've transposed the arguments.
Prime.SieveOfEratosthenesRecursive (head::accumulator) is a partial function application wherein you're applying (head::accumulator) as the first argument (sequence). This partial function application yields a unary function (expecting accumulator), to which you are passing (via |>) what is called rest in the first version of your code.
Changing SieveOfEratosthenesRecursive's argument order is the easiest solution, but I would consider something like the following idiomatic as well:
static member internal SieveOfEratosthenesRecursive sequence accumulator =
match sequence with
| [] -> accumulator
| head::tail ->
tail
|> List.filter(fun number -> number % head <> 0L)
|> Prime.SieveOfEratosthenesRecursive <| (head::accumulator)
or
static member internal SieveOfEratosthenesRecursive sequence accumulator =
let inline flipzip a b = b, a
match sequence with
| [] -> accumulator
| head::tail ->
tail
|> List.filter(fun number -> number % head <> 0L)
|> flipzip (head::accumulator)
||> Prime.SieveOfEratosthenesRecursive
FWIW, eliminating rest and newAccumulator as named variables here is not going to impact your memory usage in the slightest.
The last call in your second function is equivalent to:
Prime.SieveOfEratosthenesRecursive newAccumulator rest
where you switch positions of two params. Since newAccumulator grows bigger after each recursive call, you will never reach the base case of empty list.
The rule of thumb is putting the most frequently changing parameter at last:
let rec sieve acc xs =
match xs with
| [] -> acc
| x::xs' -> xs' |> List.filter (fun y -> y % x <> 0L)
|> sieve (x::acc)
The above function could be shortened using function keyword:
let rec sieve acc = function
| [] -> acc
| x::xs' -> xs' |> List.filter (fun y -> y % x <> 0L)
|> sieve (x::acc)
Using pipe (|>) operator only makes the function more readable, it doesn't affect memory usage at all.