I'm taking a functional programming class and I'm having a hard time leaving the OOP mindset behind and finding answers to a lot of my questions.
I have to create a function that takes an ordered list and converts it into specified size sublists using a variation of fold.
This isn't right, but it's what I have:
splitList :: (Ord a) => Int -> [a] -> [[a]]
splitList size xs
| [condition] = foldr (\item subList -> item:subList) [] xs
| otherwise =
I've been searching and I found out that foldr is the variation that works better for what I want, and I think I've understood how fold works, I just don't know how I'll set up the guards so that when length sublist == size haskell resets the accumulator and goes on to the next list.
If I didn't explain myself correctly, here's the result I want:
> splitList 3 [1..10]
> [[1,2,3],[4,5,6],[7,8,9],[10]]
Thanks!
While Fabián's and chi's answers are entirely correct, there is actually an option to solve this puzzle using foldr. Consider the following code:
splitList :: Int -> [a] -> [[a]]
splitList n =
foldr (\el acc -> case acc of
[] -> [[el]]
(h : t) | length h < n -> (el : h) : t
_ -> [el] : acc
) []
The strategy here is to build up a list by extending its head as long as its length is lesser than desired. This solution has, however, two drawbacks:
It does something slightly different than in your example;
splitList 3 [1..10] produces [[1],[2,3,4],[5,6,7],[8,9,10]]
It's complexity is O(n * length l), as we measure length of up to n–sized list on each of the element which yields linear number of linear operations.
Let's first take care of first issue. In order to start counting at the beginning we need to traverse the list left–to–right, while foldr does it right–to–left. There is a common trick called "continuation passing" which will allow us to reverse the direction of the walk:
splitList :: Int -> [a] -> [[a]]
splitList n l = map reverse . reverse $
foldr (\el cont acc ->
case acc of
[] -> cont [[el]]
(h : t) | length h < n -> cont ((el : h) : t)
_ -> cont ([el] : acc)
) id l []
Here, instead of building the list in the accumulator we build up a function that will transform the list in the right direction. See this question for details. The side effect is reversing the list so we need to counter that by reverse application to the whole list and all of its elements. This goes linearly and tail-recursively tho.
Now let's work on the performance issue. The problem was that the length is linear on casual lists. There are two solutions for this:
Use another structure that caches length for a constant time access
Cache the value by ourselves
Because I guess it is a list exercise, let's go for the latter option:
splitList :: Int -> [a] -> [[a]]
splitList n l = map reverse . reverse . snd $
foldr (\el cont (countAcc, listAcc) ->
case listAcc of
[] -> cont (countAcc, [[el]])
(h : t) | countAcc < n -> cont (countAcc + 1, (el : h) : t)
(h : t) -> cont (1, [el] : (h : t))
) id l (1, [])
Here we extend our computational state with a counter that at each points stores the current length of the list. This gives us a constant check on each element and results in linear time complexity in the end.
A way to simplify this problem would be to split this into multiple functions. There are two things you need to do:
take n elements from the list, and
keep taking from the list as much as possible.
Lets try taking first:
taking :: Int -> [a] -> [a]
taking n [] = undefined
taking n (x:xs) = undefined
If there are no elemensts then we cannot take any more elements so we can only return an empty list, on the other hand if we do have an element then we can think of taking n (x:xs) as x : taking (n-1) xs, we would only need to check that n > 0.
taking n (x:xs)
| n > 0 = x :taking (n-1) xs
| otherwise = []
Now, we need to do that multiple times with the remainder so we should probably also return whatever remains from taking n elements from a list, in this case it would be whatever remains when n = 0 so we could try to adapt it to
| otherwise = ([], x:xs)
and then you would need to modify the type signature to return ([a], [a]) and the other 2 definitions to ensure you do return whatever remained after taking n.
With this approach your splitList would look like:
splitList n [] = []
splitList n l = chunk : splitList n remainder
where (chunk, remainder) = taking n l
Note however that folding would not be appropriate since it "flattens" whatever you are working on, for example given a [Int] you could fold to produce a sum which would be an Int. (foldr :: (a -> b -> b) -> b -> [a] -> b or "foldr function zero list produces an element of the function return type")
You want:
splitList 3 [1..10]
> [[1,2,3],[4,5,6],[7,8,9],[10]]
Since the "remainder" [10] in on the tail, I recommend you use foldl instead. E.g.
splitList :: (Ord a) => Int -> [a] -> [[a]]
splitList size xs
| size > 0 = foldl go [] xs
| otherwise = error "need a positive size"
where go acc x = ....
What should go do? Essentially, on your example, we must have:
splitList 3 [1..10]
= go (splitList 3 [1..9]) 10
= go [[1,2,3],[4,5,6],[7,8,9]] 10
= [[1,2,3],[4,5,6],[7,8,9],[10]]
splitList 3 [1..9]
= go (splitList 3 [1..8]) 9
= go [[1,2,3],[4,5,6],[7,8]] 9
= [[1,2,3],[4,5,6],[7,8,9]]
splitList 3 [1..8]
= go (splitList 3 [1..7]) 8
= go [[1,2,3],[4,5,6],[7]] 8
= [[1,2,3],[4,5,6],[7,8]]
and
splitList 3 [1]
= go [] 1
= [[1]]
Hence, go acc x should
check if acc is empty, if so, produce a singleton list [[x]].
otherwise, check the last list in acc:
if its length is less than size, append x
otherwise, append a new list [x] to acc
Try doing this by hand on your example to understand all the cases.
This will not be efficient, but it will work.
You don't really need the Ord a constraint.
Checking the accumulator's first sublist's length would lead to information flow from the right and the first chunk ending up the shorter one, potentially, instead of the last. Such function won't work on infinite lists either (not to mention the foldl-based variants).
A standard way to arrange for the information flow from the left with foldr is using an additional argument. The general scheme is
subLists n xs = foldr g z xs n
where
g x r i = cons x i (r (i-1))
....
The i argument to cons will guide its decision as to where to add the current element into. The i-1 decrements the counter on the way forward from the left, instead of on the way back from the right. z must have the same type as r and as the foldr itself as a whole, so,
z _ = [[]]
This means there must be a post-processing step, and some edge cases must be handled as well,
subLists n xs = post . foldr g z xs $ n
where
z _ = [[]]
g x r i | i == 1 = cons x i (r n)
g x r i = cons x i (r (i-1))
....
cons must be lazy enough not to force the results of the recursive call prematurely.
I leave it as an exercise finishing this up.
For a simpler version with a pre-processing step instead, see this recent answer of mine.
Just going to give another answer: this is quite similar to trying to write groupBy as a fold, and actually has a couple gotchas w.r.t. laziness that you have to bear in mind for an efficient and correct implementation. The following is the fastest version I found that maintains all the relevant laziness properties:
splitList :: Int -> [a] -> [[a]]
splitList m xs = snd (foldr f (const ([],[])) xs 1)
where
f x a i
| i <= 1 = let (ys,zs) = a m in ([], (x : ys) : zs)
| otherwise = let (ys,zs) = a (i-1) in (x : ys , zs)
The ys and the zs gotten from the recursive processing of the rest of list indicate the first and the rest of the groups into which the rest of the list will be broken up, by said recursive processing. So we either prepend the current element before that first subgroup if it is still shorter than needed, or we prepend before the first subgroup when it is just right and start a new, empty subgroup.
How do you write a F# recursive function that accepts a positive integer n and a list xs as input, and returns a list except first n elements in xs?
let rec something n xs = .. something 7 [1..10] = [8; 9; 10]
I don't think that recursion is the most efficient way to solve this problem, but you can do it like this:
let rec something n xs =
if n > List.length xs || n < 0 then failwith "incorrect parameter n - out of range"
else if n = 0 then xs
else something (n-1) (xs |> List.tail)
let res = something 7 [1..10]
open System
Console.WriteLine(res)
//something 7 [1..10] = [8; 9; 10]
The simple answer is to use List.skip ... i.e. [0..10] |> List.skip 5
To reimplement List.skip you'd be looking at something like:
let rec listSkip n list =
match (n, list) with
| 0, list -> list
| _, [] -> failwith "The index is outside the legal range"
| n, _ when n < 0 -> failwith "The index cannot be negative"
| n, _ :: tl -> listSkip (n - 1) tl
As this is recursion is eligible for tail-call optimization, performance should be similar to an explicit loop.
I've avoided an explicit guard checking List.length against n because List.length requires iteration of the entire list ( which we'd have to check each round of the recursion ). Thus it's cheaper just to try and remove n items and fail if we run into an empty list before n reaches 0.
Implementing Haskell's take and drop functions using foldl.
Any suggestions on how to implement take and drop functions using foldl ??
take x ls = foldl ???
drop x ls = foldl ???
i've tried these but it's showing errors:
myFunc :: Int -> [a] -> [a]
myFunc n list = foldl func [] list
where
func x y | (length y) > n = x : y
| otherwise = y
ERROR PRODUCED :
*** Expression : foldl func [] list
*** Term : func
*** Type : a -> [a] -> [a]
*** Does not match : [a] -> [a] -> [a]
*** Because : unification would give infinite type
Can't be done.
Left fold necessarily diverges on infinite lists, but take n does not. This is so because left fold is tail recursive, so it must scan through the whole input list before it can start the processing.
With the right fold, it's
ntake :: Int -> [a] -> [a]
ntake 0 _ = []
ntake n xs = foldr g z xs 0
where
g x r i | i>=n = []
| otherwise = x : r (i+1)
z _ = []
ndrop :: Int -> [a] -> [a]
ndrop 0 xs = xs
ndrop n xs = foldr g z xs 0 xs
where
g x r i xs#(_:t) | i>=n = xs
| otherwise = r (i+1) t
z _ _ = []
ndrop implements a paramorphism nicely and faithfully, up to the order of arguments to the reducer function g, giving it access to both the current element x and the current list node xs (such that xs == (x:t)) as well as the recursive result r. A catamorphism's reducer has access only to x and r.
Folds usually encode catamorphisms, but this shows that right fold can be used to code up a paramorphism just as well. It's universal that way. I think it is beautiful.
As for the type error, to fix it just switch the arguments to your func:
func y x | ..... = .......
The accumulator in the left fold comes as the first argument to the reducer function.
If you really want it done with the left fold, and if you're really sure the lists are finite, two options:
ltake n xs = post $ foldl' g (0,id) xs
where
g (i,f) x | i < n = (i+1, f . (x:))
| otherwise = (i,f)
post (_,f) = f []
rltake n xs = foldl' g id xs r n
where
g acc x = acc . f x
f x r i | i > 0 = x : r (i-1)
| otherwise = []
r _ = []
The first counts from the left straight up, potentially stopping assembling the prefix in the middle of the full list traversal that it does carry to the end nevertheless, being a left fold.
The second also traverses the list in full turning it into a right fold which then gets to work counting down from the left again, being able to actually stop working as soon as the prefix is assembled.
Implementing drop this way is bound to be (?) even clunkier. Could be a nice exercise.
I note that you never specified the fold had to be over the supplied list. So, one approach that meets the letter of your question, though probably not the spirit, is:
sillytake :: Int -> [a] -> [a]
sillytake n xs = foldl go (const []) [1..n] xs
where go f _ (x:xs) = x : f xs
go _ _ [] = []
sillydrop :: Int -> [a] -> [a]
sillydrop n xs = foldl go id [1..n] xs
where go f _ (_:xs) = f xs
go _ _ [] = []
These each use left folds, but over the list of numbers [1..n] -- the numbers themselves are ignored, and the list is just used for its length to build a custom take n or drop n function for the given n. This function is then applied to the original supplied list xs.
These versions work fine on infinite lists:
> sillytake 5 $ sillydrop 5 $ [1..]
[6,7,8,9,10]
Will Ness showed a nice way to implement take with foldr. The least repulsive way to implement drop with foldr is this:
drop n0 xs0 = foldr go stop xs0 n0
where
stop _ = []
go x r n
| n <= 0 = x : r 0
| otherwise = r (n - 1)
Take the efficiency loss and rebuild the whole list if you have no choice! Better to drive a nail in with a screwdriver than drive a screw in with a hammer.
Both ways are horrible. But this one helps you understand how folds can be used to structure functions and what their limits are.
Folds just aren't the right tools for implementing drop; a paramorphism is the right tool.
You are not too far. Here are a pair of fixes.
First, note that func is passed the accumulator first (i.e. a list of a, in your case) and then the list element (an a). So, you need to swap the order of the arguments of func.
Then, if we want to mimic take, we need to add x when the length y is less than n, not greater!
So we get
myFunc :: Int -> [a] -> [a]
myFunc n list = foldl func [] list
where
func y x | (length y) < n = x : y
| otherwise = y
Test:
> myFunc 5 [1..10]
[5,4,3,2,1]
As you can see, this is reversing the string. This is because we add x at the front (x:y) instead of at the back (y++[x]). Or, alternatively, one could use reverse (foldl ....) to fix the order at the end.
Also, since foldl always scans the whole input list, myFunc 3 [1..1000000000] will take a lot of time, and myFunc 3 [1..] will fail to terminate. Using foldr would be much better.
drop is more tricky to do. I don't think you can easily do that without some post-processing like myFunc n xs = fst (foldl ...) or making foldl return a function which you immediately call (which is also a kind of post-processing).
This is probably a stupid question, but I've been stuck on this problem for some hours now.. I have made a genetic algorithm but thought that I could try to improve it a bit. I want to make a fitness function that compare two lists of digits and returns a value. If both lists contains a number that is the same and are in the same "place" the function should return + 2. If the lists contains a number that is the same but in the wrong place it should return + 1.
I've made two different functions which both fulfill one of these tasks, but I can't manage to incorperate them into one function. Here are the functions:
samePlace _ [] = 0
samePlace [] _ = 0
samePlace (x:xs) (y:ys)
| x == y = (sP xs ys) + 2
| otherwise = sP xs (ys)
This function returns +2 for every digit that is the same and is in the right place.
notSamePlace [] _ = 0
notSamePlace _ [] = 0
notSamePlace (x:xs) (ys)
| elem x (ys) = (notSamePlace xs ys) + 1
| otherwise = (notSamePlace xs ys)
This function returns + 1 is one of the digits in the first list exists in the second list.
The problem I got is that the same-place function requires to split up the two lists and go through them one digit at a time to compare them while the not-the-same-place function needs to keep the second list intact without splitting it up in a head and tail. Would be so thankful if someone could point me in the right direction on how to go about this problem.
Also, my thought was that this function could improve the time it takes to find the solution in the genetic algorithm. If my solution is to find the string "hello world", my thought is that an individual with the gene "leolh owdrl" should have more fitness than a gene that looks like "hFz%l r0M/z". In my program so far the first gene would have a fitness value of 1 (because the 'space' is the only character in the same place as the targets characters) but the second gene has the 'h' and the 'space' right so it would be given a fitness value of 2. Is this a good thought or not?
Thanks!
Below function uses zip to index every character, which allows to pass the full second list into recursive calls.
places :: String -> String -> Int
places _ [] = 0
places [] _ = 0
places xs ys = zippedPlaces (zip xs [1..length xs]) (zip ys [1..length ys])
zippedPlaces :: [(Char, Int)] -> [(Char, Int)] -> Int
zippedPlaces [] _ = 0
zippedPlaces (x:xs) ys =
let match = filter (\(num, i) -> fst x == num) ys
in case match of
[] -> zippedPlaces xs ys
(a:_) -> (if snd a == snd x then 2 else 1) + zippedPlaces xs ys
Assumes that no list contains duplicates:
place [] _ = 0
place _ [] = 0
place (x:xs) (y:ys) = place xs ys +
if x == y then 1 else (if elem x ys then 2 else 0) + (if elem y xs then 2 else 0)
I'm trying to write a simple recursive function that look over list and return a pair of integer. This is easy to write in c/c++/java but i'm new to ocaml so somehow hard to find out the solution due to type conflict
it should goes like ..
let rec test p l = ... ;;
val separate : (’a -> bool) -> ’a list -> int * int = <fun>
test (fun x -> x mod 2 = 0) [-3; 5; 2; -6];;
- : int * int = (2, 2)
so the problem is how can i recursively return value on tuple ..
One problem here is that you are returning two different types: an int for an empty list, or a tuple otherwise. It needs to be one or the other.
Another problem is that you are trying to add 1 to test, but test is a function, not a value. You need to call test on something else for it to return a value, but even then it is supposed to return a tuple, which you can't add to an integer.
I can't figure out what you want the code to do, but if you update your question with that info I can help more.
One guess that I have is that you want to count the positive numbers in the list, in which case you could write it like this:
let rec test l =
match l with [] -> 0
| x::xs -> if x > 0 then 1 + (test xs)
else test xs;;
Update: since you've edited to clarify the problem, modify the above code as follows:
let test l =
let rec test_helper l pos nonpos =
match l with [] -> (pos, nonpos)
| x::xs -> if x > 0 then test_helper xs 1+pos, nonpos
else test_helper xs pos 1+nonpos
in test_helper l 0 0;;
Using the accumulators help a lot in this case. It also makes the function tail-recursive which is always good practice.
Been away from OCaml for a bit, but I think this will do the trick in regards to REALFREE's description in the comment
let rec test l =
match l with
[] -> (0,0)
| x::xs ->
if x > 0 then match (test xs) with (x,y) -> (x+1, y)
else match (test xs) with (x,y) -> (x, y+1);;
You can used the nested match statements to pull out pieces of the tuple to modify
EDIT:
I didn't know about the syntax Pascal Cuoq mentioned in his comment below, here's the code like that, it's neater and a little shorter:
let rec test l =
match l with
[] -> (0,0)
| x::xs ->
if x > 0 then let (x,y) = test xs in (x+1, y)
else let (x,y) = test xs in (x, y+1);;
But the accepted answer is still much better, especially with the tail recursion ;).