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I'm trying to write the code for Haskell concatmap without using the ++ operator where
concatMap :: (a -> [b]) -> [a] -> [b]
and producing the same result of
concatMap f = foldr ((++) . f) []
I'm quite new to Haskell and this was just an exercise I found. Actually, I do not even know if this can be done.
Here's a way that makes the state of the computation explicit:
concatMap :: (a -> [b]) -> [a] -> [b]
concatMap f = go []
where
-- We have b values; use one.
go (b:bs) as = b : go bs as
-- No bs left; get some more.
go [] (a:as) = go (f a) as
-- Nothing left; we're done.
go [] [] = []
This maintains the current list of bs, filling it up whenever it's empty.
This might be cheating, but how about:
myConcatMap f s = concat (map f s)
The concat function uses some sort of ++ in its source code, so that is why you might not like it. You can try to use an alternative concat that does list comprehensions, it has a more "from scratch" feeling.
myconcat ll = [y | x <- ll, y <- x]
You can use the fact that foldr (:) = flip (++)
concatMap f = foldr (flip (foldr (:)) . f) []
Or pointfree:
concatMap = flip foldr [] . (flip (foldr (:)) .)
In this question, the author brings up an interesting programming question: given two string, find possible 'interleaved' permutations of those that preserves order of original strings.
I generalized the problem to n strings instead of 2 in OP's case, and came up with:
-- charCandidate is a function that finds possible character from given strings.
-- input : list of strings
-- output : a list of tuple, whose first value holds a character
-- and second value holds the rest of strings with that character removed
-- i.e ["ab", "cd"] -> [('a', ["b", "cd"])] ..
charCandidate xs = charCandidate' xs []
charCandidate' :: [String] -> [String] -> [(Char, [String])]
charCandidate' [] _ = []
charCandidate' ([]:xs) prev =
charCandidate' xs prev
charCandidate' (x#(c:rest):xs) prev =
(c, prev ++ [rest] ++ xs) : charCandidate' xs (x:prev)
interleavings :: [String] -> [String]
interleavings xs = interleavings' xs []
-- interleavings is a function that repeatedly applies 'charCandidate' function, to consume
-- the tuple and build permutations.
-- stops looping if there is no more tuple from charCandidate.
interleavings' :: [String] -> String -> [String]
interleavings' xs prev =
let candidates = charCandidate xs
in case candidates of
[] -> [prev]
_ -> concat . map (\(char, ys) -> interleavings' ys (prev ++ [char])) $ candidates
-- test case
input :: [String]
input = ["ab", "cd"]
-- interleavings input == ["abcd","acbd","acdb","cabd","cadb","cdab"]
it works, however I'm quite concerned with the code:
it is ugly. no point-free!
explicit recursion and additional function argument prev to preserve states
using tuples as intermediate form
How can I rewrite the above program to be more "haskellic", concise, readable and more conforming to "functional programming"?
I think I would write it this way. The main idea is to treat creating an interleaving as a nondeterministic process which chooses one of the input strings to start the interleaving and recurses.
Before we start, it will help to have a utility function that I have used countless times. It gives a convenient way to choose an element from a list and know which element it was. This is a bit like your charCandidate', except that it operates on a single list at a time (and is consequently more widely applicable).
zippers :: [a] -> [([a], a, [a])]
zippers = go [] where
go xs [] = []
go xs (y:ys) = (xs, y, ys) : go (y:xs) ys
With that in hand, it is easy to make some non-deterministic choices using the list monad. Notionally, our interleavings function should probably have a type like [NonEmpty a] -> [[a]] which promises that each incoming string has at least one character in it, but the syntactic overhead of NonEmpty is too annoying for a simple exercise like this, so we'll just give wrong answers when this precondition is violated. You could also consider making this a helper function and filtering out empty lists from your top-level function before running this.
interleavings :: [[a]] -> [[a]]
interleavings [] = [[]]
interleavings xss = do
(xssL, h:xs, xssR) <- zippers xss
t <- interleavings ([xs | not (null xs)] ++ xssL ++ xssR)
return (h:t)
You can see it go in ghci:
> interleavings ["abc", "123"]
["abc123","ab123c","ab12c3","ab1c23","a123bc","a12bc3","a12b3c","a1bc23","a1b23c","a1b2c3","123abc","12abc3","12ab3c","12a3bc","1abc23","1ab23c","1ab2c3","1a23bc","1a2bc3","1a2b3c"]
> interleavings ["a", "b", "c"]
["abc","acb","bac","bca","cba","cab"]
> permutations "abc" -- just for fun, to compare
["abc","bac","cba","bca","cab","acb"]
This is fastest implementation I've come up with so far. It interleaves a list of lists pairwise.
interleavings :: [[a]] -> [[a]]
interleavings = foldr (concatMap . interleave2) [[]]
This horribly ugly mess is the best way I could find to interleave two lists. It's intended to be asymptotically optimal (which I believe it is); it's not very pretty. The constant factors could be improved by using a special-purpose queue (such as the one used in Data.List to implement inits) rather than sequences, but I don't feel like including that much boilerplate.
{-# LANGUAGE BangPatterns #-}
import Data.Monoid
import Data.Foldable (toList)
import Data.Sequence (Seq, (|>))
interleave2 :: [a] -> [a] -> [[a]]
interleave2 xs ys = interleave2' mempty xs ys []
interleave2' :: Seq a -> [a] -> [a] -> [[a]] -> [[a]]
interleave2' !prefix xs ys rest =
(toList prefix ++ xs ++ ys)
: interleave2'' prefix xs ys rest
interleave2'' :: Seq a -> [a] -> [a] -> [[a]] -> [[a]]
interleave2'' !prefix [] _ = id
interleave2'' !prefix _ [] = id
interleave2'' !prefix xs#(x : xs') ys#(y : ys') =
interleave2' (prefix |> y) xs ys' .
interleave2'' (prefix |> x) xs' ys
Using foldr over interleave2
interleave :: [[a]] -> [[a]]
interleave = foldr ((concat .) . map . iL2) [[]] where
iL2 [] ys = [ys]
iL2 xs [] = [xs]
iL2 (x:xs) (y:ys) = map (x:) (iL2 xs (y:ys)) ++ map (y:) (iL2 (x:xs) ys)
Another approach would be to use the list monad:
interleavings xs ys = interl xs ys ++ interl ys xs where
interl [] ys = [ys]
interl xs [] = [xs]
interl xs ys = do
i <- [1..(length xs)]
let (h, t) = splitAt i xs
map (h ++) (interl ys t)
So the recursive part will alternate between the two lists, taking all from 1 to N elements from each list in turns and then produce all possible combinations of that. Fun use of the list monad.
Edit: Fixed bug causing duplicates
Edit: Answer to dfeuer. It turned out tricky to do code in the comment field. An example of solutions that do not use length could look something like:
interleavings xs ys = interl xs ys ++ interl ys xs where
interl [] ys = [ys]
interl xs [] = [xs]
interl xs ys = splits xs >>= \(h, t) -> map (h ++) (interl ys t)
splits [] = []
splits (x:xs) = ([x], xs) : map ((h, t) -> (x:h, t)) (splits xs)
The splits function feels a bit awkward. It could be replaced by use of takeWhile or break in combination with splitAt, but that solution ended up a bit awkward as well. Do you have any suggestions?
(I got rid of the do notation just to make it slightly shorter)
Combining the best ideas from the existing answers and adding some of my own:
import Control.Monad
interleave [] ys = return ys
interleave xs [] = return xs
interleave (x : xs) (y : ys) =
fmap (x :) (interleave xs (y : ys)) `mplus` fmap (y :) (interleave (x : xs) ys)
interleavings :: MonadPlus m => [[a]] -> m [a]
interleavings = foldM interleave []
This is not the fastest possible you can get, but it should be good in terms of general and simple.
Can I rewrite this using library functions?
chunks :: ([a] -> ([a], [a])) -> [a] -> [[a]]
chunks f [] = []
chunks f xs = case c of
[] -> cs
ys -> ys : cs
where
(c, rest) = f xs
cs = chunks f rest
If I give it a span-like function that always takes at least one element off the list, it'll consume the list and return a list with sublists of the elements that were broken off each time the function was called.
This looks very much like an unfold:
http://hackage.haskell.org/package/base-4.8.0.0/docs/Data-List.html#v:unfoldr
Maybe something like (untested):
chunks f xs = unfoldr f' xs
where f' [] = Nothing
f' xs' = Just $ f xs'
I want to filter a string with a string.
What I want is to use delete every first occurring char.
myFunc :: String -> String -> String
Like:
myFunc "dddog" "bigdddddog" = "biddg"
In "dddog": 3x d, 1x o, 1x g
In the second string it removed 3x d, 1x o and 1x g
So the output: biddg
I can't use filter for it, because it will delete all occurring chars.
And I struggled a long time with it.
Thanks in advance:)
How about
Prelude> :m +Data.List
Prelude Data.List> "bigdddddog" \\ "dddog"
"biddg"
Not the nicest solution, but you can understand easier what's going on:
myfunc :: String -> String -> String
myfunc [] xs = xs
myfunc (x:xs) ys = myfunc xs $ remove x ys
where
remove _ [] = []
remove x (y:ys) = if x == y then ys else y : remove x ys
As you commented, you want to use guards. Do you mean this?
myfunc :: String -> String -> String
myfunc [] xs = xs
myfunc (x:xs) ys = myfunc xs $ remove x ys
remove :: Char -> String -> String
remove _ [] = []
remove x (y:ys)
| x == y = ys
| otherwise = y : remove x ys
some of the other solutions don't seem to produce the same result you posted. I think I have a simple solution that does what you asked for but I may be misunderstanding what you want. All I do in the following code is go though the list and apply 'delete' to every element in the list. It's not exactly efficient but it gets the job done.
import Data.List
myFunc (x:xs) ys = myFunc xs (delete x ys)
myFunc [] ys = ys
There are perhaps more efficient solutions like storing the "to remove" list in a tree with the number of occurences stored as the value then traversing the main list testing to see if the count at that key was still greater than zero. I think that would give you O(n*lg(m)) (where n is the size of the list to be removed from and m is the size of the "to remove" list) rather than O(n*m) as is the case above. This version could also be maid to be lazy I think.
edit:
Here is the tree version I was talking abut using Data.Map. It's a bit complex but should be more efficient for large lists and it is somewhat lazy
myFunc l ys = myFunc' (makeCount l) ys
where makeCount xs = foldr increment (Map.fromList []) xs
increment x a = Map.insertWith (+) x 1 a
decrement x a = Map.insertWith (flip (-)) x 1 a
getCount x a = case Map.lookup x a of
Just c -> c
Nothing -> 0
myFunc' counts (x:xs) = if (getCount x counts) > 0
then myFunc' (decrement x counts) xs
else x : myFunc' counts xs
myFunc' _ [] = []
I am not quite sure about how you want your function to behave, how about this?
import Data.List (isPrefixOf)
myFunc :: String -> String -> String
myFunc _ [] = []
myFunc y x'#(x:xs) | y `isPrefixOf` x' = drop (length y) x'
| otherwise = x : myFilter xs y
This gives the following output in GHCi:
> myFunc "dddog" "bigdddddog"
> "bigdd"
If this is not what you had in mind, please give another input/output example.
I like kaan's elegant solution. In case you meant this...here's one where the "ddd" would only be removed if matched as a whole:
import Data.List (group,isPrefixOf,delete)
f needles str = g (group needles) str where
g needles [] = []
g needles xxs#(x:xs)
| null needle' = [x] ++ g needles xs
| otherwise = let needle = head needle'
in g (delete needle needles) (drop (length needle) xxs)
where needle' = dropWhile (not . flip isPrefixOf xxs) needles
Output:
*Main> f "dddog" "bigdddddog"
"biddg"
*Main> f "dddog" "bdigdogd"
"bdidgd"
No monadic solution yet, there you go:
import Control.Monad.State
myFunc :: String -> State String String
myFunc [] = return ""
myFunc (x:xs) = get >>= f where
f [] = return (x:xs)
f (y:ys) = if y == x then put ys >> myFunc xs
else myFunc xs >>= return . (x:)
main = do
let (a,b) = runState (myFunc "bigdddddog") "dddog" in
putStr a
Using predefined functions from Data.List,
-- mapAccumL :: (acc -> x -> (acc, y)) -> acc -> [x] -> (acc, [y])
-- lookup :: (Eq a) => a -> [(a, b)] -> Maybe b
{-# LANGUAGE PatternGuards #-}
import Data.List
picks [] = [] -- http://stackoverflow.com/a/9889702/849891
picks (x:xs) = (x,xs) : [ (y,x:ys) | (y,ys) <- picks xs]
myFunc a b = concat . snd $ mapAccumL f (picks a) b
where
f acc x | Just r <- lookup x acc = (picks r,[])
f acc x = (acc,[x])
Testing:
Prelude Data.List> myFunc "dddog" "bigdddddog"
"biddg"
edit: this is of course a bit more complex than (\\). I'll let it stand as an illustration. There could be some merit to it still, as it doesn't copy the 2nd (longer?) string over and over, for each non-matching character from the 1st (shorter) string, as delete apparently does, used in (\\) = foldl (flip delete).
I've been trying to learn a bit of functional programming (with Haskell & Erlang) lately and I'm always amazed at the succinct solutions people can come up with when they can think recursively and know the tools.
I want a function to convert a list of sorted, unique, non-contiguous integers into a list of contiguous lists, i.e:
[1,2,3,6,7,8,10,11]
to:
[[1,2,3], [6,7,8], [10,11]
This was the best I could come up with in Haskell (two functions)::
make_ranges :: [[Int]] -> [Int] -> [[Int]]
make_ranges ranges [] = ranges
make_ranges [] (x:xs)
| null xs = [[x]]
| otherwise = make_ranges [[x]] xs
make_ranges ranges (x:xs)
| (last (last ranges)) + 1 == x =
make_ranges ((init ranges) ++ [(last ranges ++ [x])]) xs
| otherwise = make_ranges (ranges ++ [[x]]) xs
rangify :: [Int] -> [[Int]]
rangify lst = make_ranges [] lst
It might be a bit subjective but I'd be interested to see a better, more elegant, solution to this in either Erlang or Haskell (other functional languages too but I might not understand it.) Otherwise, points for just fixing my crappy beginner's Haskell style!
Most straightforward way in my mind is a foldr:
ranges = foldr step []
where step x [] = [[x]]
step x acc#((y:ys):zs) | y == x + 1 = (x:y:ys):zs
| otherwise = [x]:acc
Or, more concisely:
ranges = foldr step []
where step x ((y:ys):zs) | y == x + 1 = (x:y:ys):zs
step x acc = [x]:acc
But wait, there's more!
abstractRanges f = foldr step []
where step x ((y:ys):zs) | f x y = (x:y:ys):zs
step x acc = [x]:acc
ranges = abstractRanges (\x y -> y == x + 1)
powerRanges = abstractRanges (\x y -> y == x*x) -- mighty morphin
By turning the guard function into a parameter, you can group more interesting things than just +1 sequences.
*Main> powerRanges [1,1,1,2,4,16,3,9,81,5,25]
[[1,1,1],[2,4,16],[3,9,81],[5,25]]
The utility of this particular function is questionable...but fun!
I can't believe I got the shortest solution. I know this is no code golf, but I think it is still quite readable:
import GHC.Exts
range xs = map (map fst) $ groupWith snd $ zipWith (\a b -> (a, a-b)) xs [0..]
or pointfree
range = map (map snd) . groupWith fst . zipWith (\a b -> (b-a, b)) [0..]
BTW, groupWith snd can be replaced with groupBy (\a b -> snd a == snd b) if you prefer Data.List over GHC.Exts
[Edit]
BTW: Is there a nicer way to get rid of the lambda (\a b -> (b-a, b)) than (curry $ (,) <$> ((-) <$> snd <*> fst) <*> snd) ?
[Edit 2]
Yeah, I forgot (,) is a functor. So here is the obfuscated version:
range = map (map fst) . groupWith snd . (flip $ zipWith $ curry $ fmap <$> (-).fst <*> id) [0..]
Suggestions are welcome...
import Data.List (groupBy)
ranges xs = (map.map) snd
. groupBy (const fst)
. zip (True : zipWith ((==) . succ) xs (tail xs))
$ xs
As to how to come up with such a thing: I started with the zipWith f xs (tail xs), which is a common idiom when you want to do something on consecutive elements of a list. Likewise is zipping up a list with information about the list, and then acting (groupBy) upon it. The rest is plumbing.
Then, of course, you can feed it through #pl and get:
import Data.List (groupBy)
import Control.Monad (ap)
import Control.Monad.Instances()
ranges = (((map.map) snd)
. groupBy (const fst))
.) =<< zip
. (True:)
. ((zipWith ((==) . succ)) `ap` tail)
, which, by my authoritative definition, is evil due to Mondad ((->) a). Twice, even. The data flow is meandering too much to lay it out in any sensible way. zipaptail is an Aztec god, and Aztec gods aren't to be messed with.
Another version in Erlang:
part(List) -> part(List,[]).
part([H1,H2|T],Acc) when H1 =:= H2 - 1 ->
part([H2|T],[H1|Acc]);
part([H1|T],Acc) ->
[lists:reverse([H1|Acc]) | part(T,[])];
part([],Acc) -> Acc.
k z = map (fst <$>) . groupBy (const snd) .
zip z . (False:) . (zipWith ((==) . succ) <*> tail) $ z
Try reusing standard functions.
import Data.List (groupBy)
rangeify :: (Num a) => [a] -> [[a]]
rangeify l = map (map fst) $ groupBy (const snd) $ zip l contigPoints
where contigPoints = False : zipWith (==) (map (+1) l) (drop 1 l)
Or, following (mixed) advice to use unfoldr, stop abusing groupBy, and be happy using partial functions when it doesn't matter:
import Control.Arrow ((***))
import Data.List (unfoldr)
spanContig :: (Num a) => [a] -> [[a]]
spanContig l =
map fst *** map fst $ span (\(a, b) -> a == b + 1) $ zip l (head l - 1 : l)
rangeify :: (Num a) => [a] -> [[a]]
rangeify = unfoldr $ \l -> if null l then Nothing else Just $ spanContig l
Erlang using foldr:
ranges(List) ->
lists:foldr(fun (X, [[Y | Ys], Acc]) when Y == X + 1 ->
[[X, Y | Ys], Acc];
(X, Acc) ->
[[X] | Acc]
end, [], List).
This is my v0.1 and I can probably make it better:
makeCont :: [Int] -> [[Int]]
makeCont [] = []
makeCont [a] = [[a]]
makeCont (a:b:xs) = if b - a == 1
then (a : head next) : tail next
else [a] : next
where
next :: [[Int]]
next = makeCont (b:xs)
And I will try and make it better. Edits coming I think.
As a comparison, here's an implementation in Erlang:
partition(L) -> [lists:reverse(T) || T <- lists:reverse(partition(L, {[], []}))].
partition([E|L], {R, [EL|_] = T}) when E == EL + 1 -> partition(L, {R, [E|T]});
partition([E|L], {R, []}) -> partition(L, {R, [E]});
partition([E|L], {R, T}) -> partition(L, {[T|R], [E]});
partition([], {R, []}) -> R;
partition([], {R, T}) -> [T|R].
The standard paramorphism recursion scheme isn't in Haskell's Data.List module, though I think it should be. Here's a solution using a paramorphism, because you are building a list-of-lists from a list, the cons-ing is a little tricksy:
contig :: (Eq a, Num a) => [a] -> [[a]]
contig = para phi [] where
phi x ((y:_),(a:acc)) | x + 1 == y = (x:a):acc
phi x (_, acc) = [x]:acc
Paramorphism is general recursion or a fold with lookahead:
para :: (a -> ([a], b) -> b) -> b -> [a] -> b
para phi b [] = b
para phi b (x:xs) = phi x (xs, para phi b xs)
It can be pretty clear and simple in the Erlang:
partition([]) -> [];
partition([A|T]) -> partition(T, [A]).
partition([A|T], [B|_]=R) when A =:= B+1 -> partition(T, [A|R]);
partition(L, P) -> [lists:reverse(P)|partition(L)].
Edit: Just for curiosity I have compared mine and Lukas's version and mine seems about 10% faster either in native either in bytecode version on testing set what I generated by lists:usort([random:uniform(1000000)||_<-lists:seq(1,1000000)]) on R14B01 64b version at mine notebook. (Testing set is 669462 long and has been partitioned to 232451 sublists.)
Edit2: Another test data lists:usort([random:uniform(1000000)||_<-lists:seq(1,10000000)]), length 999963 and 38 partitions makes bigger diference in native code. Mine version finish in less than half of time. Bytecode version is only about 20% faster.
Edit3: Some microoptimizations which provides additional performance but leads to more ugly and less maintainable code:
part4([]) -> [];
part4([A|T]) -> part4(T, A, []).
part4([A|T], B, R) when A =:= B+1 -> part4(T, A, [B|R]);
part4([A|T], B, []) -> [[B]|part4(T, A, [])];
part4([A|T], B, R) -> [lists:reverse(R, [B])|part4(T, A, [])];
part4([], B, R) -> [lists:reverse(R,[B])].
Here's an attempt from a haskell noob
ranges ls = let (a, r) = foldl (\(r, a#(h:t)) e -> if h + 1 == e then (r, e:a) else (a:r, [e])) ([], [head ls]) (tail ls)
in reverse . map reverse $ r : a