Filling a Tuple consisting of two lists - list

I am trying to fill a tuple consisting of two lists in my function and depending on a condition I want to each fill a different list in this tuple. Code goes as follows:
type One = []
type Two = []
bar :: Int -> Bool
bar ...
foo :: Somelist -> (One, Two)
foo somelist
| null somelist = ([],[])
| bar yesno = {-I want to fill the list "One" here if bar == true-} foo (tail somelist)
| otherwise = {-and the list "Two" here if bar == false-} foo (tail somelist)
What is an elegant and haskelly way to approach this problem :) ?
Thank you for your suggestions.

I have changed the types a little compared to your example to make the code testable.
type One = [Integer]
type Two = [Integer]
bar :: Integer -> Bool
bar x = x > 0
foo :: [Integer] -> (One, Two)
foo [] = ([], [])
foo (x:xs)
| bar x = (x:one, two)
| otherwise = (one, x:two) where
(one, two) = foo xs
A quick test:
λ> foo [-10..10]
([1,2,3,4,5,6,7,8,9,10],[-10,-9,-8,-7,-6,-5,-4,-3,-2,-1,0])
The idea is to recurse down up to the end of the list and return a tuple of lists, then while you come up the recursive stack, grab the returning tuple from the function below and add the value of the current element to the list based on your predicate.
Or you can use partition from Data.List with the type partition :: (a -> Bool) -> [a] -> ([a], [a]). This function takes a list and a predicate and returns a tuple of 2 lists: one where the predicate returned true and the other where it returned false.
import Data.List (partition)
foo2 :: [Integer] -> (One, Two)
foo2 xs = partition bar xs
You can eta reduce the above, but I haven't done that for clarity.

Related

How to compare elements in a [[]]?

I am dealing with small program with Haskell. Probably the answer is really simple but I try and get no result.
So one of the part in my program is the list:
first = [(3,3),(4,6),(7,7),(5,43),(9,9),(32,1),(43,43) ..]
and according to that list I want to make new one with element that are equal in the () =:
result = [3,7,9,43, ..]
Even though you appear to have not made the most minimal amount of effort to solve this question by yourself, I will give you the answer because it is so trivial and because Haskell is a great language.
Create a function with this signature:
findIdentical :: [(Int, Int)] -> [Int]
It takes a list of tuples and returns a list of ints.
Implement it like this:
findIdentical [] = []
findIdentical ((a,b) : xs)
| a == b = a : (findIdentical xs)
| otherwise = findIdentical xs
As you can see, findIdentical is a recursive function that compares a tuple for equality between both items, and then adds it to the result list if there is found equality.
You can do this for instance with list comprehension. We iterate over every tuple f,s) in first, so we write (f,s) <- first in the right side of the list comprehension, and need to filter on the fact that f and s are equal, so f == s. In that case we add f (or s) to the result. So:
result = [ f | (f,s) <- first, f == s ]
We can turn this into a function that takes as input a list of 2-tuples [(a,a)], and compares these two elements, and returns a list [a]:
f :: Eq a => [(a,a)] -> [a]
f dat = [f | (f,s) <- dat, f == s ]
An easy way to do this is to use the Prelude's filter function, which has the type definition:
filter :: (a -> Bool) -> [a] -> [a]
All you need to do is supply predicate on how to filter the elements in the list, and the list to filter. You can accomplish this easily below:
filterList :: (Eq a) => [(a, a)] -> [a]
filterList xs = [x | (x, y) <- filter (\(a, b) -> a == b) xs]
Which behaves as expected:
*Main> filterList [(3,3),(4,6),(7,7),(5,43),(9,9),(32,1),(43,43)]
[3,7,9,43]

Grouping consecutive duplicates in a list?

Very basic but I'm finding the problem frustrating. I'm trying to group consecutive elements of a list:
myList = [1,2,3,4,4,4,5]
becomes
myList = [[1],[2],[3],[4,4,4],[5]]
This is my attempt using foldr with an accumulator:
print $ foldr (\ el acc -> if el /= head (head acc) then el ++ (head acc) else acc) [['a']] myList
I don't understand why I'm getting the following error:
Couldn't match expected type ‘[a0]’ with actual type ‘Int’
In the expression: 'a'
In the expression: ['a']
In the second argument of ‘foldr’, namely ‘[['a']]’
Any advice would be great!
Writing a fold on lists requires us to answer just two cases: [] (the empty list, or "nil") and x:xs (an element followed by a list, or "cons").
What is the answer when the list is empty? Lets say the answer is also an empty list. Therefore:
nilCase = []
What is the answer when the list is not empty? It depends on what we have already accumulated. Lets say we have already accumulated a group. We know that groups are non-empty.
consCase x ((g11:_):gs)
If x == g11 then we add it to the group. Otherwise we begin a new group. Therefore:
consCase x ggs#(g1#(g11:_):gs)
| x == g11 = (x:g1):gs
| otherwise = [x]:ggs
What if we have not accumulated any groups yet? Then we just create a new group.
consCase x [] = [[x]]
We can consolidate the three cases down to two:
consCase x ggs
| g1#(g11:_):gs <- ggs, x == g11 = (x:g1):gs
| otherwise = [x]:ggs
Then the desired fold is simply:
foldr consCase nilCase
Using foldr, it should be:
group :: (Eq a) => [a] -> [[a]]
group = foldr (\x acc -> if head acc == [] || head (head acc) == x then (x:head acc) : tail acc else [x] : acc) [[]]
The type of your case case is [[Char]], you are attempting to build a value of type [[Int]]. Our base case should be an empty list, and we'll add list elements in each step.
Let's look at the anonymous function you're written next. Note that we'll fail due to type based on your current if within the accumulator (they must return values of the same type, and the same type as the accumulator. It'll be better, and cleaner, if we pattern match the accumulator and apply the function differently in each case:
func :: Eq a => [a] -> [[a]]
func = foldr f []
where f x [] = undefined
f x (b#(b1:_):bs)
| x == b1 = undefined
| otherwise = undefined
When we encounter the base case, we should just add the our element wrapped in a list:
f x [] = [[x]]
Next, we'll deal with the non-empty list. If x is equal to the next head of the head of the list, we should add it to that list. Otherwise, we shou
f x (b#(b1:_):bs)
| == b1 = (x:b):bs
| = [x]:b:bs
Putting this together, we have:
func :: Eq a => [a] -> [[a]]
func = foldr f []
where f x [] = [[x]]
f x (b#(b1:_):bs)
| x == b1 = (x:b):bs
| otherwise = [x]:b:bs
Having broken the problem down, it's much easier to rewrite this more compactly with a lambda function. Notice that the head [[]] is just [], so we can handle the empty list case and the equality case as one action. Thus, we can rewrite:
func :: (Eq a) => [a] -> [[a]]
func = foldr (\x (b:bs) -> if b == [] || x == head b then (x:b):bs else [x]:b:bs) [[]]
However, this solution ends up requiring the use of head since we must pattern match all versions of the accumulator.

Haskell function that outputs all combinations within the input list that add to the input number

I want to write a function in haskell that takes a list of integers and an integer value as input and outputs a list of all the lists that contain combinations of elements that add up to the input integer.
For example:
myFunc [3,7,5,9,13,17] 30 = [[13,17],[3,5,9,13]]
Attempt:
myFunc :: [Integer] -> Integer -> [[Integer]]
myFunc list sm = case list of
[] -> []
[x]
| x == sm -> [x]
| otherwise -> []
(x : xs)
| x + myFunc xs == sm -> [x] ++ myFunc[xs]
| otherwise -> myFunc xs
My code produces just one combination and that combination must be consecutive, which is not what I want to achieve
Write a function to create all subsets
f [] = [[]]
f (x:xs) = f xs ++ map (x:) (f xs)
then use the filter
filter ((==30) . sum) $ f [3,7,5,9,13,17]
[[13,17],[3,5,9,13]]
as suggested by #Ingo you can prune the list while it's generated, for example
f :: (Num a, Ord a) => [a] -> [[a]]
f [] = [[]]
f (x:xs) = f xs ++ (filter ((<=30) . sum) $ map (x:) $ f xs)
should work faster than generating all 2^N elements.
You can use subsequences from Data.List to give you every possible combination of values, then filter based on your requirement that they add to 30.
myFunc :: [Integer] -> Integer -> [[Integer]]
myFunc list sm =
filter (\x -> sum x == sm) $ subsequences list
An alternative would be to use a right fold:
fun :: (Foldable t, Num a, Eq a) => t a -> a -> [[a]]
fun = foldr go $ \a -> if a == 0 then [[]] else []
where go x f a = f a ++ ((x:) <$> f (a - x))
then,
\> fun [3,7,5,9,13,17] 30
[[13,17],[3,5,9,13]]
\> fun [3,7,5,9,13,17] 12
[[7,5],[3,9]]
An advantage of this approach is that it does not create any lists unless it adds up to the desired value.
Whereas, an approach based on filtering, will create all the possible sub-sequence lists only to drop most of them during filtering step.
Here is an alternate solution idea: Generate a list of lists that sum up to the target number, i.e.:
[30]
[29,1]
[28,2]
[28,1,1]
...
and only then filter the ones that could be build from your given list.
Pro: could be much faster, especially if your input list is long and your target number comparatively small, such that the list of list of summands is much smaller than the list of subsets of your input list.
Con: does only work when 0 is not in the game.
Finally, you can it do both ways and write a function that decides which algorthm will be faster given some input list and the target number.

Is there a function that takes a list and returns a list of duplicate elements in that list?

Is there a Haskell function that takes a list and returns a list of duplicates/redundant elements in that list?
I'm aware of the the nub and nubBy functions, but they remove the duplicates; I would like to keep the dupes and collects them in a list.
The simplest way to do this, which is extremely inefficient, is to use nub and \\:
import Data.List (nub, (\\))
getDups :: Eq a => [a] -> [a]
getDups xs = xs \\ nub xs
If you can live with an Ord constraint, everything gets much nicer:
import Data.Set (member, empty, insert)
getDups :: Ord a => [a] -> [a]
getDups xs = foldr go (const []) xs empty
where
go x cont seen
| member x seen = x : r seen
| otherwise = r (insert x seen)
I wrote these functions which seems to work well.
The first one return the list of duplicates element in a list with a basic equlity test (==)
duplicate :: Eq a => [a] -> [a]
duplicate [] = []
duplicate (x:xs)
| null pres = duplicate abs
| otherwise = x:pres++duplicate abs
where (pres,abs) = partition (x ==) xs
The second one make the same job by providing a equality test function (like nubBy)
duplicateBy :: (a -> a -> Bool) -> [a] -> [a]
duplicateBy eq [] = []
duplicateBy eq (x:xs)
| null pres = duplicateBy eq abs
| otherwise = x:pres++duplicateBy eq abs
where (pres,abs) = partition (eq x) xs
Is there a Haskell function that takes a list and returns a list of duplicates/redundant elements in that list?
You can write such a function yourself easily enough. Use a helper function that takes two list arguments, the first one of which being the list whose dupes are sought; walk along that list and accumulate the dupes in the second argument; finally, return the latter when the first argument is the empty list.
dupes l = dupes' l []
where
dupes' [] ls = ls
dupes' (x:xs) ls
| not (x `elem` ls) && x `elem` xs = dupes' xs (x:ls)
| otherwise = dupes' xs ls
Test:
λ> dupes [1,2,3,3,2,2,3,4]
[3,2]
Be aware that the asymptotic time complexity is as bad as that of nub, though: O(n^2). If you want better asymptotics, you'll need an Ord class constraint.
If you are happy with an Ord constraint you can use group from Data.List:
getDups :: Ord a => [a] -> [a]
getDups = concatMap (drop 1) . group . sort

unique elements in a haskell list

okay, this is probably going to be in the prelude, but: is there a standard library function for finding the unique elements in a list? my (re)implementation, for clarification, is:
has :: (Eq a) => [a] -> a -> Bool
has [] _ = False
has (x:xs) a
| x == a = True
| otherwise = has xs a
unique :: (Eq a) => [a] -> [a]
unique [] = []
unique (x:xs)
| has xs x = unique xs
| otherwise = x : unique xs
I searched for (Eq a) => [a] -> [a] on Hoogle.
First result was nub (remove duplicate elements from a list).
Hoogle is awesome.
The nub function from Data.List (no, it's actually not in the Prelude) definitely does something like what you want, but it is not quite the same as your unique function. They both preserve the original order of the elements, but unique retains the last
occurrence of each element, while nub retains the first occurrence.
You can do this to make nub act exactly like unique, if that's important (though I have a feeling it's not):
unique = reverse . nub . reverse
Also, nub is only good for small lists.
Its complexity is quadratic, so it starts to get slow if your list can contain hundreds of elements.
If you limit your types to types having an Ord instance, you can make it scale better.
This variation on nub still preserves the order of the list elements, but its complexity is O(n * log n):
import qualified Data.Set as Set
nubOrd :: Ord a => [a] -> [a]
nubOrd xs = go Set.empty xs where
go s (x:xs)
| x `Set.member` s = go s xs
| otherwise = x : go (Set.insert x s) xs
go _ _ = []
In fact, it has been proposed to add nubOrd to Data.Set.
import Data.Set (toList, fromList)
uniquify lst = toList $ fromList lst
I think that unique should return a list of elements that only appear once in the original list; that is, any elements of the orginal list that appear more than once should not be included in the result.
May I suggest an alternative definition, unique_alt:
unique_alt :: [Int] -> [Int]
unique_alt [] = []
unique_alt (x:xs)
| elem x ( unique_alt xs ) = [ y | y <- ( unique_alt xs ), y /= x ]
| otherwise = x : ( unique_alt xs )
Here are some examples that highlight the differences between unique_alt and unqiue:
unique [1,2,1] = [2,1]
unique_alt [1,2,1] = [2]
unique [1,2,1,2] = [1,2]
unique_alt [1,2,1,2] = []
unique [4,2,1,3,2,3] = [4,1,2,3]
unique_alt [4,2,1,3,2,3] = [4,1]
I think this would do it.
unique [] = []
unique (x:xs) = x:unique (filter ((/=) x) xs)
Another way to remove duplicates:
unique :: [Int] -> [Int]
unique xs = [x | (x,y) <- zip xs [0..], x `notElem` (take y xs)]
Algorithm in Haskell to create a unique list:
data Foo = Foo { id_ :: Int
, name_ :: String
} deriving (Show)
alldata = [ Foo 1 "Name"
, Foo 2 "Name"
, Foo 3 "Karl"
, Foo 4 "Karl"
, Foo 5 "Karl"
, Foo 7 "Tim"
, Foo 8 "Tim"
, Foo 9 "Gaby"
, Foo 9 "Name"
]
isolate :: [Foo] -> [Foo]
isolate [] = []
isolate (x:xs) = (fst f) : isolate (snd f)
where
f = foldl helper (x,[]) xs
helper (a,b) y = if name_ x == name_ y
then if id_ x >= id_ y
then (x,b)
else (y,b)
else (a,y:b)
main :: IO ()
main = mapM_ (putStrLn . show) (isolate alldata)
Output:
Foo {id_ = 9, name_ = "Name"}
Foo {id_ = 9, name_ = "Gaby"}
Foo {id_ = 5, name_ = "Karl"}
Foo {id_ = 8, name_ = "Tim"}
A library-based solution:
We can use that style of Haskell programming where all looping and recursion activities are pushed out of user code and into suitable library functions. Said library functions are often optimized in ways that are way beyond the skills of a Haskell beginner.
A way to decompose the problem into two passes goes like this:
produce a second list that is parallel to the input list, but with duplicate elements suitably marked
eliminate elements marked as duplicates from that second list
For the first step, duplicate elements don't need a value at all, so we can use [Maybe a] as the type of the second list. So we need a function of type:
pass1 :: Eq a => [a] -> [Maybe a]
Function pass1 is an example of stateful list traversal where the state is the list (or set) of distinct elements seen so far. For this sort of problem, the library provides the mapAccumL :: (s -> a -> (s, b)) -> s -> [a] -> (s, [b]) function.
Here the mapAccumL function requires, besides the initial state and the input list, a step function argument, of type s -> a -> (s, Maybe a).
If the current element x is not a duplicate, the output of the step function is Just x and x gets added to the current state. If x is a duplicate, the output of the step function is Nothing, and the state is passed unchanged.
Testing under the ghci interpreter:
$ ghci
GHCi, version 8.8.4: https://www.haskell.org/ghc/ :? for help
λ>
λ> stepFn s x = if (elem x s) then (s, Nothing) else (x:s, Just x)
λ>
λ> import Data.List(mapAccumL)
λ>
λ> pass1 xs = mapAccumL stepFn [] xs
λ>
λ> xs2 = snd $ pass1 "abacrba"
λ> xs2
[Just 'a', Just 'b', Nothing, Just 'c', Just 'r', Nothing, Nothing]
λ>
Writing a pass2 function is even easier. To filter out Nothing non-values, we could use:
import Data.Maybe( fromJust, isJust)
pass2 = (map fromJust) . (filter isJust)
but why bother at all ? - as this is precisely what the catMaybes library function does.
λ>
λ> import Data.Maybe(catMaybes)
λ>
λ> catMaybes xs2
"abcr"
λ>
Putting it all together:
Overall, the source code can be written as:
import Data.Maybe(catMaybes)
import Data.List(mapAccumL)
uniques :: (Eq a) => [a] -> [a]
uniques = let stepFn s x = if (elem x s) then (s, Nothing) else (x:s, Just x)
in catMaybes . snd . mapAccumL stepFn []
This code is reasonably compatible with infinite lists, something occasionally referred to as being “laziness-friendly”:
λ>
λ> take 5 $ uniques $ "abacrba" ++ (cycle "abcrf")
"abcrf"
λ>
Efficiency note:
If we anticipate that it is possible to find many distinct elements in the input list and we can have an Ord a instance, the state can be implemented as a Set object rather than a plain list, this without having to alter the overall structure of the solution.
Here's a solution that uses only Prelude functions:
uniqueList theList =
if not (null theList)
then head theList : filter (/= head theList) (uniqueList (tail theList))
else []
I'm assuming this is equivalent to running two or three nested "for" loops (running through each element, then running through each element again to check for other elements with the same value, then removing those other elements) so I'd estimate this is O(n^2) or O(n^3)
Might even be better than reversing a list, nubbing it, then reversing it again, depending on your circumstances.