Modify a list's elements based on element index - list

Using Haskell:
Let's say I have list: [1,3,4,2,3]
And I want to modify all 3's in the list. I know that I can apply this to select the 3's in this case:
map (\x -> if p x then f x else x) xs
However, the functions being applied to the threes is dependent on their index within the list.
So for example if the index was added to the desired number the output of the function I'm going for would be: [1,4,4,2,7].

You can use zipWith :: (a -> b -> c) -> [a] -> [b] -> [c] for this:
zipWith (\i x -> if p x then f i x else x) [0..] xs
where f thus takes i (the index) and x (the element) both into account.
For example:
zipWith (\i x -> if x == 3 then (i+x) else x) [0..] xs
Which generates the desired output:
Prelude> let xs = [1,3,4,2,3]
Prelude> zipWith (\i x -> if x == 3 then (i+x) else x) [0..] xs
[1,4,4,2,7]
You can encapsulate this logic into a separate function, for instance imap :: (Enum n, Num n) => (n -> a -> b) -> [a] -> b:
imap :: (Enum n, Num n) => (n -> a -> b) -> [a] -> b
imap = flip zipWith [0..]
This will work with any type that is an instance of Num and Enum (so Integer, Int, Float,...).

While zipWith is probably the right way, just for a variety you may go recursive as follows;
tpi :: [Int] -> [Int]
tpi = runner 0
where runner _ [] = []
runner n (x:xs) | x == 3 = (n + x) : runner (n+1) xs
| otherwise = x : runner (n+1) xs

Related

Sum corresponding elements of two lists, with the extra elements of the longer list added at the end

I'm trying to add two lists together and keep the extra elements that are unused and add those into the new list e.g.
addLists [1,2,3] [1,3,5,7,9] = [2,5,8,7,9]
I have this so far:
addLists :: Num a => [a] -> [a] -> [a]
addLists xs ys = zipWith (+) xs ys
but unsure of how to get the extra elements into the new list.
and the next step is changing this to a higher order function that takes the combining function
as an argument:
longZip :: (a -> a -> a) -> [a] -> [a] -> [a]
zipWith :: (a -> b -> c) -> [a] -> [b] -> [c] is implemented as [src]:
zipWith :: (a->b->c) -> [a]->[b]->[c]
zipWith f = go
where
go [] _ = []
go _ [] = []
go (x:xs) (y:ys) = f x y : go xs ys
It thus uses explicit recursion where go will check if the two lists are non-empty and in that case yield f x y, otherwise it stops and returns an empty list [].
You can implement a variant of zipWith which will continue, even if one of the lists is empty. THis will look like:
zipLongest :: (a -> a -> a) -> [a] -> [a] -> [a]
zipLongest f = go
where go [] ys = …
go xs [] = …
go (x:xs) (y:ys) = f x y : go xs ys
where you still need to fill in ….
You can do it with higher order functions as simple as
import Data.List (transpose)
addLists :: Num a => [a] -> [a] -> [a]
addLists xs ys = map sum . transpose $ [xs, ys]
because the length of transpose[xs, ys, ...] is the length of the longest list in its argument list, and sum :: (Foldable t, Num a) => t a -> a is already defined to sum the elements of a list (since lists are Foldable).
transpose is used here as a kind of a zip (but cutting on the longest instead of the shortest list), with [] being a default element for the lists addition ++, like 0 is a default element for the numbers addition +:
cutLongest [xs, ys] $
zipWith (++) (map pure xs ++ repeat []) (map pure ys ++ repeat [])
See also:
Zip with default value instead of dropping values?
You're looking for the semialign package. It gives you an operation like zipping, but that keeps going until both lists run out. It also generalizes to types other than lists, such as rose trees. In your case, you'd use it like this:
import Data.Semialign
import Data.These
addLists :: (Semialign f, Num a) => f a -> f a -> f a
addLists = alignWith (mergeThese (+))
longZip :: Semialign f => (a -> a -> a) -> f a -> f a -> f a
longZip = alignWith . mergeThese
The new type signatures are optional. If you want, you can keep using your old ones that restrict them to lists.

How to enhance small Haskell Code Snippet

just recently I started to try out haskell.
It's fun trying out different exercises, but sometimes I get the feeling, that my found solutions are far from elegant: The following Code Snipplet will find the longest sub-sequence in a list, which will satisfy a given condition (for example uppercase letters etc.)
Could you help a noob to make everything shorter and more elegant - every advice is highly appreciated.
import Data.Char
longer :: [a] -> [a] -> [a]
longer x y = if length x > length y
then x
else y
longest :: [[a]]->[a]
longest = foldl longer []
nextSequence :: (a->Bool) -> [a] ->([a],[a])
nextSequence f x = span f (dropWhile (not . f) x)
longestSubsequence :: (a -> Bool) -> [a] -> [a]
longestSubsequence _ x | null x = []
longestSubsequence f x =
longest $ (\y -> [fst y , longestSubsequence f $ snd y]) (nextSequence f x)
testSequence :: String
testSequence = longestSubsequence Data.Char.isUpper
"hkerhklehrERJKJKJERKJejkrjekERHkhkerHERKLJHERJKHKJHERdjfkj"
At first, you can define your longest like this:
import Data.Function
import Data.List
longest :: [[a]] -> [a]
longest = maximumBy (compare `on` length)
And to get all subsequences that satisfy a given condition you can write a function like this:
import Data.List
getSatisfyingSubseqs :: (a -> Bool) -> [a] -> [[a]]
getSatisfyingSubseqs f = filter (f . head) . groupBy same
where same x y = f x == f y
Here we group elements where the condition yields the same result and filter only subsequences that satisfy the condition.
In the total:
longestSubsequence :: (a -> Bool) -> [a] -> [a]
longestSubsequence f = longest . getSatisfyingSubseqs f
UPDATE: And if you want to make it shorter, you can just throw out the auxiliary functions and write the whole at a time:
longestSubsequence :: (a -> Bool) -> [a] -> [a]
longestSubsequence f = maximumBy (compare `on` length) . filter (f . head) . groupBy same
where same x y = f x == f y
(Don't forget the imports)
You can run it there: https://repl.it/#Yuri12358/so-longestsequence
The span :: (a -> Bool) -> [a] -> ([a], [a]) function could be very handy here. Also note that f <$> (a,b) = (a,f b). Probably not very efficient due to the length checks but it should do the job.
lss :: (a -> Bool) -> [a] -> [a]
lss f [] = []
lss f ls#(x:xs) = if f x then longer (lss f <$> span f ls)
else lss f xs
where
longer ::([a],[a]) -> [a]
longer (xs,ys) = if length xs >= length ys then xs else ys
Your longer function uses length, which means it doesn't work if either input is infinite. However, it can be improved to work when at most one is infinite:
longer l1 l2 = go l1 l2
where
go [] _ = l2
go _ [] = l1
go (_:xs) (_:ys) = go xs ys
This is also a performance optimization. Before, if you had a 10-element list and a 10-million-element list, it would walk through all 10 million elements of the 10-million-element list before returning it. Here, it will return it as soon as it gets to the 11th element instead.

Breaking up a list into sublists with recursion

I'm trying to write a function with the type declaration [(Int, Bool)] -> [[Int]]. I want the function to only add Ints to the same nested sublist if the Boolean is True. However if the Boolean is False, I want the Int associated with the next True bool to be added to a new sublist. For example: An input of
[(1,True),(2,True),(3,False),(4,True),(5,False),(6,False),(7,True)]
should return
[[1,2],[4],[7]].
My code so far:
test:: [(Int, Bool)] -> [[Int]]
test xs = case xs of
[]->[]
x:xs
| snd x == True -> [(fst x)] : test xs
| snd x == False -> test xs
I'm currently having issues on adding concurrent Ints to the same list if their bools are both True.
You can break this problem into two sub-problems.
For any given list, take the head of this list and match it against the rest of list. There are two possibilities during this matching: i) You are successful i.e. you match, and if so, you collect the matched value and continue looking for more values, or ii) You fail, i.e. you don't match, and if so, you stop immediately and return the so far matched result with rest of, not-inspected, list.
collectF :: (Eq a) => (a -> Bool) -> [a] -> ([a], [a])
collectF f [] = ([], [])
collectF f (x : xs)
| f x = let (ys, zs) = collectF f xs in (x : ys, zs)
| otherwise = ([], x : xs)
Now that you have the collectF function, you can use it recursively on input list. In each call, you would get a successful list with rest of, not-inspected, list. Apply collectF again on rest of list until it is exhausted.
groupBy :: (Eq a) => (a -> a -> Bool) -> [a] -> [[a]]
groupBy _ [] = []
groupBy f (x : xs) =
let (ys, zs) = collectF (f x) xs in
(x : ys) : groupBy f zs
*Main> groupBy (\x y -> snd x == snd y) [(1,True),(2,True),(3,False),(4,True),(5,False),(6,False),(7,True)]
[[(1,True),(2,True)],[(3,False)],[(4,True)],[(5,False),(6,False)],[(7,True)]]
I am leaving it to you to remove the True and False values from List. Also, have a look at List library of Haskell [1]. Hope, I am clear enough, but let me know if you have any other question.
[1] http://hackage.haskell.org/package/base-4.12.0.0/docs/src/Data.OldList.html#groupBy
Repeatedly, drop the Falses, grab the Trues. With view patterns:
{-# LANGUAGE ViewPatterns #-}
test :: [(a, Bool)] -> [[a]]
test (span snd . dropWhile (not . snd) -> (a,b))
| null a = []
| otherwise = map fst a : test b
Works with infinite lists as well, inasmuch as possible.
Here's how I'd write this:
import Data.List.NonEmpty (NonEmpty(..), (<|))
import qualified Data.List.NonEmpty as NE
test :: [(Int, Bool)] -> [[Int]]
test = NE.filter (not . null) . foldr go ([]:|[])
where
go :: (Int, Bool) -> NonEmpty [Int] -> NonEmpty [Int]
go (n, True) ~(h:|t) = (n:h):|t
go (n, False) l = []<|l
Or with Will Ness's suggestion:
import Data.List.NonEmpty (NonEmpty(..))
test :: [(Int, Bool)] -> [[Int]]
test = removeHeadIfEmpty . foldr prependOrStartNewList ([]:|[])
where
prependOrStartNewList :: (Int, Bool) -> NonEmpty [Int] -> NonEmpty [Int]
prependOrStartNewList (n, True) ~(h:|t) = (n:h):|t
prependOrStartNewList (n, False) l = []:|removeHeadIfEmpty l
removeHeadIfEmpty :: NonEmpty [Int] -> [[Int]]
removeHeadIfEmpty (h:|t) = if null h then t else h:t

Combine 2 list functions into 1?

How would I combine the following 2 functions:
replaceNth n newVal (x:xs)
| n == 0 = newVal:xs
| otherwise = x:replaceNth (n-1) newVal xs
replaceMthNth m n v arg = replaceNth m (replaceNth n v (arg !! m)) arg
into a single function?
Is it possible?
This is pretty hideous but it does the job:
replacemn 0 0 z ((x : xs) : xss) = (z : xs) : xss
replacemn 0 n z ((x : xs) : xss) =
let (ys : yss) = replacemn 0 (n-1) z (xs : xss)
in ((x : ys) : yss)
replacemn m n z (xs:xss) = xs : replacemn (m-1) n z xss
Function composition
Functions in Haskell may be composed at no cost. E.g. given two functions, f and g, you can compose them into a new function: f . g, which applies g to an argument, then applies f to the result. You should be able to use composition in the same way here.
Ok, here it is with no other named functions in the global namespace, or using any where or let clauses or any other global functions.
{-# LANGUAGE ScopedTypeVariables,RankNTypes #-}
module Temp where
newtype Mu a = Mu (Mu a -> a)
replaceMthNth :: Int -> Int -> a -> [[a]] -> [[a]]
replaceMthNth = (\h (f :: Int -> forall b . b -> [b] -> [b]) -> h f f)
( \replaceNth replaceNth' ->
-- definition of replaceMthNth in terms of some replaceNth and replaceNth'
\m n v arg -> replaceNth m (replaceNth' n v (arg !! m)) arg
)
$
-- y combinator
((\f -> (\h -> h $ Mu h) $ \x -> f $ (\(Mu g) -> g) x $ x) :: (a -> a) -> a) $
(\replaceNth ->
-- definition of replaceNth given a recursive definition
(\(n::Int) newVal xs -> case xs of
[] -> []
(x:xs) -> if n == 0 then newVal:xs else x:replaceNth (n-1) newVal xs
)
)
I don't understand what the question is at all :), but here is how I would implement it:
modifyNth :: Int -> (a -> a) -> [a] -> [a]
modifyNth n f (x:xs)
| n == 0 = f x : xs
| otherwise = x : modifyNth (n-1) f xs
replaceNthMth :: Int -> Int -> a -> [[a]] -> [[a]]
replaceNthMth m n v = modifyNth m (modifyNth n (const v))
This way you don't need to traverse the list twice (first time with !!, second time with replaceNth)
Here's a grotesque implementation that rebuilds the 2d list structure with nested list comprehensions over zips with infinite lists:
replaceMthNth :: Int -> Int -> a -> [[a]] -> [[a]]
replaceMthNth m n v ass = [[if (x,y) == (m,n) then v else a
| (y, a) <- zip [0..] as]
| (x, as) <- zip [0..] ass]

Remove elements by index in haskell

I'm new in haskell and I'm looking for some standard functions to work with lists by indexes.
My exact problem is that i want to remove 3 elements after every 5. If its not clear enough here is illustration:
OOOOOXXXOOOOOXXX...
I know how to write huge function with many parameters, but is there any clever way to do this?
Two completely different approaches
You can use List.splitAt together with drop:
import Data.List (splitAt)
f :: [a] -> [a]
f [] = []
f xs = let (h, t) = splitAt 5 xs in h ++ f (drop 3 t)
Now f [1..12] yields [1,2,3,4,5,9,10,11,12]. Note that this function can be expressed more elegantly using uncurry and Control.Arrow.second:
import Data.List (splitAt)
import Control.Arrow (second)
f :: [a] -> [a]
f [] = []
f xs = uncurry (++) $ second (f . drop 3) $ splitAt 5 xs
Since we're using Control.Arrow anyway, we can opt to drop splitAt and instead call in the help of Control.Arrow.(&&&), combined with take:
import Control.Arrow ((&&&))
f :: [a] -> [a]
f [] = []
f xs = uncurry (++) $ (take 5 &&& (f . drop 8)) xs
But now it's clear that an even shorter solution is the following:
f :: [a] -> [a]
f [] = []
f xs = take 5 xs ++ (f . drop 8) xs
As Chris Lutz notes, this solution can then be generalized as follows:
nofm :: Int -> Int -> [a] -> [a]
nofm _ _ [] = []
nofm n m xs = take n xs ++ (nofm n m . drop m) xs
Now nofm 5 8 yields the required function. Note that a solution with splitAt may still be more efficient!
Apply some mathematics using map, snd, filter, mod and zip:
f :: [a] -> [a]
f = map snd . filter (\(i, _) -> i `mod` 8 < (5 :: Int)) . zip [0..]
The idea here is that we pair each element in the list with its index, a natural number i. We then remove those elements for which i % 8 > 4. The general version of this solution is:
nofm :: Int -> Int -> [a] -> [a]
nofm n m = map snd . filter (\(i, _) -> i `mod` m < n) . zip [0..]
Here is my take:
deleteAt idx xs = lft ++ rgt
where (lft, (_:rgt)) = splitAt idx xs
You can count your elements easily:
strip' (x:xs) n | n == 7 = strip' xs 0
| n >= 5 = strip' xs (n+1)
| n < 5 = x : strip' xs (n+1)
strip l = strip' l 0
Though open-coding looks shorter:
strip (a:b:c:d:e:_:_:_:xs) = a:b:c:d:e:strip xs
strip (a:b:c:d:e:xs) = a:b:c:d:e:[]
strip xs = xs
Since nobody did a version with "unfoldr", here is my take:
drop3after5 lst = concat $ unfoldr chunk lst
where
chunk [] = Nothing
chunk lst = Just (take 5 lst, drop (5+3) lst)
Seems to be the shortest thus far
the take and drop functions may be able to help you here.
drop, take :: Int -> [a] -> [a]
from these we could construct a function to do one step.
takeNdropM :: Int -> Int -> [a] -> ([a], [a])
takeNdropM n m list = (take n list, drop (n+m) list)
and then we can use this to reduce our problem
takeEveryNafterEveryM :: Int -> Int -> [a] -> [a]
takeEveryNafterEveryM n m [] = []
takeEveryNafterEveryM n m list = taken ++ takeEveryNafterEveryM n m rest
where
(taken, rest) = takeNdropM n m list
*Main> takeEveryNafterEveryM 5 3 [1..20]
[1,2,3,4,5,9,10,11,12,13,17,18,19,20]
since this is not a primitive form of recursion, it is harder to express this as a simple fold.
so a new folding function could be defined to fit your needs
splitReduce :: ([a] -> ([a], [a])) -> [a] -> [a]
splitReduce f [] = []
splitReduce f list = left ++ splitReduce f right
where
(left, right) = f list
then the definition of takeEveryNafterEveryM is simply
takeEveryNafterEveryM2 n m = splitReduce (takeNdropM 5 3)
This is my solution. It's a lot like #barkmadley's answer, using only take and drop, but with less clutter in my opinion:
takedrop :: Int -> Int -> [a] -> [a]
takedrop _ _ [] = []
takedrop n m l = take n l ++ takedrop n m (drop (n + m) l)
Not sure if it'll win any awards for speed or cleverness, but I think it's pretty clear and concise, and it certainly works:
*Main> takedrop 5 3 [1..20]
[1,2,3,4,5,9,10,11,12,13,17,18,19,20]
*Main>
Here is my solution:
remElements step num=rem' step num
where rem' _ _ []=[]
rem' s n (x:xs)
|s>0 = x:rem' (s-1) num xs
|n==0 = x:rem' (step-1) num xs
|otherwise= rem' 0 (n-1) xs
example:
*Main> remElements 5 3 [1..20]
[1,2,3,4,5,9,10,11,12,13,17,18,19,20]
myRemove = map snd . filter fst . zip (cycle $ (replicate 5 True) ++ (replicate 3 False))