Convert list haskell - list

I have this list ([Integer],[Integer])
which I want to convert into [(Integer,Integer)].
From what I've read I should use high order functions like map.
alterList :: ([Integer],[Integer]) -> [(Integer,Integer)]
alterList a = map(\a -> .....?)
Any guidelines? Both lists are of the same size.
Like I have two lists ([1,2,3,4],[5,6,7,9]) which I want to convert to [(1,5),(2,6),(3,7),(4,8)]

So after you've corrected your post, I think you want
alterList :: ([Integer],[Integer]) -> [(Integer,Integer)]
alterList (l1, l2) = zip l1 l2
Example:
>>> alterList ([1,2,3,4],[5,6,7,9])
[(1,5),(2,6),(3,7),(4,9)]
This is equivalent to
alterList' :: ([Integer],[Integer]) -> [(Integer,Integer)]
alterList' = uncurry zip
Note that this function works even if the two lists have not the same size: in this case it acts as if the longest list were truncated to the length of the shortest one.

Related

Manipulating a list using pattern-matching

I want to write a function which takes a list as input value and manipulates it the following way:
Step 1: Put every 3 elements of the list in a sublist.
Should there remain less then 3 elements the remaining elements are put together in a specific sublist which is not going to be relevant in Step 2.
Step 2: Reverse the order of the elements in the created sublists.
The first element should be placed at the position of the third element, the second at the position of first element and the third element at the position of the second element. ([1,2,3] transformed to [2,3,1])
Example:
[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17]
-- should be transformed to
[[2,3,1],[5,6,4],[8,9,7],[11,12,10],[14,15,13],[16,17]]
So far I found the following approach to put every 3 elements together in sublists but I am not quite sure how to change the order of the elements in every sublist to match the requirements.
splitEvery :: Int -> [a] -> [[a]]
splitEvery _ [] = []
splitEvery n xs = as : splitEvery n bs
where (as,bs) = splitAt n xs
If the inner lists are always 3 elements, then you can hardcode that fact and use a simple solution like this:
f :: [a] -> [[a]]
f [] = []
f (x1:x2:x3:xs) = [x2,x3,x1]:f xs
f xs = [xs]
You can achieve your goal using take and drop as well
f [] = []
f xs = (take 3 xs) : f2 (drop 3 xs)
Idiomatic Haskell would be much better than other answers here. Basically, try to always design the API so it contains the proof that no corner case could occur. Hardcoding literals or hardcoding flip-like operations on lists (without guarantees of its length) are ALWAYS BAD.
{-# LANGUAGE LambdaCase #-}
divide : [a] -> [Either [a] (a,a,a)]
divide = \case
[] -> []
t1:t2:t3:ts -> Right (t1,t2,t3) : divide ts
ts -> [Left ts]
process :: [Either [a] (a,a,a)] -> [[a]]
process = fmap (flatten . flipEls) where
flipEls = fmap $ \(t1,t2,t3) -> [t2,t1,t3]
flatten = either id id
Now, you can just it like process . divide

Haskell function to keep the repeating elements of a list

Here is the expected input/output:
repeated "Mississippi" == "ips"
repeated [1,2,3,4,2,5,6,7,1] == [1,2]
repeated " " == " "
And here is my code so far:
repeated :: String -> String
repeated "" = ""
repeated x = group $ sort x
I know that the last part of the code doesn't work. I was thinking to sort the list then group it, then I wanted to make a filter on the list of list which are greater than 1, or something like that.
Your code already does half of the job
> group $ sort "Mississippi"
["M","iiii","pp","ssss"]
You said you want to filter out the non-duplicates. Let's define a predicate which identifies the lists having at least two elements:
atLeastTwo :: [a] -> Bool
atLeastTwo (_:_:_) = True
atLeastTwo _ = False
Using this:
> filter atLeastTwo . group $ sort "Mississippi"
["iiii","pp","ssss"]
Good. Now, we need to take only the first element from such lists. Since the lists are non-empty, we can use head safely:
> map head . filter atLeastTwo . group $ sort "Mississippi"
"ips"
Alternatively, we could replace the filter with filter (\xs -> length xs >= 2) but this would be less efficient.
Yet another option is to use a list comprehension
> [ x | (x:_y:_) <- group $ sort "Mississippi" ]
"ips"
This pattern matches on the lists starting with x and having at least another element _y, combining the filter with taking the head.
Okay, good start. One immediate problem is that the specification requires the function to work on lists of numbers, but you define it for strings. The list must be sorted, so its elements must have the typeclass Ord. Therefore, let’s fix the type signature:
repeated :: Ord a => [a] -> [a]
After calling sort and group, you will have a list of lists, [[a]]. Let’s take your idea of using filter. That works. Your predicate should, as you said, check the length of each list in the list, then compare that length to 1.
Filtering a list of lists gives you a subset, which is another list of lists, of type [[a]]. You need to flatten this list. What you want to do is map each entry in the list of lists to one of its elements. For example, the first. There’s a function in the Prelude to do that.
So, you might fill in the following skeleton:
module Repeated (repeated) where
import Data.List (group, sort)
repeated :: Ord a => [a] -> [a]
repeated = map _
. filter (\x -> _)
. group
. sort
I’ve written this in point-free style with the filtering predicate as a lambda expression, but many other ways to write this are equally good. Find one that you like! (For example, you could also write the filter predicate in point-free style, as a composition of two functions: a comparison on the result of length.)
When you try to compile this, the compiler will tell you that there are two typed holes, the _ entries to the right of the equal signs. It will also tell you the type of the holes. The first hole needs a function that takes a list and gives you back a single element. The second hole needs a Boolean expression using x. Fill these in correctly, and your program will work.
Here's some other approaches, to evaluate #chepner's comment on the solution using group $ sort. (Those solutions look simpler, because some of the complexity is hidden in the library routines.)
While it's true that sorting is O(n lg n), ...
It's not just the sorting but especially the group: that uses span, and both of them build and destroy temporary lists. I.e. they do this:
a linear traversal of an unsorted list will require some other data structure to keep track of all possible duplicates, and lookups in each will add to the space complexity at the very least. While carefully chosen data structures could be used to maintain an overall O(n) running time, the constant would probably make the algorithm slower in practice than the O(n lg n) solution, ...
group/span adds considerably to that complexity, so O(n lg n) is not a correct measure.
while greatly complicating the implementation.
The following all traverse the input list just once. Yes they build auxiliary lists. (Probably a Set would give better performance/quicker lookup.) They maybe look more complex, but to compare apples with apples look also at the code for group/span.
repeated2, repeated3, repeated4 :: Ord a => [a] -> [a]
repeated2/inserter2 builds an auxiliary list of pairs [(a, Bool)], in which the Bool is True if the a appears more than once, False if only once so far.
repeated2 xs = sort $ map fst $ filter snd $ foldr inserter2 [] xs
inserter2 :: Ord a => a -> [(a, Bool)] -> [(a, Bool)]
inserter2 x [] = [(x, False)]
inserter2 x (xb#(x', _): xs)
| x == x' = (x', True): xs
| otherwise = xb: inserter2 x xs
repeated3/inserter3 builds an auxiliary list of pairs [(a, Int)], in which the Int counts how many of the a appear. The aux list is sorted anyway, just for the heck of it.
repeated3 xs = map fst $ filter ((> 1).snd) $ foldr inserter3 [] xs
inserter3 :: Ord a => a -> [(a, Int)] -> [(a, Int)]
inserter3 x [] = [(x, 1)]
inserter3 x xss#(xc#(x', c): xs) = case x `compare` x' of
{ LT -> ((x, 1): xss)
; EQ -> ((x', c+1): xs)
; GT -> (xc: inserter3 x xs)
}
repeated4/go4 builds an output list of elements known to repeat. It maintains an intermediate list of elements met once (so far) as it traverses the input list. If it meets a repeat: it adds that element to the output list; deletes it from the intermediate list; filters that element out of the tail of the input list.
repeated4 xs = sort $ go4 [] [] xs
go4 :: Ord a => [a] -> [a] -> [a] -> [a]
go4 repeats _ [] = repeats
go4 repeats onces (x: xs) = case findUpd x onces of
{ (True, oncesU) -> go4 (x: repeats) oncesU (filter (/= x) xs)
; (False, oncesU) -> go4 repeats oncesU xs
}
findUpd :: Ord a => a -> [a] -> (Bool, [a])
findUpd x [] = (False, [x])
findUpd x (x': os) | x == x' = (True, os) -- i.e. x' removed
| otherwise =
let (b, os') = findUpd x os in (b, x': os')
(That last bit of list-fiddling in findUpd is very similar to span.)

Haskell list length alternative

Hi I've got a list on Haskell with close to 10^15 Int's in it and I'm trying print the length of the list.
let list1 = [1..1000000000000000] -- this is just a dummy list I dont
print list1 length -- know the actual number of elements
printing this takes a very long time to do, is there another way to get the number of elements in the list and print that number?
I've occasionally gotten some value out of lists that carry their length. The poor man's version goes like this:
import Data.Monoid
type ListLength a = (Sum Integer, [a])
singletonLL :: a -> ListLength a
singletonLL x = (1, [x])
lengthLL :: ListLength a -> Integer
lengthLL (Sum len, _) = len
The Monoid instance that comes for free gives you empty lists, concatenation, and a fromList-alike. Other standard Prelude functions that operate on lists like map, take, drop aren't too hard to mimic, though you'll need to skip the ones like cycle and repeat that produce infinite lists, and filter and the like are a bit expensive. For your question, you would also want analogs of the Enum methods; e.g. perhaps something like:
enumFromToLL :: Integral a => a -> a -> ListLength a
enumFromToLL lo hi = (fromIntegral hi-fromIntegral lo+1, [lo..hi])
Then, in ghci, your example is instant:
> lengthLL (enumFromToLL 1 1000000000000000)
1000000000000000

How to double elements in an F# list and set them in a new list

I am very new to F# and functional programming in general, and would like to recursively create a function that takes a list, and doubles all elements.
This is what I used to search for a spacific element, but im not sure how exactly I can change it to do what I need.
let rec returnN n theList =
match n, theList with
| 0, (head::_) -> head
| _, (_::theList') -> returnN (n - 1) theList'
| _, [] -> invalidArg "n" "n is larger then list length"
let list1 = [5; 10; 15; 20; 50; 25; 30]
printfn "%d" (returnN 3 list1 )
Is there a way for me to augment this to do what I need to?
I would like to take you through the thinking process.
Step 1. I need a recursive function that takes a list and doubles all the elements:
So, let's implement this in a naive way:
let rec doubleAll list =
match list with
| [] -> []
| hd :: tl -> hd * 2 :: doubleAll tl
Hopefully this logic is quite simple:
If we have an empty list, we return another empty list.
If we have a list with at least one element, we double the element and then prepend that to the result of calling the doubleAll function on the tail of the list.
Step 2. Actually, there are two things going on here:
I want a function that lets me apply another function to each element of a list.
In this case, I want that function to be "multiply by 2".
So, now we have two functions, let's do a simple implementation like this:
let rec map f list =
match list with
| [] -> []
| hd :: tl -> f hd :: map f tl
let doubleAll list = map (fun x -> x * 2) list
Step 3. Actually, the idea of map is such a common one that it's already built into the F# standard library, see List.map
So, all we need to do is this:
let doubleAll list = List.map (fun x -> x * 2) list

Add a list to a list of lists in Haskell

How can I add a list to a list of lists? Say I want to add itemz to bagList, which is a list of lists. How can I do that?
bagList itemz = mappend bagList itemz
You might want to consider adding it at the front, this is faster:
bagItem bag item = item : bag
Also it looks like you're coming from an imperative mindset, the way you use bagList before and after the = is not quite right: the expressions before and after the = do not really represent the same construction. Before the = bagItem is used as a function, after the = it's used as some Monoid (which if itemz is a list would also need to be a list).
If you really do want to append the item (this will be slower, because the operation will require going all the way through the list to add the new item at the end, and the whole list will need to be reconstructed) you can do what Christoph suggests or you can go for a recursive formulation something like this:
appendItem :: a -> [a] -> [a]
appendItem i (x:xs) = x : appendItem i xs
appendItem i [] = i : []
If you both want to append and are also worried about performance, you should have a look at difference lists, for example look for the section on difference lists in this chapter in Learn You a Haskell.
Update
From the comments it seems what you are actually looking for is Maps. We can make a Map with each item as a key, and the number of occurrences as the value. In your case it seems this will be a Map String Int.
import Data.List (foldl')
import qualified Data.Map as M
bag :: M.Map String Int
bag = M.empty
addToBag :: M.Map String Int -> [String] -> M.Map String Int
addToBag = foldl' go
where go m i = M.insertWith (+) i 1 m
main = print $ addToBag bag ["a","b","c","a"]
-- fromList [("a",2), ("b", 1), ("c", 1)]