So for an assignment I have been given, I had three functions to complete, those being to extract an HCodeMap from each leaf node of a given tree, to encode a string into a list of Bits, and to decode that string of bits back into a string.
I have successfully completed the code extraction and encoding functions, but I am struggling to make progress with the last decoding function as we are not allowed to traverse a tree as we are not given one to use.
This is the format of the function, followed by some of the types we are supplied with:
decode :: [Bit] -> HCodeMap -> Maybe String
data Bit = Zero | One deriving (Show, Eq)
type HCodeMap = [(Char, [Bit])]
I initially tried creating my own lookup function, which would swap the values of the HCodeMap, and then to lookup the first n bits from the list of Bits we are given.
I will use an example to demonstrate if I have not made myself very clear:
[Bit] we are given : [One,Zero,One,One,Zero]
HCodeMap we are given: [('c',[Zero]),('a',[One,Zero]),('b',[One,One])]
I planned to take the first bit we are given from the list, being One, and then to search through HCodeMap testing to see if that was equal to any of the [Bit]s there.
This is where my reverse lookup function would come in, as I could lookup the list of bits within the HCodeMap, as I cannot lookup by letter. It was along the lines of:
lookup (bits we are given here) (each tuple of HCodeMap) $ map swap code
In this case, we see that One does not match any of the HCodeMap tuples, so I then test One,Zero. This matches with 'a', so I add 'a' to a string, and then carry on with the next [Bit] we are passed, being One again.
etc etc this goes on and we are left with the string "abc".
I am really struggling with how to actually put this into a function however.
I hope I have not made this too confusing, thanks for any help in advance!
Try parsing all codes successively, then repeat after a successful match. Repeat until there's no more input.
import Control.Monad
data Bit = Zero | One deriving (Show, Eq)
type HCodeMap = [(Char, [Bit])]
decode :: [Bit] -> HCodeMap -> Maybe String
decode bits codes = process bits where
-- if the code matches the input, return the corresponding
-- Char value along with the rest of of the input
match :: (Char, [Bit]) -> [Bit] -> Maybe (Char, [Bit])
match (v, xs) ys = go xs ys where
go (x:xs) (y:ys) | x == y = go xs ys
go [] ys = Just (v, ys)
go _ _ = Nothing
-- match and consume until there's no more input, or fail if there is no match.
-- note that msum takes the first Just from a list of Maybe-s,
-- or returns Nothing if there isn't any
process :: [Bit] -> Maybe String
process [] = Just []
process xs = do
(v, xs) <- msum $ map (`match` xs) codes
(v:) `fmap` process xs
For those who are unfamiliar with msum, here's its implementation specialized to Maybe:
msum :: [Maybe a] -> Maybe a
msum (Just a:xs) = Just a
msum (Nothing:xs) = msum xs
msum [] = Nothing
Related
I'm writing a function that gets the index of the first even number from a list. The list I get may or may not contain even numbers, and I'd like to return -1 if there are no even numbers in the list. The list can be infinite.
I wrote this
posicPrimerPar'' :: [Int] -> Int
posicPrimerPar'' a = fromJust (elemIndex (head (filter (even) a)) a)
I could do something like:
posicPrimerPar' :: [Int] -> Int
posicPrimerPar' a = case length evens of
0 -> -1;
n -> fromJust elemIndex (head evens) a
where evens = filter (even) a
But as you can see, this is not the most efficient way of doing it. A list [1..100000] contains a lot of even numbers, and I just need the first one. I need Haskell's laziness, so I need to ask for the head right there, but head throws an empty list exception when the list is empty (i.e. there are no even numbers in the list). I cannot find the Haskell equivalent of Python's try: ... except: .... All I could find regarding exceptions were IO related. What I need is except Prelude.head = -1 or something like that.
Haskell is lazy, so evens will not be fully evaluated. The problematic part is the length evens which is not necessary. You can check with null :: Foldable f => f a -> Bool, or with pattern matching. For example:
import Data.List(findIndex)
posicPrimerPar' :: [Int] -> Maybe Int
posicPrimerPar' [] = Nothing
posicPrimerPar' xs = findIndex even xs
for findIndex :: (a -> Bool) -> [a] -> Maybe Int, you however do not need to take into account the empty list, since it already considers this.
or we can return -1 in case there is no such item:
import Data.List(findIndex)
import Data.Maybe(fromMaybe)
posicPrimerPar' :: [Int] -> Int
posicPrimerPar' = fromMaybe (-1) . findIndex even
I'm trying to parse a string "A1B2C3D4" to [('A',1),('B',2),('C',3)] in Haskell.
I'm trying to use a map like this map (\[a, b] -> (a :: Char, b :: Int)) x where x is the string.
This is the function signature I need to follow :: String -> [(Char, Int)].
Unfortunately i'm getting type mismatches, can anyone give any hint how to solve this?
I'm in the right direction?
Well, map is really meant for applying a single function to every element of something, one-by-one. Splitting the string how you want requires context (knowing the next letter), so map isn't the best choice here.
However, you said your solution is required to be in terms of map. It can be done, but it's a bit roundabout. I couldn't think of any way to make map split the actual string, but it can certainly be used to transform it to the correct type:
isDigit :: Char -> Bool
isDigit c = elem c ['0'..'9']
split :: String -> [(Char, Int)]
split str = let chars = filter (not . isDigit) str
nums = filter isDigit str
zipped = zip chars nums in
map (\(a, b) -> (a, read [b])) zipped
There's a few problems.
The pattern [a, b] in map (\[a, b] -> ...) x only matches lists of two elements, so the compiler infers that the function \[a, b] -> ... has type [r] -> s for some r and s.
The compiler knows that map has the type (u -> v) -> [u] -> [v], so it unifies u with [r] and v with s to infer the type [[r]] -> [s] for map (\[a, b] -> ...).
This means x must have type [[r]], that is, it must be a list of lists. But you want x to be a String which is a synonym for [Char]. The compiler can't unify [[r]] and [Char], so it objects.
You're attempting to "cast" a to a Char and b to an Int like you would in C, but you can't do that in Haskell. If you want to convert a Char like '1' into the Int 1, you need a different approach, like read, which you can use to convert from a String to an Int.
Here's some advice. Don't use map. Try writing a recursive solution instead.
Start by considering a few cases:
what does myParser "" return?
what does myParser "a1" return?
what does myParser [a,b] return?
what does myParser (a:b:cs) return?
I came up with this but it's really not safe as it doesn't handle incorrect string like "AA11B2C3"!
splitingN :: Int -> [a] -> [[a]]
splitingN _ [] = []
splitingN n l
| n > 0 = take n l : splitingN n (drop n l)
| otherwise = error "uhhhhhh"
tuplify :: String -> (Char, Int)
tuplify a = (head a, read $ tail a)
stringy :: String -> [(Char, Int)]
stringy s = tuplify <$> splitingN 2 s
> stringy "A1B2C3D4" == [('A',1),('B',2),('C',3),('D',4)]
A much nicer way but still not fully safe would be:
stringy :: [a] -> [(a, a)]
stringy [] = []
stringy (a : b : rest) = (a, b) : splitting rest
stringy [a] = error "uhhhhh"
Should really check if a and b from (a : b : rest) are indeed Char & Int. Also this uses recursion and you mentioned using map so might not suffice and it's pretty polymorphic in it's types.
As others have pointed out, you need to understand that map applies the given function over each member of the list. Once you understand that, you will realize that there is no way you can get the conversion you want by applying a function on the existing list.
This leads to realization that once you have a list of "A1", "B2",... then you can take these and convert it using a map function.
I have given the code for function below. The split' function is not safe as it can blow up in lot of cases (expected a string which can be perfectly split into 2 chars). I am also using the function digitToInt, for which you need to import Data.Char. You did say you want no import, in that case you can write your own digitToInt function, look into the library code, it is fairly straightforward.
import Data.Char
split' :: String -> [String]
split' [] = []
split' (x:y:xs) = (x:[y]) : split' xs
convert :: String -> [(Char, Int)]
convert input = map (\s -> (s!!0 , digitToInt(s!!1) )) $ split' input
I want to write a function pack such that
pack ['a','a','a','b','c','c','a','a','d','e','e','e']
= ["aaa","b","cc","aa","d","eee"]
How can I do this? I'm stuck...
Use Data.List.group:
λ> import Data.List (group)
λ> :t group
group :: Eq a => [a] -> [[a]]
λ> group ['a','a','a','b','c','c','a','a','d','e','e','e']
["aaa","b","cc","aa","d","eee"]
Unless you want to write the function yourself (see Michael Foukarakis answer)
Here's something off the top of my head:
pack :: (Eq a) => [a] -> [[a]]
pack [] = []
-- We split elements of a list recursively into those which are equal to the first one,
-- and those that are not. Then do the same for the latter:
pack (x:xs) = let (first, rest) = span (==x) xs
in (x:first) : pack rest
Data.List already has what you're looking for, though.
I think it's worth adding a more explicit/beginner version:
pack :: [Char] -> [String]
pack [] = []
pack (c:cs) =
let (v, s) = findConsecutive [c] cs
in v : pack s
where
findConsecutive ds [] = (ds, [])
findConsecutive s#(d:ds) t#(e:es)
| d /= e = (s, t)
| otherwise = findConsecutive (e:s) es
If the input is an empty list, the outcome is also an empty list. Otherwise, we find the next consecutive Chars that are equal and group them together into a String, which is returned in the result list. In order to do that we use the findConsecutive auxiliary function. This function's behavior resembles the takeWhile function, with the difference that we know in advance the predicate to use (equality comparison) and that we return both the consumed and the remaining list.
In other words, the signature of findConsecutive could be written as:
findConsecutive :: String -> [Char] -> (String, String)
which means that it takes a string containing only repeated characters to be used as an accumulator and a list whose characters are "extracted" from. It returns a tuple containing the current sequence of elements and the remaining list. Its body should be intuitive to follow: while the characters list is not empty and the current element is equal to the ones in the accumulator, we add the character to the accumulator and recursive into the function. The function returns when we reach the end of the list or a different character is encountered.
The same rationale can be used to understand the body of pack.
isTogether' :: String -> Bool
isTogether' (x:xs) = isTogether (head xs) (head (tail xs))
For the above code, I want to go through every character in the string. I am not allowed to use recursion.
isTogether' (x:xs) = isTogether (head xs) (head (tail xs))
If I've got it right, you are interested in getting consequential char pairs from some string. So, for example, for abcd you need to test (a,b), (b,c), (c,d) with some (Char,Char) -> Bool or Char -> Char -> Bool function.
Zip could be helpful here:
> let x = "abcd"
> let pairs = zip x (tail x)
it :: [(Char, Char)]
And for some f :: Char -> Char -> Bool function we can get uncurry f :: (Char, Char) -> Bool.
And then it's easy to get [Bool] value of results with map (uncurry f) pairs :: [Bool].
In Haskell, a String is just a list of characters ([Char]). Thus, all of the normal higher-order list functions like map work on strings. So you can use whichever higher-order function is most applicable to your problem.
Note that these functions themselves are defined recursively; in fact, there is no way to go through the entire list in Haskell without either recursing explicitly or using a function that directly or indirectly recurses.
To do this without recursion, you will need to use a higher order function or a list comprehension. I don't understand what you're trying to accomplish so I can only give generic advice. You probably will want one of these:
map :: (a -> b) -> [a] -> [b]
Map converts a list of one type into another. Using map lets you perform the same action on every element of the list, given a function that operates on the kinds of things you have in the list.
filter :: (a -> Bool) -> [a] -> [a]
Filter takes a list and a predicate, and gives you a new list with only the elements that satisfy the predicate. Just with these two tools, you can do some pretty interesting things:
import Data.Char
map toUpper (filter isLower "A quick test") -- => "QUICKTEST"
Then you have folds of various sorts. A fold is really a generic higher order function for doing recursion on some type, so using it takes a bit of getting used to, but you can accomplish pretty much any recursive function on a list with a fold instead. The basic type of foldr looks like this:
foldr :: (a -> b -> b) -> b -> [a] -> b
It takes three arguments: an inductive step, a base case and a value you want to fold. Or, in less mathematical terms, you could think of it as taking an initial state, a function to take the next item and the previous state to produce the next state, and the list of values. It then returns the final state it arrived at. You can do some pretty surprising things with fold, but let's say you want to detect if a list has a run of two or more of the same item. This would be hard to express with map and filter (impossible?), but it's easy with recursion:
hasTwins :: (Eq a) => [a] -> Bool
hasTwins (x:y:xs) | x == y = True
hasTwins (x:y:xs) | otherwise = hasTwins (y:xs)
hasTwins _ = False
Well, you can express this with a fold like so:
hasTwins :: (Eq a) => [a] -> Bool
hasTwins (x:xs) = snd $ foldr step (x, False) xs
where
step x (prev, seenTwins) = (x, prev == x || seenTwins)
So my "state" in this fold is the previous value and whether we've already seen a pair of identical values. The function has no explicit recursion, but my step function passes the current x value along to the next invocation through the state as the previous value. But you don't have to be happy with the last state you have; this function takes the second value out of the state and returns that as the overall return value—which is the boolean whether or not we've seen two identical values next to each other.
The question is to compute the mode (the value that occurs most frequently) of a sorted list of integers.
[1,1,1,1,2,2,3,3] -> 1
[2,2,3,3,3,3,4,4,8,8,8,8] -> 3 or 8
[3,3,3,3,4,4,5,5,6,6] -> 3
Just use the Prelude library.
Are the functions filter, map, foldr in Prelude library?
Starting from the beginning.
You want to make a pass through a sequence and get the maximum frequency of an integer.
This sounds like a job for fold, as fold goes through a sequence aggregating a value along the way before giving you a final result.
foldl :: (a -> b -> a) -> a -> [b] -> a
The type of foldl is shown above. We can fill in some of that already (I find that helps me work out what types I need)
foldl :: (a -> Int -> a) -> a -> [Int] -> a
We need to fold something through that to get the value. We have to keep track of the current run and the current count
data BestRun = BestRun {
currentNum :: Int,
occurrences :: Int,
bestNum :: Int,
bestOccurrences :: Int
}
So now we can fill in a bit more:
foldl :: (BestRun -> Int -> BestRun) -> BestRun -> [Int] -> BestRun
So we want a function that does the aggregation
f :: BestRun -> Int -> BestRun
f (BestRun current occ best bestOcc) x
| x == current = (BestRun current (occ + 1) best bestOcc) -- continuing current sequence
| occ > bestOcc = (BestRun x 1 current occ) -- a new best sequence
| otherwise = (BestRun x 1 best bestOcc) -- new sequence
So now we can write the function using foldl as
bestRun :: [Int] -> Int
bestRun xs = bestNum (foldl f (BestRun 0 0 0 0) xs)
Are the functions filter, map, foldr in Prelude library?
Stop...Hoogle time!
Did you know Hoogle tells you which module a function is from? Hoolging map results in this information on the search page:
map :: (a -> b) -> [a] -> [b]
base Prelude, base Data.List
This means map is defined both in Prelude and in Data.List. You can hoogle the other functions and likewise see that they are indeed in Prelude.
You can also look at Haskell 2010 > Standard Prelude or the Prelude hackage docs.
So we are allowed to map, filter, and foldr, as well as anything else in Prelude. That's good. Let's start with Landei's idea, to turn the list into a list of lists.
groupSorted :: [a] -> [[a]]
groupSorted = undefined
-- groupSorted [1,1,2,2,3,3] ==> [[1,1],[2,2],[3,3]]
How are we supposed to implement groupSorted? Well, I dunno. Let's think about that later. Pretend that we've implemented it. How would we use it to get the correct solution? I'm assuming it is OK to choose just one correct solution, in the event that there is more than one (as in your second example).
mode :: [a] -> a
mode xs = doSomething (groupSorted xs)
where doSomething :: [[a]] -> a
doSomething = undefined
-- doSomething [[1],[2],[3,3]] ==> 3
-- mode [1,2,3,3] ==> 3
We need to do something after we use groupSorted on the list. But what? Well...we should find the longest list in the list of lists. Right? That would tell us which element appears the most in the original list. Then, once we find the longest sublist, we want to return the element inside it.
chooseLongest :: [[a]] -> a
chooseLongest xs = head $ chooseBy (\ys -> length ys) xs
where chooseBy :: ([a] -> b) -> [[a]] -> a
chooseBy f zs = undefined
-- chooseBy length [[1],[2],[3,3]] ==> [3,3]
-- chooseLongest [[1],[2],[3,3]] ==> 3
chooseLongest is the doSomething from before. The idea is that we want to choose the best list in the list of lists xs, and then take one of its elements (its head does just fine). I defined this by creating a more general function, chooseBy, which uses a function (in this case, we use the length function) to determine which choice is best.
Now we're at the "hard" part. Folds. chooseBy and groupSorted are both folds. I'll step you through groupSorted, and leave chooseBy up to you.
How to write your own folds
We know groupSorted is a fold, because it consumes the entire list, and produces something entirely new.
groupSorted :: [Int] -> [[Int]]
groupSorted xs = foldr step start xs
where step :: Int -> [[Int]] -> [[Int]]
step = undefined
start :: [[Int]]
start = undefined
We need to choose an initial value, start, and a stepping function step. We know their types because the type of foldr is (a -> b -> b) -> b -> [a] -> b, and in this case, a is Int (because xs is [Int], which lines up with [a]), and the b we want to end up with is [[Int]].
Now remember, the stepping function will inspect the elements of the list, one by one, and use step to fuse them into an accumulator. I will call the currently inspected element v, and the accumulator acc.
step v acc = undefined
Remember, in theory, foldr works its way from right to left. So suppose we have the list [1,2,3,3]. Let's step through the algorithm, starting with the rightmost 3 and working our way left.
step 3 start = [[3]]
Whatever start is, when we combine it with 3 it should end up as [[3]]. We know this because if the original input list to groupSorted were simply [3], then we would want [[3]] as a result. However, it isn't just [3]. Let's pretend now that it's just [3,3]. [[3]] is the new accumulator, and the result we would want is [[3,3]].
step 3 [[3]] = [[3,3]]
What should we do with these inputs? Well, we should tack the 3 onto that inner list. But what about the next step?
step 2 [[3,3]] = [[2],[3,3]]
In this case, we should create a new list with 2 in it.
step 1 [[2],[3,3]] = [[1],[2],[3,3]]
Just like last time, in this case we should create a new list with 1 inside of it.
At this point we have traversed the entire input list, and have our final result. So how do we define step? There appear to be two cases, depending on a comparison between v and acc.
step v acc#((x:xs):xss) | v == x = (v:x:xs) : xss
| otherwise = [v] : acc
In one case, v is the same as the head of the first sublist in acc. In that case we prepend v to that same sublist. But if such is not the case, then we put v in its own list and prepend that to acc. So what should start be? Well, it needs special treatment; let's just use [] and add a special pattern match for it.
step elem [] = [[elem]]
start = []
And there you have it. All you have to do to write your on fold is determine what start and step are, and you're done. With some cleanup and eta reduction:
groupSorted = foldr step []
where step v [] = [[v]]
step v acc#((x:xs):xss)
| v == x = (v:x:xs) : xss
| otherwise = [v] : acc
This may not be the most efficient solution, but it works, and if you later need to optimize, you at least have an idea of how this function works.
I don't want to spoil all the fun, but a group function would be helpful. Unfortunately it is defined in Data.List, so you need to write your own. One possible way would be:
-- corrected version, see comments
grp [] = []
grp (x:xs) = let a = takeWhile (==x) xs
b = dropWhile (==x) xs
in (x : a) : grp b
E.g. grp [1,1,2,2,3,3,3] gives [[1,1],[2,2],[3,3,3]]. I think from there you can find the solution yourself.
I'd try the following:
mostFrequent = snd . foldl1 max . map mark . group
where
mark (a:as) = (1 + length as, a)
mark [] = error "cannot happen" -- because made by group
Note that it works for any finite list that contains orderable elements, not just integers.