Non-exhaustive patterns in lambda - haskell

I am getting Non-exhaustive patterns in lambda. I am not sure of the cause yet. Please anyone how to fix it. The code is below:
import Control.Monad
import Data.List
time_spent h1 h2 = max (abs (fst h1 - fst h2)) (abs (snd h1 - snd h2))
meeting_point xs = foldl' (find_min_time) maxBound xs
where
time_to_point p = foldl' (\tacc p' -> tacc + (time_spent p p')) 0 xs
find_min_time min_time p = let x = time_to_point p in if x < min_time then x else min_time
main = do
n <- readLn :: IO Int
points <- fmap (map (\[x,y] -> (x,y)) . map (map (read :: String->Int)) . map words . lines) getContents
putStrLn $ show $ meeting_point points

This is the lambda with the non-exhaustive patterns: \[x,y] -> (x,y).
The non-exhaustive pattern is because the argument you've specified, [x,y] doesn't match any possible list - it only matches lists with precisely two elements.
I would suggest replacing it with a separate function with an error case to print out the unexpected data in an error message so you can debug further, e.g.:
f [x,y] = (x, y)
f l = error $ "Unexpected list: " ++ show l
...
points <- fmap (map f . map ...)

As an addition to #GaneshSittampalam's answer, you could also do this with more graceful error handling using the Maybe monad, the mapM function from Control.Monad, and readMaybe from Text.Read. I would also recommend refactoring your code so that the parsing is its own function, it makes your main function much cleaner and easier to debug.
import Control.Monad (mapM)
import Text.Read (readMaybe)
toPoint :: [a] -> Maybe (a, a)
toPoint [x, y] = Just (x, y)
toPoint _ = Nothing
This is just a simple pattern matching function that returns Nothing if it gets a list with length not 2. Otherwise it turns it into a 2-tuple and wraps it in Just.
parseData :: String -> Maybe [(Int, Int)]
parseData text = do
-- returns Nothing if a non-Int is encountered
values <- mapM (mapM readMaybe . words) . lines $ text
-- returns Nothing if a line doesn't have exactly 2 values
mapM toPoint values
Your parsing can actually be simplified significantly by using mapM and readMaybe. The type of readMaybe is Read a => String -> Maybe a, and in this case since we've specified the type of parseData to return Maybe [(Int, Int)], the compiler can infer that readMaybe should have the local type of String -> Maybe Int. We still use lines and words in the same way, but now since we use mapM the type of the right hand side of the <- is Maybe [[Int]], so the type of values is [[Int]]. What mapM also does for us is if any of those actions fails, the overall computation exits early with Nothing. Then we simply use mapM toPoint to convert values into a list of points, but also with the failure mechanism built in. We actually could use the more general signature of parseData :: Read a => String -> Maybe [(a, a)], but it isn't necessary.
main = do
n <- readLn :: IO Int
points <- fmap parseData getContents
case points of
Just ps -> print $ meeting_point ps
Nothing -> putStrLn "Invalid data!"
Now we just use fmap parseData on getContents, making points have the type Maybe [(Int, Int)]. Finally, we pattern match on points to print out the result of the meeting_point computation or print a helpful message if something went wrong.
If you wanted even better error handling, you could leverage the Either monad in a similar fashion:
toPoint :: [a] -> Either String (a, a)
toPoint [x, y] = Right (x, y)
toPoint _ = Left "Invalid number of points"
readEither :: Read a => String -> Either String a
readEither text = maybe (Left $ "Invalid parse: " ++ text) Right $ readMaybe text
-- default value ^ Wraps output on success ^
-- Same definition with different type signature and `readEither`
parseData :: String -> Either String [(Int, Int)]
parseData text = do
values <- mapM (mapM readEither . words) . lines $ text
mapM toPoint values
main = do
points <- fmap parseData getContents
case points of
Right ps -> print $ meeting_point ps
Left err -> putStrLn $ "Error: " ++ err

Related

How to randomly shuffle a list

I have random number generator
rand :: Int -> Int -> IO Int
rand low high = getStdRandom (randomR (low,high))
and a helper function to remove an element from a list
removeItem _ [] = []
removeItem x (y:ys) | x == y = removeItem x ys
| otherwise = y : removeItem x ys
I want to shuffle a given list by randomly picking an item from the list, removing it and adding it to the front of the list. I tried
shuffleList :: [a] -> IO [a]
shuffleList [] = []
shuffleList l = do
y <- rand 0 (length l)
return( y:(shuffleList (removeItem y l) ) )
But can't get it to work. I get
hw05.hs:25:33: error:
* Couldn't match expected type `[Int]' with actual type `IO [Int]'
* In the second argument of `(:)', namely
....
Any idea ?
Thanks!
Since shuffleList :: [a] -> IO [a], we have shuffleList (xs :: [a]) :: IO [a].
Obviously, we can't cons (:) :: a -> [a] -> [a] an a element onto an IO [a] value, but instead we want to cons it onto the list [a], the computation of which that IO [a] value describes:
do
y <- rand 0 (length l)
-- return ( y : (shuffleList (removeItem y l) ) )
shuffled <- shuffleList (removeItem y l)
return y : shuffled
In do notation, values to the right of <- have types M a, M b, etc., for some monad M (here, IO), and values to the left of <- have the corresponding types a, b, etc..
The x :: a in x <- mx gets bound to the pure value of type a produced / computed by the M-type computation which the value mx :: M a denotes, when that computation is actually performed, as a part of the combined computation represented by the whole do block, when that combined computation is performed as a whole.
And if e.g. the next line in that do block is y <- foo x, it means that a pure function foo :: a -> M b is applied to x and the result is calculated which is a value of type M b, denoting an M-type computation which then runs and produces / computes a pure value of type b to which the name y is then bound.
The essence of Monad is thus this slicing of the pure inside / between the (potentially) impure, it is these two timelines going on of the pure calculations and the potentially impure computations, with the pure world safely separated and isolated from the impurities of the real world. Or seen from the other side, the pure code being run by the real impure code interacting with the real world (in case M is IO). Which is what computer programs must do, after all.
Your removeItem is wrong. You should pick and remove items positionally, i.e. by index, not by value; and in any case not remove more than one item after having picked one item from the list.
The y in y <- rand 0 (length l) is indeed an index. Treat it as such. Rename it to i, too, as a simple mnemonic.
Generally, with Haskell it works better to maximize the amount of functional code at the expense of non-functional (IO or randomness-related) code.
In your situation, your “maximum” functional component is not removeItem but rather a version of shuffleList that takes the input list and (as mentioned by Will Ness) a deterministic integer position. List function splitAt :: Int -> [a] -> ([a], [a]) can come handy here. Like this:
funcShuffleList :: Int -> [a] -> [a]
funcShuffleList _ [] = []
funcShuffleList pos ls =
if (pos <=0) || (length(take (pos+1) ls) < (pos+1))
then ls -- pos is zero or out of bounds, so leave list unchanged
else let (left,right) = splitAt pos ls
in (head right) : (left ++ (tail right))
Testing:
λ>
λ> funcShuffleList 4 [0,1,2,3,4,5,6,7,8,9]
[4,0,1,2,3,5,6,7,8,9]
λ>
λ> funcShuffleList 5 "#ABCDEFGH"
"E#ABCDFGH"
λ>
Once you've got this, you can introduce randomness concerns in simpler fashion. And you do not need to involve IO explicitely, as any randomness-friendly monad will do:
shuffleList :: MonadRandom mr => [a] -> mr [a]
shuffleList [] = return []
shuffleList ls =
do
let maxPos = (length ls) - 1
pos <- getRandomR (0, maxPos)
return (funcShuffleList pos ls)
... IO being just one instance of MonadRandom.
You can run the code using the default IO-hosted random number generator:
main = do
let inpList = [0,1,2,3,4,5,6,7,8]::[Integer]
putStrLn $ "inpList = " ++ (show inpList)
-- mr automatically instantiated to IO:
outList1 <- shuffleList inpList
putStrLn $ "outList1 = " ++ (show outList1)
outList2 <- shuffleList outList1
putStrLn $ "outList2 = " ++ (show outList2)
Program output:
$ pickShuffle
inpList = [0,1,2,3,4,5,6,7,8]
outList1 = [6,0,1,2,3,4,5,7,8]
outList2 = [8,6,0,1,2,3,4,5,7]
$
$ pickShuffle
inpList = [0,1,2,3,4,5,6,7,8]
outList1 = [4,0,1,2,3,5,6,7,8]
outList2 = [2,4,0,1,3,5,6,7,8]
$
The output is not reproducible here, because the default generator is seeded by its launch time in nanoseconds.
If what you need is a full random permutation, you could have a look here and there - Knuth a.k.a. Fisher-Yates algorithm.

Haskell: Exception <<loop>> on recursive data entry

So I'm trying to make a little program that can take in data captured during an experiment, and for the most part I think I've figured out how to recursively take in data until the user signals there is no more, however upon termination of data taking haskell throws Exception: <<loop>> and I can't really figure out why. Here's the code:
readData :: (Num a, Read a) => [Point a] -> IO [Point a]
readData l = do putStr "Enter Point (x,y,<e>) or (d)one: "
entered <- getLine
if (entered == "d" || entered == "done")
then return l
else do let l = addPoint l entered
nl <- readData l
return nl
addPoint :: (Num a, Read a) => [Point a] -> String -> [Point a]
addPoint l s = l ++ [Point (dataList !! 0) (dataList !! 1) (dataList !! 2)]
where dataList = (map read $ checkInputData . splitOn "," $ s) :: (Read a) => [a]
checkInputData :: [String] -> [String]
checkInputData xs
| length xs < 2 = ["0","0","0"]
| length xs < 3 = (xs ++ ["0"])
| length xs == 3 = xs
| length xs > 3 = ["0","0","0"]
As far as I can tell, the exception is indication that there is an infinite loop somewhere, but I can't figure out why this is occurring. As far as I can tell when "done" is entered the current level should simply return l, the list it's given, which should then cascade up the previous iterations of the function.
Thanks for any help. (And yes, checkInputData will have proper error handling once I figure out how to do that.)
<<loop>> basically means GHC has detected an infinite loop caused by a value which depends immediately on itself (cf. this question, or this one for further technical details if you are curious). In this case, that is triggered by:
else do let l = addPoint l entered
This definition, which shadows the l you passed as an argument, defines l in terms of itself. You meant to write something like...
else do let l' = addPoint l entered
... which defines a new value, l', in terms of the original l.
As Carl points out, turning on -Wall (e.g. by passing it to GHC at the command line, or with :set -Wall in GHCi) would make GHC warn you about the shadowing:
<interactive>:171:33: warning: [-Wname-shadowing]
This binding for ‘l’ shadows the existing binding
bound at <interactive>:167:10
Also, as hightlighted by dfeuer, the whole do-block in the else branch can be replaced by:
readData (addPoint l entered)
As an unrelated suggestion, in this case it is a good idea to replace your uses of length and (!!) with pattern matching. For instance, checkInputData can be written as:
checkInputData :: [String] -> [String]
checkInputData xs = case xs of
[_,_] -> xs ++ ["0"]
[_,_,_] -> xs
_ -> ["0","0","0"]
addPoint, in its turn, might become:
addPoint :: (Num a, Read a) => [Point a] -> String -> [Point a]
addPoint l s = l ++ [Point x y z]
where [x,y,z] = (map read $ checkInputData . splitOn "," $ s) :: (Read a) => [a]
That becomes even neater if you change checkInputData so that it returns a (String, String, String) triple, which would better express the invariant that you are reading exactly three values.

Reading multiline user's input

I want to lazily read user input and do something with it line by line. But if user ends a line with , (comma) followed by any number of spaces (including zero), I want give him opportunity to finish his input on the next line.
And here is what I've got:
import System.IO
import Data.Char
chop :: String -> [String]
chop = f . map (++ "\n") . lines
where f [] = []
f [x] = [x]
f (x : y : xs) = if (p . tr) x
then f ((x ++ y) : xs)
else x : f (y : xs)
p x = (not . null) x && ((== ',') . last) x
tr xs | all isSpace xs = ""
tr (x : xs) = x :tr xs
main :: IO ()
main =
do putStrLn "Welcome to hell, version 0.1.3!"
putPrompt
mapM_ process . takeWhile (/= "quit\n") . chop =<< getContents
where process str = putStr str >> putPrompt
putPrompt = putStr ">>> " >> hFlush stdout
Sorry, it doesn't work at all. Bloody mess.
P.S. I want to preserve \n characters on end of every chunk. Currently I add them manually with map (++ "\n") after lines.
How about changing the type of chop a little:
readMultiLine :: IO [String]
readMultiLine = do
ln <- getLine
if (endswith (rstrip ln) ",") then
liftM (ln:) readMultiLine
else
return [ln]
Now you know that if the last list is not empty, then the user didn't finish typing (the last input ended with ',').
Of course, either import Data.String.Utils, or write your own. Could be as simple as:
endswith xs ys = (length xs >= length ys)
&& (and $ zipWith (==) (reverse xs) (reverse ys))
rstrip = reverse . dropWhile isSpace . reverse
But I missed the point at first. Here's the actual thing.
unfoldM :: (Monad m) => (a -> Maybe (m b, m a)) -> a -> m [b]
unfoldM f z = case f z of
Nothing -> return []
Just (x, y) -> liftM2 (:) x $ y >>= unfoldM f
main = unfoldM (\x -> if (x == ["quit"]) then Nothing
else Just (print x, readMultiLine)) =<< readMultiLine
The reason is, you need to be able to insert the "action" to be done on input between reading one multi-line input and the next. Here print x is the action inserted between two readMultiLine
Since you have questions about getContents, let me add. Even though getContents provides a lazy String, its effectful changes to the world are ordered with the subsequent effects of processing the list. But the processing of the list attempts to insert effects between effects of reading particular list items. To do that, you need a function that exposes the chain of effects, so you can insert your own effects between them.
You can do this using pipes, preserving the laziness of the user's input
import Data.Char (isSpace)
import Pipes
import qualified Pipes.Prelude as Pipes
endsWithComma :: String -> Bool
endsWithComma str =
case (dropWhile isSpace $ reverse str) of
',':_ -> True
_ -> False
finish :: Monad m => Pipe String String m ()
finish = do
str <- await
yield str
if endsWithComma str
then do
str' <- await
yield str'
else finish
user :: Producer String IO ()
user = Pipes.stdinLn >-> finish
You can then hook up the user Producer to any downstream Consumer. For example, to echo the stream back out you can write:
main = runEffect (user >-> Pipes.stdoutLn)
To learn more about pipes you can read the tutorial.
Sorry, I wrote something wrong in a comment and I thought that now that I understood what you were trying to do, I'd give an answer with a little more substance. The core idea is that you're going to need a state buffer while you loop through the string, as far as I can tell. You have f :: [String] -> [String] but you'll need an extra string of buffer before you can solve this puzzle.
So let me assume an answer which looks like:
chop = joinCommas "" . map (++ "\n") . lines
Then the structure of joinCommas is going to look like:
import Data.List (isSuffixOf)
-- override with however you want to handle the ",\n" between lines.
joinLines = (++)
incomplete = isSuffixOf ",\n"
joinCommas :: String -> [String] -> [String]
joinCommas prefix (line : rest)
| incomplete prefix = joinCommas (joinLines prefix line) rest
| otherwise = prefix : joinCommas line rest
joinCommas prefix []
| incomplete prefix = error "Incomplete input"
| otherwise = [prefix]
The prefix stores up lines until it doesn't end with ",\n" at which point it emits the prefix and continues with the rest of the lines. On EOF we process the last line unless that line is incomplete.

How do I parse a matrix of integers in Haskell?

So I've read the theory, now trying to parse a file in Haskell - but am not getting anywhere. This is just so weird...
Here is how my input file looks:
m n
k1, k2...
a11, ...., an
a21,.... a22
...
am1... amn
Where m,n are just intergers, K = [k1, k2...] is a list of integers, and a11..amn is a "matrix" (a list of lists): A=[[a11,...a1n], ... [am1... amn]]
Here is my quick python version:
def parse(filename):
"""
Input of the form:
m n
k1, k2...
a11, ...., an
a21,.... a22
...
am1... amn
"""
f = open(filename)
(m,n) = f.readline().split()
m = int(m)
n = int(n)
K = [int(k) for k in f.readline().split()]
# Matrix - list of lists
A = []
for i in range(m):
row = [float(el) for el in f.readline().split()]
A.append(row)
return (m, n, K, A)
And here is how (not very) far I got in Haskell:
import System.Environment
import Data.List
main = do
(fname:_) <- getArgs
putStrLn fname --since putStrLn goes to IO ()monad we can't just apply it
parsed <- parse fname
putStrLn parsed
parse fname = do
contents <- readFile fname
-- ,,,missing stuff... ??? how can I get first "element" and match on it?
return contents
I am getting confused by monads (and the context that the trap me into!), and the do statement. I really want to write something like this, but I know it's wrong:
firstLine <- contents.head
(m,n) <- map read (words firstLine)
because contents is not a list - but a monad.
Any help on the next step would be great.
So I've just discovered that you can do:
liftM lines . readFile
to get a list of lines from a file. However, still the example only only transforms the ENTIRE file, and doesn't use just the first, or the second lines...
The very simple version could be:
import Control.Monad (liftM)
-- this operates purely on list of strings
-- and also will fail horribly when passed something that doesn't
-- match the pattern
parse_lines :: [String] -> (Int, Int, [Int], [[Int]])
parse_lines (mn_line : ks_line : matrix_lines) = (m, n, ks, matrix)
where [m, n] = read_ints mn_line
ks = read_ints ks_line
matrix = parse_matrix matrix_lines
-- this here is to loop through remaining lines to form a matrix
parse_matrix :: [String] -> [[Int]]
parse_matrix lines = parse_matrix' lines []
where parse_matrix' [] acc = reverse acc
parse_matrix' (l : ls) acc = parse_matrix' ls $ (read_ints l) : acc
-- this here is to give proper signature for read
read_ints :: String -> [Int]
read_ints = map read . words
-- this reads the file contents and lifts the result into IO
parse_file :: FilePath -> IO (Int, Int, [Int], [[Int]])
parse_file filename = do
file_lines <- (liftM lines . readFile) filename
return $ parse_lines file_lines
You might want to look into Parsec for fancier parsing, with better error handling.
*Main Control.Monad> parse_file "test.txt"
(3,3,[1,2,3],[[1,2,3],[4,5,6],[7,8,9]])
An easy to write solution
import Control.Monad (replicateM)
-- Read space seperated words on a line from stdin
readMany :: Read a => IO [a]
readMany = fmap (map read . words) getLine
parse :: IO (Int, Int, [Int], [[Int]])
parse = do
[m, n] <- readMany
ks <- readMany
xss <- replicateM m readMany
return (m, n, ks, xss)
Let's try it:
*Main> parse
2 2
123 321
1 2
3 4
(2,2,[123,321],[[1,2],[3,4]])
While the code I presented is quite expressive. That is, you get work done quickly with little code, it has some bad properties. Though I think if you are still learning haskell and haven't started with parser libraries. This is the way to go.
Two bad properties of my solution:
All code is in IO, nothing is testable in isolation
The error handling is very bad, as you see the pattern matching is very aggressive in [m, n]. What happens if we have 3 elements on the first line of the input file?
liftM is not magic! You would think it does some arcane thing to lift a function f into a monad but it is actually just defined as:
liftM f x = do
y <- x
return (f y)
We could actually use liftM to do what you wanted to, that is:
[m,n] <- liftM (map read . words . head . lines) (readFile fname)
but what you are looking for are let statements:
parseLine = map read . words
parse fname = do
(x:y:xs) <- liftM lines (readFile fname)
let [m,n] = parseLine x
let ks = parseLine y
let matrix = map parseLine xs
return (m,n,ks,matrix)
As you can see we can use let to mean variable assignment rather then monadic computation. In fact let statements are you just let expressions when we desugar the do notation:
parse fname =
liftM lines (readFile fname) >>= (\(x:y:xs) ->
let [m,n] = parseLine x
ks = parseLine y
matrix = map parseLine xs
in return matrix )
A Solution Using a Parsing Library
Since you'll probably have a number of people responding with code that parses strings of Ints into [[Int]] (map (map read . words) . lines $ contents), I'll skip that and introduce one of the parsing libraries. If you were to do this task for real work you'd probably use such a library that parses ByteString (instead of String, which means your IO reads everything into a linked list of individual characters).
import System.Environment
import Control.Monad
import Data.Attoparsec.ByteString.Char8
import qualified Data.ByteString as B
First, I imported the Attoparsec and bytestring libraries. You can see these libraries and their documentation on hackage and install them using the cabal tool.
main = do
(fname:_) <- getArgs
putStrLn fname
parsed <- parseX fname
print parsed
main is basically unchanged.
parseX :: FilePath -> IO (Int, Int, [Int], [[Int]])
parseX fname = do
bs <- B.readFile fname
let res = parseOnly parseDrozzy bs
-- We spew the error messages right here
either (error . show) return res
parseX (renamed from parse to avoid name collision) uses the bytestring library's readfile, which reads in the file packed, in contiguous bytes, instead of into cells of a linked list. After parsing I use a little shorthand to return the result if the parser returned Right result or print an error if the parser returned a value of Left someErrorMessage.
-- Helper functions, more basic than you might think, but lets ignore it
sint = skipSpace >> int
int = liftM floor number
parseDrozzy :: Parser (Int, Int, [Int], [[Int]])
parseDrozzy = do
m <- sint
n <- sint
skipSpace
ks <- manyTill sint endOfLine
arr <- count m (count n sint)
return (m,n,ks,arr)
The real work then happens in parseDrozzy. We get our m and n Int values using the above helper. In most Haskell parsing libraries we must explicitly handle whitespace - so I skip the newline after n to get to our ks. ks is just all the int values before the next newline. Now we can actually use the previously specified number of rows and columns to get our array.
Technically speaking, that final bit arr <- count m (count n sint) doesn't follow your format. It will grab n ints even if it means going to the next line. We could copy Python's behavior (not verifying the number of values in a row) using count m (manyTill sint endOfLine) or we could check for each end of line more explicitly and return an error if we are short on elements.
From Lists to a Matrix
Lists of lists are not 2 dimensional arrays - the space and performance characteristics are completely different. Let's pack our list into a real matrix using Data.Array.Repa (import Data.Array.Repa). This will allow us to access the elements of the array efficiently as well as perform operations on the entire matrix, optionally spreading the work among all the available CPUs.
Repa defines the dimensions of your array using a slightly odd syntax. If your row and column lengths are in variables m and n then Z :. n :. m is much like the C declaration int arr[m][n]. For the one dimensional example, ks, we have:
fromList (Z :. (length ks)) ks
Which changes our type from [Int] to Array DIM1 Int.
For the two dimensional array we have:
let matrix = fromList (Z :. m :. n) (concat arr)
And change our type from [[Int]] to Array DIM2 Int.
So there you have it. A parsing of your file format into an efficient Haskell data structure using production-oriented libraries.
What about something simple like this?
parse :: String -> (Int, Int, [Int], [[Int]])
parse stuff = (m, n, ks, xss)
where (line1:line2:rest) = lines stuff
readMany = map read . words
(m:n:_) = readMany line1
ks = readMany line2
xss = take m $ map (take n . readMany) rest
main :: IO ()
main = do
stuff <- getContents
let (m, n, ks, xss) = parse stuff
print m
print n
print ks
print xss

awkward monad transformer stack

Solving a problem from Google Code Jam (2009.1A.A: "Multi-base happiness") I came up with an awkward (code-wise) solution, and I'm interested in how it could be improved.
The problem description, shortly, is: Find the smallest number bigger than 1 for which iteratively calculating the sum of squares of digits reaches 1, for all bases from a given list.
Or description in pseudo-Haskell (code that would solve it if elem could always work for infinite lists):
solution =
head . (`filter` [2..]) .
all ((1 `elem`) . (`iterate` i) . sumSquareOfDigitsInBase)
And my awkward solution:
By awkward I mean it has this kind of code: happy <- lift . lift . lift $ isHappy Set.empty base cur
I memoize results of the isHappy function. Using the State monad for the memoized results Map.
Trying to find the first solution, I did not use head and filter (like the pseudo-haskell above does), because the computation isn't pure (changes state). So I iterated by using StateT with a counter, and a MaybeT to terminate the computation when condition holds.
Already inside a MaybeT (StateT a (State b)), if the condition doesn't hold for one base, there is no need to check the other ones, so I have another MaybeT in the stack for that.
Code:
import Control.Monad.Maybe
import Control.Monad.State
import Data.Maybe
import qualified Data.Map as Map
import qualified Data.Set as Set
type IsHappyMemo = State (Map.Map (Integer, Integer) Bool)
isHappy :: Set.Set Integer -> Integer -> Integer -> IsHappyMemo Bool
isHappy _ _ 1 = return True
isHappy path base num = do
memo <- get
case Map.lookup (base, num) memo of
Just r -> return r
Nothing -> do
r <- calc
when (num < 1000) . modify $ Map.insert (base, num) r
return r
where
calc
| num `Set.member` path = return False
| otherwise = isHappy (Set.insert num path) base nxt
nxt =
sum . map ((^ (2::Int)) . (`mod` base)) .
takeWhile (not . (== 0)) . iterate (`div` base) $ num
solve1 :: [Integer] -> IsHappyMemo Integer
solve1 bases =
fmap snd .
(`runStateT` 2) .
runMaybeT .
forever $ do
(`when` mzero) . isJust =<<
runMaybeT (mapM_ f bases)
lift $ modify (+ 1)
where
f base = do
cur <- lift . lift $ get
happy <- lift . lift . lift $ isHappy Set.empty base cur
unless happy mzero
solve :: [String] -> String
solve =
concat .
(`evalState` Map.empty) .
mapM f .
zip [1 :: Integer ..]
where
f (idx, prob) = do
s <- solve1 . map read . words $ prob
return $ "Case #" ++ show idx ++ ": " ++ show s ++ "\n"
main :: IO ()
main =
getContents >>=
putStr . solve . tail . lines
Other contestants using Haskell did have nicer solutions, but solved the problem differently. My question is about small iterative improvements to my code.
Your solution is certainly awkward in its use (and abuse) of monads:
It is usual to build monads piecemeal by stacking several transformers
It is less usual, but still happens sometimes, to stack several states
It is very unusual to stack several Maybe transformers
It is even more unusual to use MaybeT to interrupt a loop
Your code is a bit too pointless :
(`when` mzero) . isJust =<<
runMaybeT (mapM_ f bases)
instead of the easier to read
let isHappy = isJust $ runMaybeT (mapM_ f bases)
when isHappy mzero
Focusing now on function solve1, let us simplify it.
An easy way to do so is to remove the inner MaybeT monad. Instead of a forever loop which breaks when a happy number is found, you can go the other way around and recurse only if the
number is not happy.
Moreover, you don't really need the State monad either, do you ? One can always replace the state with an explicit argument.
Applying these ideas solve1 now looks much better:
solve1 :: [Integer] -> IsHappyMemo Integer
solve1 bases = go 2 where
go i = do happyBases <- mapM (\b -> isHappy Set.empty b i) bases
if and happyBases
then return i
else go (i+1)
I would be more han happy with that code.
The rest of your solution is fine.
One thing that bothers me is that you throw away the memo cache for every subproblem. Is there a reason for that?
solve :: [String] -> String
solve =
concat .
(`evalState` Map.empty) .
mapM f .
zip [1 :: Integer ..]
where
f (idx, prob) = do
s <- solve1 . map read . words $ prob
return $ "Case #" ++ show idx ++ ": " ++ show s ++ "\n"
Wouldn't your solution be more efficient if you reused it instead ?
solve :: [String] -> String
solve cases = (`evalState` Map.empty) $ do
solutions <- mapM f (zip [1 :: Integer ..] cases)
return (unlines solutions)
where
f (idx, prob) = do
s <- solve1 . map read . words $ prob
return $ "Case #" ++ show idx ++ ": " ++ show s
The Monad* classes exist to remove the need for repeated lifting. If you change your signatures like this:
type IsHappyMemo = Map.Map (Integer, Integer) Bool
isHappy :: MonadState IsHappyMemo m => Set.Set Integer -> Integer -> Integer -> m Bool
This way you can remove most of the 'lift's. However, the longest sequence of lifts cannot be removed, since it is a State monad inside a StateT, so using the MonadState type class will give you the outer StateT, where you need tot get to the inner State. You could wrap your State monad in a newtype and make a MonadHappy class, similar to the existing monad classes.
ListT (from the List package) does a much nicer job than MaybeT in stopping the calculation when necessary.
solve1 :: [Integer] -> IsHappyMemo Integer
solve1 bases = do
Cons result _ <- runList . filterL cond $ fromList [2..]
return result
where
cond num = andL . mapL (isHappy Set.empty num) $ fromList bases
Some elaboration on how this works:
Had we used a regular list the code would had looked like this:
solve1 bases = do
result:_ <- filterM cond [2..]
return result
where
cond num = fmap and . mapM (isHappy Set.empty num) bases
This calculation happens in a State monad, but if we'd like to get the resulting state, we'd have a problem, because filterM runs the monadic predicate it gets for every element of [2..], an infinite list.
With the monadic list, filterL cond (fromList [2..]) represents a list that we can access one item at a time as a monadic action, so our monadic predicate cond isn't actually executed (and affecting the state) unless we consume the corresponding list items.
Similarly, implementing cond using andL makes us not calculate and update the state if we already got a False result from one of the isHappy Set.empty num calculations.

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