"Sequence full of colors" challenge on HackerRank This is the challenge:

You are given a sequence of N balls in 4 colors: red, green, yellow and blue. The sequence is full of colors if and only if all of the following conditions are true:

There are as many red balls as green balls.
There are as many yellow balls as blue balls.
Difference between the number of red balls and green balls in every prefix of the sequence is at most 1.
Difference between the number of yellow balls and blue balls in every prefix of the sequence is at most 1.
Your task is to write a program, which for a given sequence prints True if it is full of colors, otherwise it prints False.


and this is my solution:
import Control.Monad (replicateM, foldM)

main :: IO ()
main = do
  n &lt;- getLine
  list &lt;- replicateM (read n :: Int) getLine
  mapM_ (print . isgood) list

isgood :: String -&gt; Bool
isgood = isValidFinal . foldM step (0,0)
  where
    step (x,y) c
      | c == 'R' = wrapValidInJust (x - 1, y)
      | c == 'G' = wrapValidInJust (x + 1, y)
      | c == 'Y' = wrapValidInJust (x, y - 1)
      | c == 'B' = wrapValidInJust (x, y + 1)
    isValid (x,y) = abs x &lt;= 1 &amp;&amp; abs y &lt;= 1
    wrapValidInJust xy = if isValid xy then Just xy else Nothing
    isValidFinal (Just x) = x == (0,0)
    isValidFinal Nothing = False

I'm kind of happy with main and isgood, but the step function seems very hard to read.
Any feedback?
step does two things: (1) step to the next state, and (2) check that the state is valid. Its name suggests only the first meaning. The repetition of wrapValidInJust suggests that they can be separated.

Instead of == you can use pattern-matching.


isgood :: String -&gt; Bool
isgood = isValidFinal . foldM (check . step) (0, 0)
  where

    step (x, y) 'R' = (x-1, y)
    step (x, y) 'G' = (x+1, y)
    step (x, y) 'Y' = (x, y-1)
    step (x, y) 'B' = (x, y+1)

    check (x, y) = if abs x &lt;= 1 &amp;&amp; abs y &lt;= 1 then Just (x, y) else Nothing

    ...

Another reason step is hard to read is that you need to keep track of differences, which complexifies the meaning of x and y. You can just as easily count the four colors independently and compute the difference only in check. This is also the opportunity to use a record or a map to make the update syntax more uniform:
data RGBY = RGBY { r, g, b, y :: Int }

isgood :: String -&gt; Bool
isgood = isValidFinal . foldM (check . step) (RGBY 0 0 0 0)
  where

    step x 'R' = x { r = r x + 1 }
    step x 'G' = x { g = g x + 1 }
    step x 'Y' = x { y = y x + 1 }
    step x 'B' = x { b = b x + 1 }

    check x = if abs (r x - g x) &lt;= 1 &amp;&amp; abs (y x - b x) &lt;= 1
      then Just (x, y) else Nothing

    ...