Optimisations for a series of functions in Haskell

Question

Hi

I am trying to do problem 254 in project euler and arrived at this set of functions and refactor in Haskell:

f  n = sum $ map fac (decToList n)
sf n = sum $ decToList (f n) 
g  i = head [ n | n <- [1..], sf n == i]
sg i = sum $ decToList (g i)

answer = sum [ sg i | i <- [1 .. 150] ]

Where:

• f (n) finds the sum of the factorials of each digit in n
• sf (n) is the sum of the digits in the result of f (n)
• g (i) is the smallest integer solution for sf (i). As there can be many results for sf (i)
• sg (i) is the sum of the digits in the result of g (i)

But not long into running the compiled version of this script, it sucked up all my RAM. Is there a better way to implement the function g (i)? If so what can they be and how could I go about it?

EDIT:

Just out of clarity, my functions for:

fac is :

`fac 0 = 1`

`fac n = n * fac (n-1)`

decToList which makes a number into a list:

decToList1 x = reverse $ decToList' x
where
decToList' 0 = []
decToList' y = let (a,b) = quotRem y 10 in [b] ++ decToList' a

Although I did since update them to Yairchu's solution for optimisation sake.

Answer 1

The memory problem might lie in decToList or fac.

I ran it with

fac = product . enumFromTo 1
decToList = map (read . return) . show
main = print answer

And it didn't come near to sucking all my RAM, it did not finish, though.

btw: I suspect an advanced project Euler problem to be harder than that. therefore this algorithm won't do.