List comprehension in Haskell
I've been using the following code to get all combinations of a pre-determined amount of numbers:
getList x = [ [a,b,c] | a <- [1..x], b <- [1..x], c <- [1..x]]
This was fine to begin with, but I'm looking to expand the program to handle very large lists, and I keep thinking there must be a better way to do this. How would I create a function that takes the same parameter x as here, and also ano开发者_StackOverflowther parameter for how many items the sublists have. For four items I would go and modify the code:
getList x = [ [a,b,c,d] | a <- [1..x], b <- [1..x], c <- [1..x], d <- [1..x]]
It doesn't need to be a list comprehension. Thank you for any help.
I believe what you want would be the replicateM
function in Control.Monad
.
The list monad is based on "trying all possible combinations", and plain replicate
creates a list by repeating an item some number of times. So the result of replicateM
is, given some list of possible values, a list of all possible ways to select an item from that list some number of times.
For example:
> replicateM 2 [0, 1]
[[0,0],[0,1],[1,0],[1,1]]
> replicateM 3 [0, 1]
[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1]]
So to extend your function to arbitrary repetitions, you'd use something like:
getListN n x = replicateM n [1..x]
...where your original getList
would be equivalent to getListN 3
.
In case, anyone likes a non-Monadic-solution to understand to inner workings (although, the soliution via replicateM
is great!):
getListN n = foldl (\ass bs -> [ b:as | b <- bs, as <- ass]) [[]] . replicate n
Essentially, this implementation via foldl
works exactly in the same way as the replacatM
-solution does.
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