# R – Haskell: recursion with array arguments

Disclaimer: I'm new to Haskell and I don't remember a lot about FP from university, so there may be more than one or two errors in my code. This is also my code for Euler Problem 3.

I'm trying to recursively call a function with two arrays as arguments and an array as a result.

The goal:

• assume n is 10 for this question
• create a list of all natural numbers from 1 to n (variable is 'allNumbers' is code)
• create another list of all natural numbers from 1 to n (variable is 'allFactors' is code)
• take the first element in 'allFactors' and multiply the rest of the numbers of 'allFactors' by this number. (this generates an array of numbers)
• remove all these numbers from 'allNumbers'
• continue from 1 to n until 'allFactors' is empty.

Here is my code:

``````mkList :: Int -> [Int]
mkList n = [1..n-1]

modArray :: Int -> Int -> [Int]
modArray a b =  [ x*b | x <- [1..a], x `mod` b == 0]

modArrayAll :: [Int] -> [Int] -> [Int]
modArrayAll [] [] = []
modArrayAll (x:xs) (y:ys) = (e)
where
m = head( ys)
n = length( xs)
e = (modArrayAll xs ys ) \\ modArray n m
``````

(in main)

``````let allNumbers =  mkList (first + 1)
let allFactors = mkList (first + 1)
let mainList2 =  modArrayAll allNumbers allFactors
``````

This results in a null list. However, if I have:

``````e = xs \\ modArray n m  --WORKS for one iteration
``````

I get all the odd numbers from 1 to 10.

My Question: Why isn't this working the way I would expect it? I would expect that the recursive stack would hit the empty array condition and just return an empty array which would not be removed from the calling array and it would continue on returning just the prime numbers?

#### Best Solution

I copied your goal notes:

``````-- assume n is 10 for this question
n=10

-- create a list of all natural numbers from 1 to n (variable is 'allNumbers' is code)
allNumbers = [1..n]

-- create another list of all natural numbers from 1 to n (variable is 'allFactors' is code)
allFactors = [2..n] -- i suspect you really wanted this rather than [1..n]

-- take the first element in 'allFactors' and
-- multiply the rest of the numbers of 'allFactors' by this number.
-- (this generates an array of numbers)
-- continue from 1 to n until 'allFactors' is empty
factorProducts = [ x*y | x <- allFactors, y <- allFactors]

--  remove all these numbers from 'allNumbers'
whatYouWanted = allNumbers \\ factorProducts
``````

At the moment you seem to still be thinking in a fairly imperative mindset. Try thinking more about what you want, not how to get it :)