Multiply list elements in Haskell

Question

I want a function which takes the product of the inits of a list and duplicates its elements.

For example the list is: [2, 3, 4, 5] .

The product of its inits : [1, 2, 6, 24, 120] .

At the end the list should look like this: [1, 1, 2, 2, 2, 6, 6, 6, 6, 24, 24, 24, 24, 24] .

My problem is that the [1, 2, 6, 24, 120] should not vary, but i can't solve it, I'm pretty new to haskell. You don't need to modify this code, you can make a new one.

makeSystem :: Integral a => [a] -> [a]
makeSystem l= replicate (l !! 0) ((map product(inits l))!!0) ++ asd (tail l) where
 inits [] = [[]]
 inits (x:xs) = [[]] ++ map (x:) (inits xs)

An other example: makeSystem [5,2,5,2,5,2]

The result: [1, 1, 1, 1, 1, 5, 5, 10, 10, 10, 10, 10, 50, 50, 100, 100, 100, 100, 100, 500, 500]

Answer 1

For the first part, you can use the standard function scanl :

> scanl (*) 1 [2, 3, 4, 5]
[1,2,6,24,120]

For the second part, zipWith with replicate gets us most of the way there:

> zipWith replicate [2, 3, 4, 5] [1, 2, 6, 24, 120]
[[1,1],[2,2,2],[6,6,6,6],[24,24,24,24,24]]

then we just need to concat these lists.

Putting it all together:

> let makeSystem xs = concat $ zipWith replicate xs (scanl (*) 1 xs)
> makeSystem [2, 3, 4, 5]
[1,1,2,2,2,6,6,6,6,24,24,24,24,24]
> makeSystem [5, 2, 5, 2, 5, 2]
[1,1,1,1,1,5,5,10,10,10,10,10,50,50,100,100,100,100,100,500,500]