transpose of a list of lists

Question

I'm trying to make a recursive function to get the transpose of a list of lists, n x p to p x n. But i'm unable to do so. I've been able to make a function to transpose a 3 x n list of lists to an n x 3 one:

let rec drop1 list=
    [(match (List.nth list 0) with [] -> [] | a::b -> b);
     (match (List.nth list 1) with [] -> [] | a::b -> b);
     (match (List.nth list 2) with [] -> [] | a::b -> b);]

let rec transpose list=
    if List.length (List.nth list 0) == 0 then []
    else [(match (List.nth list 0) with [] -> 0 | a::b -> a);
          (match (List.nth list 1) with [] -> 0 | a::b -> a);
          (match (List.nth list 2) with [] -> 0 | a::b -> a)]
         :: transpose (drop1 list)

But I'm not able to generalize it. I'm surely thinking in the wrong direction. Is this generalizable? Is there a better solution? Please help.

Answer 1

let rec transpose list = match list with
| []             -> []
| []   :: xss    -> transpose xss
| (x::xs) :: xss ->
    (x :: List.map List.hd xss) :: transpose (xs :: List.map List.tl xss)