Get lists from where each list will contain the elements from a x position from another collection of lists

Question

basically having this:

[
[1;2;3];
[4;5;7];
[8;9;0];
]

I would like to get this (read vertically/ turn 90 degrees):

[
[1;4;8];
[         


        

Answer 1

What you need is called matrix transposition.

PowerPack

The simplest way is using FSharp.PowerPack; Microsoft.FSharp.Math.Matrix module has Transpose method.

Simple algorithm

If you prefer your own solution, here's the one that demonstrates a good combination of short code and executing efficiency:

let rec transpose = function
    | (_::_)::_ as M -> List.map List.head M :: transpose (List.map List.tail M)
    | _ -> []

// use
[[1; 2; 3]; [4; 5; 6]; [7; 8; 9]]
|> transpose
|> printfn "%A"

In-place matrix transposition

Yet another approach is in-place matrix transposition. It has complexity of O(n), but requires mutable data.

Answer 2

I would do it by converting to arrays -

let arr = input |> List.map (List.toArray) |> List.toArray //a array of arrays
let out = Array2D.create size1 size2 (fun x y -> arr.[y].[x])