[Typescript Challenges] 144 Hard - Transpose

The transpose of a matrix is an operator which flips a matrix over its diagonal; that is, it switches the row and column indices of the matrix A by producing another matrix, often denoted by A^T.

type Matrix = Transpose <[[1]]>; // expected to be [[1]]
type Matrix1 = Transpose <[[1, 2], [3, 4]]>; // expected to be [[1, 3], [2, 4]]
type Matrix2 = Transpose <[[1, 2, 3], [4, 5, 6]]>; // expected to be [[1, 4], [2, 5], [3, 6]]

Solution:

type Transpose<M extends number[][],R = M['length'] extends 0?[]:M[0]> = {
  [X in keyof R]:{
    [Y in keyof M]:X extends keyof M[Y]?M[Y][X]:never
  }
}

/* _____________ Test Cases _____________ */
import type { Equal, Expect } from '@type-challenges/utils'
import { ExpectFalse, NotEqual } from '@type-challenges/utils'

type cases = [
  Expect<Equal<Transpose<[]>, []>>,
  Expect<Equal<Transpose<[[1]]>, [[1]]>>,
  Expect<Equal<Transpose<[[1, 2]]>, [[1], [2]]>>,
  Expect<Equal<Transpose<[[1, 2], [3, 4]]>, [[1, 3], [2, 4]]>>,
  Expect<Equal<Transpose<[[1, 2, 3], [4, 5, 6]]>, [[1, 4], [2, 5], [3, 6]]>>,
  Expect<Equal<Transpose<[[1, 4], [2, 5], [3, 6]]>, [[1, 2, 3], [4, 5, 6]]>>,
  Expect<Equal<Transpose<[[1, 2, 3], [4, 5, 6], [7, 8, 9]]>, [[1, 4, 7], [2, 5, 8], [3, 6, 9]]>>,
]