#31820 - Transposed Matrix

questions/31820-hard-transpose-2/README.md

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+Transposition is a math concept.
+We can use a 2d tuples to describe a matrix in TS.
+But tuples in TS aren't always squares, which makes the transposition of 2d tuples become more difficult.
+
+```ts
+type SomeMatrix = [
+  [1, 2, 3],
+  [4, 5],
+  [6]
+];
+type TransposedSomeMatrix = [
+  [1, 4, 6],
+  [2, 5],
+  [3]
+];
+``` 
+
+It's easy to understand, so the mission of making a type which can transpose given 2d tuple as accurate as possible is now assigned to you!

questions/31820-hard-transpose-2/info.yml

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+difficulty: hard
+title: transpose 2
+related: 25270
+author:
+  github: E0SelmY4V
+  name: Eosellmay Li
+

questions/31820-hard-transpose-2/template.ts

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+type Matrix = readonly (readonly any[])[];
+type Transposed<T extends Matrix> = any;

questions/31820-hard-transpose-2/test-cases.ts

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+import type { Equal, Expect } from '@type-challenges/utils'
+import { ExpectFalse, NotEqual } from '@type-challenges/utils'
+
+type cases = [
+  Expect<Equal<Transposed<[
+    [1, 2, 3],
+    [4, 5, 6],
+    [7, 8, 9]
+  ]>, [
+    [1, 4, 7],
+    [2, 5, 8],
+    [3, 6, 9]
+  ]>>,
+  Expect<Equal<Transposed<[
+    ['a', 'b', 'c', 'd'],
+    ['e', 'f', 'g', 'h'],
+    ['i', 'j', 'k', 'l']
+  ]>, [
+    ['a', 'e', 'i'],
+    ['b', 'f', 'j'],
+    ['c', 'g', 'k'],
+    ['d', 'h', 'l']
+  ]>>,
+  Expect<Equal<Transposed<[
+    [1, 2, 3],
+    [4, 5]
+  ]>, [
+    [1, 4],
+    [2, 5],
+    [3]
+  ]>>,
+  Expect<Equal<Transposed<number[][]>, number[][]>>,
+  Expect<Equal<Transposed<[
+    [1, 2],
+    [3],
+    [4, 5]
+  ]>, [
+    [1, 3, 4],
+    [2, undefined, 5]
+  ]>>,
+  Expect<Equal<Transposed<[
+    [1, 2],
+    [3],
+    ...[4][],
+  ]>, [
+    [1, 3, ...4[]],
+    [2]
+  ]>>,
+  Expect<Equal<Transposed<[
+    [1, 2],
+    [3],
+    ...[4, 5, 6][],
+  ]>, [
+    [1, 3, ...4[]],
+    [2, undefined, ...5[]],
+    [undefined, undefined, ...6[]]
+  ]>>,
+  Expect<Equal<Transposed<[
+    [1, 2, 3],
+    [4],
+    ...[5][],
+    [6, 7]
+  ]>, [
+    [1, 4, ...5[], 6],
+    [2, undefined, ...undefined[], 7],
+    [3]
+  ]>>,
+  Expect<Equal<Transposed<[
+    [1, ...2[]],
+    [3, 4, ....5[]]
+  ]>, [
+    [1, 3],
+    [2 | undefined, 4],
+    ...[2 | undefined, 5 | undefined][]
+  ]>>,
+  Expect<Equal<Transposed<[
+    [1, ...2[], 3],
+    [4, 5, ....6[], 7, 8],
+    [...9[], 0]
+  ]>, [
+    [1, 4, 9 | 0],
+    [2 | 3, 5, 9 | 0 | undefined],
+    [2 | 3 | undefined , 6 | 7, 9 | 0 | undefined],
+    [2 | 3 | undefined , 6 | 7 | 8, 9 | 0 | undefined],
+    ...[2 | 3 | undefined , 6 | 7 | 8 | undefined, 9 | 0 | undefined][]
+  ]>>,
+  Expect<Equal<Transposed<[
+    [1, 2],
+    ...[3, ...4[]][]
+  ]>, [
+    [1, ...3[]],
+    [2, ...4[]],
+    ...[undefined, ...4[]][]
+  ]>>,
+  Expect<Equal<Transposed<
+    [1, 2, 3][]
+  >, [
+    1[],
+    2[],
+    3[]
+  ]>>,
+  Expect<Equal<Transposed<[
+    [1],
+    ...[2, ...3[], 4, 5][],
+    [6, 7, ...8[], 9]
+  ]>, [
+    [1, ...2[], 6],
+    [undefined, ...(3 | 4)[], 7],
+    [undefined, ...(3 | 4 | 5)[], 8 | 9],
+    ...[undefined, ...(3 | 4 | 5 | undefined)[], 8 | 9 | undefined][]
+  ]>>
+]