Permutation

问题描述

实现联合类型的全排列，将联合类型转换成所有可能的全排列数组的联合类型。

type perm = Permutation<'A' | 'B' | 'C'>; // ['A', 'B', 'C'] | ['A', 'C', 'B'] | ['B', 'A', 'C'] | ['B', 'C', 'A'] | ['C', 'A', 'B'] | ['C', 'B', 'A']

// ============= Test Cases =============
import type { Equal, Expect } from './test-utils'
​
type cases = [
  Expect<Equal<Permutation<'A'>, ['A']>>,
  Expect<
    Equal<
      Permutation<'A' | 'B' | 'C'>,
      ['A', 'B', 'C'] | ['A', 'C', 'B'] | ['B', 'A', 'C'] | ['B', 'C', 'A'] | ['C', 'A', 'B'] | ['C', 'B', 'A']
    >
  >,
  Expect<
    Equal<
      Permutation<'B' | 'A' | 'C'>,
      ['A', 'B', 'C'] | ['A', 'C', 'B'] | ['B', 'A', 'C'] | ['B', 'C', 'A'] | ['C', 'A', 'B'] | ['C', 'B', 'A']
    >
  >,
  Expect<Equal<Permutation<boolean>, [false, true] | [true, false]>>,
  Expect<Equal<Permutation<never>, []>>
]
​
// ============= Your Code Here =============
// 答案
type Permutation<All, Item = All> = [All] extends [never]
  ? []
  : Item extends All
  ? [Item, ...Permutation<Exclude<All, Item>>]
  : never
​

废了，一点思路都没有，先记录下。

详细解析参考:

• TS 类型体操笔记 - 296 Permutation

• 296 - Permutation (with explanations)

表格很重要

Iteration	T	K in K extends K	X<T, K>	[K, ...P<X<T, K>>]	Result
1	1 | 2 | 3	1	2 | 3	[1, ...P<2 | 3>]
1.1	2 | 3	2	3	[1, 2, ...P<3>]
1.1.1	3	3	never	[1, 2, 3, ...[]]	[1, 2, 3]
1.2	2 | 3	3	2	[1, 3, ...P<2>]
1.2.1	2	2	never	[1, 3, 2, ...[]]	[1, 3, 2]
2	1 | 2 | 3	2	1 | 3	[2, ...P<1 | 3>]
2.1	1 | 3	1	3	[2, 1, ...P<3>]
2.1.1	3	3	never	[2, 1, 3, ...[]]	[2, 1, 3]
2.2	1 | 3	3	1	[2, 3, ...P<1>]
2.2.1	1	1	never	[2, 3, 1, ...[]]	[2, 3, 1]
3	1 | 2 | 3	3	1 | 2	[3, ...P<1 | 2>]
3.1	1 | 2	1	2	[3, 1, ...P<2>]
3.1.1	2	2	never	[3, 1, 2, ...[]]	[3, 1, 2]
3.2	1 | 2	2	1	[3, 2, ...P<1>]
3.2.1	1	1	never	[3, 2, 1, ...[]]	[3, 2, 1]