add sort

sort.ts

@@ -0,0 +1,135 @@
+import type { Equal, Expect } from '@type-challenges/utils'
+
+type cases = [
+  Expect<Equal<Sort<[]>, []>>,
+  Expect<Equal<Sort<[1]>, [1]>>,
+  Expect<Equal<Sort<[2, 1]>, [1, 2]>>,
+  Expect<Equal<Sort<[0, 0, 0]>, [0, 0, 0]>>,
+  Expect<Equal<Sort<[1, 2, 3]>, [1, 2, 3]>>,
+  Expect<Equal<Sort<[3, 2, 1]>, [1, 2, 3]>>,
+  Expect<Equal<Sort<[3, 2, 1, 2]>, [1, 2, 2, 3]>>,
+  Expect<Equal<Sort<[3, 2, 0, 1, 0, 0, 0]>, [0, 0, 0, 0, 1, 2, 3]>>,
+  Expect<Equal<Sort<[2, 4, 7, 6, 6, 6, 5, 8, 9]>, [2, 4, 5, 6, 6, 6, 7, 8, 9]>>,
+  Expect<Equal<Sort<[1, 1, 2, 1, 1, 1, 1, 1, 1]>, [1, 1, 1, 1, 1, 1, 1, 1, 2]>>,
+  Expect<Equal<Sort<[], true>, []>>,
+  Expect<Equal<Sort<[1], true>, [1]>>,
+  Expect<Equal<Sort<[2, 1], true>, [2, 1]>>,
+  Expect<Equal<Sort<[0, 0, 0], true>, [0, 0, 0]>>,
+  Expect<Equal<Sort<[1, 2, 3], true>, [3, 2, 1]>>,
+  Expect<Equal<Sort<[3, 2, 1], true>, [3, 2, 1]>>,
+  Expect<Equal<Sort<[3, 2, 1, 2], true>, [3, 2, 2, 1]>>,
+  Expect<Equal<Sort<[3, 2, 0, 1, 0, 0, 0], true>, [3, 2, 1, 0, 0, 0, 0]>>,
+  Expect<Equal<Sort<[2, 4, 7, 6, 6, 6, 5, 8, 9], true>, [9, 8, 7, 6, 6, 6, 5, 4, 2]>>,
+]
+
+type ApproxEqualLength<
+  T extends unknown[],
+  U extends unknown[],
+  N extends number = T['length'],
+  M extends number = U['length'],
+> =
+N extends M
+  ? true
+  : [...T, 1]['length'] extends M
+    ? true
+    : [...U, 1]['length'] extends N
+      ? true
+      : false
+;
+
+type SplitHalf<
+  T extends number[],
+  Left extends number[] = [],
+  Right extends number[] = T,
+> =
+ApproxEqualLength<Left, Right> extends true
+  ? [Left, Right]
+  : Right extends [infer Head, ...infer Tail]
+    ? Head extends number
+      ? Tail extends number[]
+        ? SplitHalf<T, [...Left, Head], Tail>
+        : never
+      : never
+    : never
+;
+
+type Greater<
+    T extends number,
+    U extends number,
+    Acc extends 1[] = []
+> = 
+Acc['length'] extends T
+    ? Acc['length'] extends U
+        ? false
+        : false
+    : Acc['length'] extends U
+        ? true
+        : Greater<T, U, [1, ...Acc]>
+;
+
+type Less<
+  T extends number,
+  U extends number,
+  Acc extends 1[] = []
+> =
+Acc['length'] extends T 
+  ? Acc['length'] extends U
+    ? false
+    : true
+  : Acc['length'] extends U
+    ? false
+    : Less<T, U, [...Acc, 1]>
+;
+
+
+type Merge<
+  T extends number[],
+  U extends number[],
+  Desc extends boolean = false,
+  Acc extends number[] = [],
+> = 
+T extends [infer THead, ...infer TTail]
+  // T has elements
+  ? U extends [infer UHead, ...infer UTail]
+    // U has elements
+    ? THead extends number
+      ? UHead extends number
+        ? TTail extends number[]
+          ? UTail extends number[]
+            ? Desc extends false
+              ? Less<THead, UHead> extends true
+                ? Merge<TTail, U, Desc, [...Acc, THead]>
+                : Merge<T, UTail, Desc, [...Acc, UHead]>
+              : Greater<THead, UHead> extends true
+                ? Merge<TTail, U, Desc, [...Acc, THead]>
+                : Merge<T, UTail, Desc, [...Acc, UHead]>
+            : never
+          : never
+        : never
+      : never
+    // U has no elements
+    : [...Acc, THead, ...TTail]
+  // T has no elements
+  : [...Acc, ...U]
+;
+
+type Sort<
+  T extends number[],
+  Desc extends boolean = false
+> =
+T['length'] extends 0
+  ? []
+  : T['length'] extends 1
+    ? T
+    : SplitHalf<T> extends [infer First, infer Second, ...infer Tail]
+      ? First extends number[]
+        ? Second extends number[]
+          ? Merge<
+              Sort<First, Desc>,
+              Sort<Second, Desc>,
+              Desc
+            >
+          : never
+        : never
+      : never
+;