27133 - Square

[DevilTea]

// your answers
// Utils
type As<Input, T> = Input extends T ? Input : never
type MakeTuple<T, Length extends number, Result extends T[] = []> = Result['length'] extends Length 
  ? Result
  : MakeTuple<T, Length, [...Result, T]>
type Shifted<T extends any[]> = T extends [any, ...infer Rest extends any[]] ? Rest : T
type Popped<T extends any[]> = T extends [...infer Rest extends any[], any] ? Rest : T
type PadLeft<SplittedNum extends number[], Padding1 extends number, Padding2 extends number> = [...MakeTuple<0, Padding1>, ...MakeTuple<0, Padding2>, ...SplittedNum]


// Input
// Split digits and reverse (ex: 123 -> [3, 2, 1])
type ToSplittedNum<S extends string | number, Result extends number[] = []> = `${S}` extends infer N extends string
  ? N extends `${infer C extends number}${infer Rest}`
    ? ToSplittedNum<Rest, [C, ...Result]>
    : Result extends number[] 
      ? Result 
      : never
  : never

// Calc
// 9x9 Multiplication Table
type Digit = 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9
type MultiplyTwoDigits<D1 extends Digit, D2 extends Digit, Loop extends 0[] = [], Result extends 0[] = []> = Loop['length'] extends D2 
  ? ToSplittedNum<Result['length']>
  : MultiplyTwoDigits<D1, D2, [...Loop, 0], As<[...Result, ...MakeTuple<0, D1>], 0[]>>
type DigitMultiplicationTableKey = `${Digit}x${Digit}`
type DigitMultiplicationTable = {
  [K in DigitMultiplicationTableKey]: K extends `${infer D1 extends Digit}x${infer D2 extends Digit}`
    ? MultiplyTwoDigits<D1, D2>
    : never
}

// Addition
type AddDigits<Digits extends number[], Result extends 0[] = []> = Digits extends [infer D extends number, ...infer Rest extends number[]]
  ? MakeTuple<0, D> extends infer Temp extends 0[] 
    ? AddDigits<Rest, [...Result, ...Temp]>
    : never
  : ToSplittedNum<Result['length']>
type AddTwoSplittedNums<
  SplittedN1 extends number[],
  SplittedN2 extends number[],
  Carry extends 0 | 1 = 0,
  Result extends number[] = [],
  NextSplittedN1 extends number[] = Shifted<SplittedN1>,
  NextSplittedN2 extends number[] = Shifted<SplittedN2>,
  DigitResult extends number[] = AddDigits<[Carry, SplittedN1[0], SplittedN2[0]]>,
> = [SplittedN1, SplittedN2, Carry] extends [[0], [0], 0]
  ? Result extends number[]
    ? Result 
    : never
  : AddTwoSplittedNums<
      (NextSplittedN1 extends [] ? [0] : NextSplittedN1),
      (NextSplittedN2 extends [] ? [0] : NextSplittedN2),
      (DigitResult['length'] extends 1 ? 0 : 1),
      [...Result, DigitResult[0]]
    >

// Two Levels Loop walk through each digits of two numbers
type Multiply_Advanced_Level1_Loop<
  SplittedN1 extends number[], 
  SplittedN2 extends number[],
  Result extends number[] = [0],
  P1 extends number = Popped<SplittedN1>['length']
> = SplittedN1 extends [...infer Rest extends number[], infer D1 extends Digit]
  ? Multiply_Advanced_Level1_Loop<
      Rest,
      SplittedN2,
      AddTwoSplittedNums<Result, Multiply_Advanced_Level2_Loop<SplittedN2, D1, P1>> extends infer Temp extends number[] ? Temp : never
    >
  : Result
type Multiply_Advanced_Level2_Loop_Calc<
  D1 extends number,
  P1 extends number,
  D2 extends number,
  P2 extends number,
> = PadLeft<Multiply_Simple<D1, D2>, P1, P2> extends infer Result extends number[]
  ? Result
  : never
type Multiply_Advanced_Level2_Loop<
  SplittedN2 extends number[], 
  D1 extends number, 
  P1 extends number, 
  Result extends number[] = [0],
  P2 extends number = Popped<SplittedN2>['length']
> = SplittedN2 extends [...infer Rest extends number[], infer D2 extends number]
  ? Multiply_Advanced_Level2_Loop<
      Rest,
      D1,
      P1,
      AddTwoSplittedNums<Result, Multiply_Advanced_Level2_Loop_Calc<D1, P1, D2, P2>>
    >
  : Result

// Output
type ToOutputString<SplittedNum extends number[]> = SplittedNum extends [infer C extends number, ...infer Rest extends number[]]
  ? `${ToOutputNumber<Rest>}${C}`
  : ''
type ToNumber<S extends string> = S extends `${infer N extends number}` ? N : S
type ToOutputNumber<SplittedNum extends number[]> = ToNumber<ToOutputString<SplittedNum>>

// Multiply
// Directly map from 9x9 Multiplication Table
type Multiply_Simple<N1 extends number, N2 extends number> = `${N1}x${N2}` extends infer K extends DigitMultiplicationTableKey 
  ? DigitMultiplicationTable[K]
  : never
// Calculate every digit and sum
type Multiply_Advanced<N1 extends number, N2 extends number> = Multiply_Advanced_Level1_Loop<ToSplittedNum<N1>, ToSplittedNum<N2>>

type Multiply<N1 extends number, N2 extends number> = ToOutputNumber<
  [ToSplittedNum<N1>['length'], ToSplittedNum<N2>['length']] extends [1, 1]
    ? Multiply_Simple<N1, N2>
    : Multiply_Advanced<N1, N2>
>

type Abs<N extends number> = `${N}` extends `-${infer _N extends number}` ? _N : N

type Square<N extends number> = Multiply<Abs<N>, Abs<N>>