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Prime factaorization with TypeScript type system.
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/* eslint-disable @typescript-eslint/no-unused-vars */ | |
type NumToTuple<N extends number, Result extends unknown[] = []> = Result['length'] extends N | |
? Result | |
: NumToTuple<N, [unknown, ...Result]> | |
type Subtraction<N extends number, M extends number> = NumToTuple<N> extends [ | |
...NumToTuple<M>, | |
...infer U | |
] | |
? U['length'] | |
: never | |
const subtraction1: Subtraction<7, 4> = 3 | |
const subtraction2: Subtraction<4, 4> = 0 | |
// @ts-expect-error | |
const subtraction3: Subtraction<4, 7> = 0 | |
type IsStrictlySmaller< | |
N extends number, | |
M extends number | |
> = Subtraction<N, M> extends never ? true : false | |
type IsDivisible<N extends number, M extends number> = 0 extends N | |
? true | |
: IsStrictlySmaller<N, M> extends true | |
? false | |
: IsDivisible<Subtraction<N, M>, M> | |
const isDivisible1: IsDivisible<3, 3> = true | |
const isDivisible2: IsDivisible<6, 3> = true | |
const isDivisible3: IsDivisible<5, 3> = false | |
// 割り算 | |
type Division<N extends number, M extends number, Q extends unknown[] = []> = IsStrictlySmaller<N, M> extends true | |
? Q['length'] | |
: Division<Subtraction<N, M>, M, [unknown, ...Q]> | |
const division1: Division<2, 3> = 0 | |
const division2: Division<3, 2> = 1 | |
const division3: Division<3, 3> = 1 | |
const division4: Division<8, 3> = 2 | |
const division5: Division<16, 4> = 4 | |
// 余り付き割り算 | |
type DivisionWithReminder< | |
N extends number, | |
M extends number, | |
Q extends unknown[] = [], | |
> = IsStrictlySmaller<N, M> extends true | |
? { | |
quotient: Q['length'], | |
reminder: N | |
} | |
: DivisionWithReminder<Subtraction<N, M>, M, [0, ...Q]> | |
// 素因数分解 | |
type PrimeFactorList<N extends number, Divisor extends unknown[] = [unknown, unknown], Result extends number[] = []> = N extends 1 | |
? Result | |
: Divisor['length'] extends N | |
? [...Result, N] | |
: IsDivisible<N, Divisor['length']> extends true | |
? PrimeFactorList<Division<N, Divisor['length']>, Divisor, [...Result, Divisor['length']]> | |
: PrimeFactorList<N, [0, ...Divisor], Result> | |
const pf1: PrimeFactorList<1> = [] | |
const pf2: PrimeFactorList<2> = [2] | |
const pf3: PrimeFactorList<3> = [3] | |
const pf4: PrimeFactorList<4> = [2, 2] | |
const pf5: PrimeFactorList<5> = [5] | |
const pf6: PrimeFactorList<6> = [2, 3] | |
const pf7: PrimeFactorList<7> = [7] | |
const pf8: PrimeFactorList<8> = [2, 2, 2] | |
const pf9: PrimeFactorList<9> = [3, 3] | |
const pf10: PrimeFactorList<10> = [2, 5] | |
const pf11: PrimeFactorList<11> = [11] | |
const pf12: PrimeFactorList<12> = [2, 2, 3] | |
const pf13: PrimeFactorList<13> = [13] | |
const pf14: PrimeFactorList<14> = [2, 7] | |
const pf15: PrimeFactorList<15> = [3, 5] | |
const pf16: PrimeFactorList<16> = [2, 2, 2, 2] | |
const pf17: PrimeFactorList<17> = [17] | |
const pf18: PrimeFactorList<18> = [2, 3, 3] | |
const pf19: PrimeFactorList<19> = [19] | |
const pf20: PrimeFactorList<20> = [2, 2, 5] | |
const pf21: PrimeFactorList<21> = [3, 7] | |
const pf22: PrimeFactorList<22> = [2, 11] | |
const pf23: PrimeFactorList<23> = [23] | |
const pf24: PrimeFactorList<24> = [2, 2, 2, 3] | |
const pf25: PrimeFactorList<25> = [5, 5] | |
const pf26: PrimeFactorList<26> = [2, 13] | |
const pf27: PrimeFactorList<27> = [3, 3, 3] | |
const pf28: PrimeFactorList<28> = [2, 2, 7] | |
const pf29: PrimeFactorList<29> = [29] | |
const pf30: PrimeFactorList<30> = [2, 3, 5] |
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