Square

Problem Link

Problem

Given a number N, return its square.

type T0 = Square<0>  // 0
type T1 = Square<1>  // 1
type T2 = Square<3>  // 9
type T3 = Square<-3> // 9  (square of absolute value)

Solution

// Build a tuple of length N
type BuildTuple<N extends number, T extends unknown[] = []> =
  T['length'] extends N ? T : BuildTuple<N, [...T, unknown]>

// Absolute value for number type (handles negatives via string)
type Abs<N extends number> =
  `${N}` extends `-${infer P extends number}` ? P : N

// Concatenate two tuples and return length = A + B
type Add<A extends number, B extends number> =
  [...BuildTuple<A>, ...BuildTuple<B>]['length']

// Repeat addition B times: A * B
type Multiply<
  A extends number,
  B extends number,
  Count extends unknown[] = [],
  Acc extends unknown[] = []
> =
  Count['length'] extends B
    ? Acc['length']
    : Multiply<A, B, [...Count, unknown], [...Acc, ...BuildTuple<A>]>

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

How it works:

1. Abs<N> strips a leading - from the string representation to get the positive value.
2. BuildTuple<N> constructs a tuple of length N for use in arithmetic.
3. Multiply<A, B> accumulates A copies of a length-A tuple, iterating B times.
4. Square<N> calls Multiply<Abs<N>, Abs<N>>.

Limitation: Works for small numbers due to TypeScript’s recursion depth limit.

Key Takeaways

• Type-level multiplication is repeated addition; addition is tuple concatenation.
• Handling negatives: convert to string, strip -, parse back with infer N extends number.
• For larger numbers a string-digit approach is needed, but tuple arithmetic is cleaner for small inputs.