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Minus One

Posted at # TypeScript # TypeChallenge # TC-Medium
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Minus One

Problem Link

Problem

Given a number (always positive) as a type, your type should return the number decreased by one.

type Zero = MinusOne<1>     // 0
type FiftyFour = MinusOne<55> // 54

Solution

Approach 1: Build an Array and Take its Length

The classic TypeScript trick for arithmetic: build a tuple of length N, then measure ['length'] after manipulating it.

To subtract 1, we build a tuple of length N and then take the length of its tail (drop the first element).

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

// Drop the first element and read length
type MinusOne<T extends number> =
  BuildTuple<T> extends [infer _, ...infer Rest]
    ? Rest['length']
    : never

How it works:

  1. BuildTuple<5> → [unknown, unknown, unknown, unknown, unknown]
  2. Destructuring [infer _, ...infer Rest] gives a 4-element Rest.
  3. Rest['length'] → 4

Limitation: TypeScript’s recursive type depth limit means this breaks for large numbers (> ~1000).

Approach 2: String-Based Digit Subtraction (handles larger numbers)

For larger numbers, convert to a string and implement digit-by-digit subtraction.

type DigitMinusOne = {
  '0': '9'
  '1': '0'
  '2': '1'
  '3': '2'
  '4': '3'
  '5': '4'
  '6': '5'
  '7': '6'
  '8': '7'
  '9': '8'
}

// Subtract 1 from a numeric string, handling borrow propagation
type SubtractOneStr<S extends string> =
  S extends `${infer Head}${infer Last}`
    ? Last extends '0'
      ? Head extends ''
        ? never  // would go negative
        : `${SubtractOneStr<Head>}9`
      : `${Head}${DigitMinusOne[Last & keyof DigitMinusOne]}`
    : never

// Remove leading zeros (e.g., "09" -> "9"), but keep single "0"
type TrimLeadingZeros<S extends string> =
  S extends `0${infer Rest}`
    ? Rest extends ''
      ? '0'
      : TrimLeadingZeros<Rest>
    : S

type MinusOne<T extends number> =
  `${T}` extends '0'
    ? never  // 0 - 1 is out of scope (problem says always positive)
    : TrimLeadingZeros<SubtractOneStr<`${T}`>> extends `${infer N extends number}`
      ? N
      : never

How it works:

  1. Convert T to its string representation with template literal.
  2. Subtract 1 from the last digit; if it was '0', borrow from the left (recursively).
  3. Strip leading zeros (e.g., 100 - 1 = 099 → 99).
  4. Parse the result string back to a number type using infer N extends number.

This approach handles numbers up to TypeScript’s template literal limits (well past 1000).

Key Takeaways

TechniqueWhen to use
Tuple lengthSmall numbers (≤ ~999), simple/readable
String digit mathLarge numbers, production-ready solutions