Demo preview: These solutions pass the automated test suite but have not been human-reviewed. Treat trade-offs and prose as draft.

Missing Number

Problem (restated)

Array of n distinct numbers in [0, n]. Find the missing one.

Intuition

XOR of 0..n with all nums cancels pairs; leftover is missing.

Approaches

XOR 0..n with nums

Tested only

Time O(n)Space O(1)

Idea. x=0..n fold with nums.

Walkthrough. [3,0,1] → 2.

Trade-offs. Sum formula also O(n); XOR avoids overflow concerns in other langs.

Solution

export function missingNumber(nums: number[]): number {
  let x = nums.length;
  for (let i = 0; i < nums.length; i++) x ^= i ^ nums[i]!;
  return x;
}

export function missingNumber(nums: number[]): number {
  let x = nums.length;
  for (let i = 0; i < nums.length; i++) x ^= i ^ nums[i]!;
  return x;
}

Template connection

Bit XOR identity (same family as single number).

Reflection

Which pattern gave this away within 90 seconds?
What changed from the standard template?
What would break the current solution?