Can the sum overflow an int in C#?

Yes, once n passes 46,340: n * (n + 1) no longer fits in an int. C# is unchecked by default, so the value wraps without an error; inside a checked block it throws an OverflowException instead. This problem stops at n = 5,000, but long math or XOR removes the risk.

Is there a LINQ one-liner?

return Enumerable.Range(0, nums.Length + 1).Except(nums).First(); reads well and is O(n), but it builds a hash set internally. nums.Length * (nums.Length + 1) / 2 - nums.Sum() is also one line; note that Enumerable.Sum on int runs in a checked context and throws on overflow.

Why clone the array before Array.Sort?

Array.Sort reorders the array it is given, and arrays are reference types, so the caller would see the change. Clone returns object, hence the (int[]) cast; nums.ToArray() from LINQ does the same without the cast.

Would a HashSet be clearer?

It reads naturally: var seen = new HashSet (nums); then return the first i from 0 to nums.Length where !seen.Contains(i). It is O(n) on average but stores every value, while the sum and XOR versions use O(1) memory.

Why start the XOR at nums.Length?

The loop visits indices 0 to n - 1, but the values run from 0 to n. Seeding the accumulator with n adds the one index the loop never reaches, so each value in the range is XORed in exactly once.

Missing Number in an Array in C#: Sort, Sum and XOR Solutions

missing_number.cs

C# 10.0

Not run yet

+ 6 hidden

Input

nums = [5, 2, 0, 3, 1]

Expected

Five numbers, so the range is 0 to 5. Every value shows up except 4.