268. Missing Number

At a Glance

Topic: bit-manipulation
Pattern: XOR / Gauss sum (Bit Manipulation)
Difficulty: Easy
Companies: Amazon, Microsoft, Google, Bloomberg, Facebook
Frequency: Very High
LeetCode: 268

Problem (one-liner)

numbers contains len(numbers) distinct values drawn from 0..len(numbers) inclusive with exactly one missing. Return the missing value in O(n) time, prefer O(1) extra space.

Recognition Cues

Range [0..n] with length n array — one hole
XOR all indices and values, or use arithmetic sum identity

Diagram

At-a-glance flow (replace with problem-specific Mermaid as you refine this note). camelCase node IDs; no spaces in IDs.

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Approaches

Brute force — sort and scan — O(n log n).
Hash set — O(n) time / O(n) space.
Optimal — XOR pairing or sum formula — O(n) time / O(1) space.

Optimal Solution

Go

package main

func missingNumber(numbers []int) int {
	xorAll := len(numbers)
	for index := range numbers {
		xorAll ^= index ^ numbers[index]
	}
	return xorAll
}

JavaScript

function missingNumber(numbers) {
	let xorAll = numbers.length;
	for (let index = 0; index < numbers.length; index++) {
		xorAll ^= index ^ numbers[index];
	}
	return xorAll;
}

Walkthrough

numbers = [3, 0, 1] (missing 2), length 3.

Accumulate xorAll starting with n, then for each index index, fold index and numbers[index]. Every present value cancels with its index partner except the missing number pairs only with its index, leaving the missing.

Invariant: XOR of multiset {0..n} xor multiset of array leaves missing.

Edge Cases

Missing 0
Missing n
Single element [0] missing 1 or inverse per length

Pitfalls

Integer overflow on sum approach — XOR avoids it
XOR vs sum when duplicates exist — wrong problem variant

Variants

Find two missing (bitmask / sum equations).
Cyclic sort template on [1..n] (different pattern).

Mind-Map Tags

#xor #missing-value #index-match #range-0-n #linear