Missing Number

Problem

Given an array nums containing n integers in the range [0, n] without any duplicates, return the single number in the range that is missing from nums.

Follow-up: Could you implement a solution using only O(1) extra space complexity and O(n) runtime complexity?

Examples

Example 1:

Input: nums = [1,2,3]

Output: 0

Explanation: Since there are 3 numbers, the range is [0,3]. The missing number is 0 since it does not appear in nums.

Example 2:

Input: nums = [0,2]

Output: 1

Constraints

• 1 <= nums.length <= 1000

You should aim for a solution with O(n) time and O(1) space, where n is the size of the input array.

Solution

Using the fact that a ^ a = 0 and a ^ 0 = a, we XOR all numbers from [0,n], then XOR all the numbers in nums. The result is the missing item.

class Solution {
public:
    int missingNumber(vector<int>& nums) {
        int n = nums.size();
        int x = n;
        for (int i = 0; i < nums.size(); ++i) {
            x ^= i;
            x ^= nums[i];
        }
        return x;
    }
};