268. Missing Number

Given an array containing n distinct numbers taken from 0, 1, 2, ..., n, find the one that is missing from the array.

Example 1:

Input: [3,0,1]
Output: 2

Example 2:

Input: [9,6,4,2,3,5,7,0,1]
Output: 8

Note: Your algorithm should run in linear runtime complexity. Could you implement it using only constant extra space complexity?

// Math
int missingNumber(vector<int>& nums) { // time: O(n); space: O(1)
    int n = nums.size(), sum = 0;
    for (int num : nums) sum += num;
    return n * (n + 1) / 2 - sum;
}

// XOR
int missingNumber(vector<int>& nums) { // time: O(n); space: O(1)
    int res = 0;
    for (int i = 0; i < nums.size(); ++i) {
        res ^= (i + 1) ^ nums[i];
    }
    return res;
}