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.

For example,

Given nums = [0, 1, 3] return 2.

Note:

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

 

Solution 1: sum(0,1,...,n)-sum(array)=missing number 

class Solution {
public:
    int missingNumber(vector<int>& nums) {
        long long sum1=0,sum2=0;
        for (int num:nums) sum1+=num;
        for (int i=0;i<nums.size()+1;i++) sum2+=i;
        return sum2-sum1;
    }
};

 Solution 2: Use the bit manipulation XOR(exclusive or). XOR has the properties: A^A=0,A^0=A. XOR all the (2n+1) numbers, the result is the missing number.

class Solution {
public:
    int missingNumber(vector<int>& nums) {
        int res=0,n=nums.size();
        for (int i=0;i<n;i++){
            res^=(i+1)^nums[i];
        }
        return res;
    }
};