面试题56 - I

一个整型数组 nums 里除两个数字之外，其他数字都出现了两次。请写程序找出这两个只出现一次的数字。要求时间复杂度是O(n)，空间复杂度是O(1)。

示例 1：

输入：nums = [4,1,4,6]
输出：[1,6] 或 [6,1]

示例 2：

输入：nums = [1,2,10,4,1,4,3,3]
输出：[2,10] 或 [10,2]

限制：

• 2 <= nums <= 10000

Solutions

1. bit operation

2. Use xor to remove numbers occurred two times and the resulting xored number res is num1 ^ num2.

3. Then partition the whole array into two parts containing num1 and num2 in each part.

   • Randomly choose one 1 bit in res as the partition criteria.

4. Repeat the first step for each part.

class Solution {
public:
    vector<int> singleNumbers(vector<int>& nums) {
        int res = 0;
        for (auto & n : nums)
            res ^= n;
        int lowbit = res & -res;
        int num1 = 0, num2 = 0;
        for (auto & n : nums) {
            if (n & lowbit)
                num1 ^= n;
            else
                num2 ^= n;
        }

        return {num1, num2};
    }
};