## Single Number III

07/16/2016 Bit Manipulation

## Question

Given an array of numbers nums, in which exactly two elements appear only once and all the other elements appear exactly twice. Find the two elements that appear only once.

For example:

Given nums = [1, 2, 1, 3, 2, 5], return [3, 5].

Note:

1. The order of the result is not important. So in the above example, [5, 3] is also correct.
2. Your algorithm should run in linear runtime complexity. Could you implement it using only constant space complexity?

## Solution

Result: Accepted Time: 8 ms

Here should be some explanations.

/**
* Return an array of size *returnSize.
* Note: The returned array must be malloced, assume caller calls free().
*/
int* singleNumber(int* nums, int numsSize, int* returnSize) {
int * ans = malloc(sizeof(int) * 2);
*returnSize = 2;
int last_bit = 0, a = 0, b = 0;
for(int i = 0; i < numsSize; i++)
last_bit ^= nums[i];
last_bit = last_bit&(-last_bit);
for(int i = 0; i < numsSize; i++)
if(nums[i] & last_bit)
a ^= nums[i];
else
b ^= nums[i];
ans[0] = a;
ans[1] = b;
return ans;
}

Complexity Analytics

• Time Complexity: $O(n)$
• Space Complexity: $O(1)$