# LeetCode 136. Single Number

## The Problem

Link to original problem on Leetcode

Given a non-empty array of integers, every element appears twice except for one. Find that single one.

Note: Your algorithm should have a linear runtime complexity. Could you implement it without using extra memory?

Examples

Example 1:

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

Example 2:

Input: [4,1,2,1,2]
Output: 4

## My Solution

This solution avoids creating anything new in memory, such as another list or hash map to keep track. I don’t really want to track numbers—just find the unique one. To make it easier to do this in a single loop over the existing array, I sort it. Then I can just compare each number to its neighbors and return whichever one doesn’t have a matching neighbor.

Time complexity of $O(n)$ for my operation not counting the sort. I think space complexity is $O(1)$, since I created nothing new. Not sure how the sort might affect that, however.

const singleNumber = nums => {
// First sort the numbers so I can loop through only once
// without creating another array or hashmap
nums.sort();

// Once sorted, if the first two don't match, the first number
// must be the unique one. (The second would have a pair in
// third position.)
if (nums !== nums) {
return nums;
}

// Loop through sorted nums starting at index 1 and ending at length - 1.
// We already checked index 0.
for (let i = 1, j = nums.length - 1; i < j; i++) {
// If nums[i] doesn't equal either of its neighbors, it is unique.
if (nums[i - 1] !== nums[i] && nums[i] !== nums[i + 1]) {
return nums[i];
}
}

// If you get this far, the final number must be unique.
return nums[nums.length - 1];
};

## Best Solution

Use bitwise operations. The XOR of number n and 0 is n. Therefore, n XOR n is 0.

If you XOR each number in the array together, all the duplicates cancel out.

Time complexity of O(N) and space complexity of O(1).

const singleNumber = nums => {
return nums.reduce((result, num) => result ^ num);
};