Single Number II: Find the Element Appearing Once

In many data processing and analysis scenarios, you might encounter collections of numbers where most elements appear a specific number of times, while one unique element appears only once. This challenge focuses on efficiently identifying that single, distinct number. This skill is fundamental in areas like anomaly detection and data integrity checks.

Problem Description

Given an array of integers nums, where every element appears exactly three times except for one, which appears exactly once. Your task is to find that single element.

Key Requirements:

• Identify the integer that appears only once.
• The solution should be efficient in terms of time and space complexity.

Expected Behavior:

• The function should return the integer that appears once.

Important Edge Cases:

• The input array can be empty.
• The input array can contain negative numbers.
• The single number could be zero.

Examples

Example 1:

Input: [2, 2, 3, 2]
Output: 3
Explanation: The number 2 appears three times, and the number 3 appears once.

Example 2:

Input: [-2, -2, 1, -2]
Output: 1
Explanation: The number -2 appears three times, and the number 1 appears once.

Example 3:

Input: [0, 1, 0, 1, 0, 1, 99]
Output: 99
Explanation: The numbers 0 and 1 appear three times, and the number 99 appears once.

Constraints

• 1 <= nums.length <= 3 * 10^4
• -2^31 <= nums[i] <= 2^31 - 1
• Every element in the array appears exactly three times except for one element that appears exactly once.
• Your algorithm should have a linear runtime complexity. Could you implement it without using extra memory?

Notes

Consider how the appearance of numbers in groups of three affects their binary representation. Think about bitwise operations. While extra memory is discouraged, a solution that uses O(1) extra space is highly preferred and often the intended solution for this problem.