Single Number II

Problem

Given an integer array nums where every element appears three times except for one, which appears exactly once, find the single element and return it. You must implement a solution with a linear runtime complexity and use only constant extra space.

Examples

The brute-force approach

Count the frequency of each element. Return the one with frequency 1.

from collections import Counter
counts = Counter(nums)
for num, cnt in counts.items():
    if cnt == 1:
        return num

O(n) time but O(n) space for the counter.

Spotting the pattern

This is a Bit Manipulation problem. The key question to ask yourself:

Why does summing each bit position modulo 3 isolate the unique number? What happens to the bits from numbers that appear three times?

Answering that is where it clicks, and it's exactly what the guided walkthrough below builds with you: the pattern reasoning, a progressive hint ladder that never spoils the answer, a row-by-row dry run, the optimized solution, and an in-browser editor to run your code against real test cases.