What is the best approach to solve Single Number?

The optimal approach for Single Number is the "Optimal — XOR Bit Trick" technique. It runs in O(n) time and uses O(1) space. Key property: a XOR a = 0 and a XOR 0 = a. XOR is commutative and associative. XOR-ing all numbers cancels every pair, leaving only the single number. One line, zero extra space.

What is the time complexity of Single Number?

The optimal solution for Single Number has a time complexity of O(n) and a space complexity of O(1), achieved using the Bit Manipulation pattern.

Is Single Number a Easy LeetCode problem?

Yes, LeetCode #136 (Single Number) is rated Easy. It uses the Bit Manipulation pattern and is commonly asked in interviews at Amazon, Bloomberg, Google.

How to solve Single Number in Python, Java, C++, and JavaScript?

LumiChats provides complete solutions for Single Number in Python, Java, C++, and JavaScript, along with step-by-step visual animations and time/space complexity analysis. All solutions are free to view.

#136EasyBit Manipulation

Single Number

XOR cancels duplicates — the cleverest single-line solution in DSA.

AmazonBloombergGoogleApple

Problem Statement

Given a non-empty array nums where every element appears twice except for one, find that single one. You must implement a solution with linear runtime complexity and use only constant extra space.

Examples

Example 1

Input:nums = [2,2,1]

Output:1

Example 2

Input:nums = [4,1,2,1,2]

Output:4

Constraints

1 ≤ nums.length ≤ 3 × 10⁴
-3 × 10⁴ ≤ nums[i] ≤ 3 × 10⁴
Each element appears twice except for one.

Solutions

Hash Map to Count Occurrences

TimeO(n)SpaceO(n)

Count occurrences of each number using a hash map. Return the number whose count is 1. Uses O(n) extra space.

Visual Animation

def singleNumber(nums: list[int]) -> int:
    counts = {}
    for num in nums:
        counts[num] = counts.get(num, 0) + 1
    return next(k for k, v in counts.items() if v == 1)

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