What is the optimal time complexity of solving Single Number?

The optimized solution achieves a time complexity of O(n) by using sorting, mathematical shortcuts, or hash table lookups.

What is the auxiliary space complexity for Single Number?

The space complexity is O(1) since we only use a minimal/constant amount of extra memory for tracking variables (or auxiliary space if dynamic structures are allocated).

What are the typical edge cases we must handle in Single Number?

Key edge cases include empty collections, negative or large bounds causing integer overflow, arrays with only one element, or inputs where target criteria are not met.

How can we optimize the brute force approach for Single Number?

Brute force methods often inspect all possible combinations. We optimize this by sorting the input list to enable binary search, or tracking processed items in a set to avoid redundant nested loop lookups.

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Single Number

Learn how to solve the 'Single Number' problem. This detailed resource details brute force and optimized approaches.

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Problem Statement

Easy

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

You must implement a solution with a linear runtime complexity and use only constant extra space.

Write a function singleNumber(nums: List[int]) -> int.

Constraints

•1 <= len(nums) <= 3 * 10^4
•-3 * 10^4 <= nums[i] <= 3 * 10^4
•Each element in the array appears twice except for one element which appears only once

Examples

Example 1

Input

nums = [2,2,1]

Output

Explanation

The element 1 appears once.

Example 2

Input

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

Output

Explanation

The element 4 appears once.

Example 3

Input

nums = [1]

Output

Explanation

The element 1 appears once.

Need a Hint?

Analyze the input constraints. Try sorting first (O(n log n)) or using a hash map/set to track seen elements in O(n) time.

Edge Cases to Watch

Empty list or null input variables
Single item lists/arrays
Extremely large input bounds causing integer or stack overflow

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