What is the optimal time complexity of solving Two Sum?

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 Two Sum?

The space complexity is O(n) 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 Two Sum?

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 Two Sum?

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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Two Sum

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

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Problem Statement

Easy

Given an array of integers nums and an integer target, return indices of the two numbers such that they add up to target.

You may assume that each input would have exactly one solution, and you may not use the same element twice.

Constraints

•2 <= nums.length <= 10^4
•-10^9 <= nums[i] <= 10^9
•-10^9 <= target <= 10^9
•Only one valid answer exists.

Examples

Example 1

Input

nums = [2,7,11,15], target = 9

Output

[0,1]

Explanation

Because nums[0] + nums[1] == 9, we return [0, 1].

Example 2

Input

nums = [3,2,4], target = 6

Output

[1,2]

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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