What is the optimal time complexity of solving Two Sum II?

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 II?

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 II?

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 II?

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 II

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

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Problem Statement

Easy

Given a 1-indexed array of integers numbers that is already sorted in non-decreasing order, find two numbers such that they add up to a specific target number.

Return the indices of the two numbers, index1 and index2, added by one as an integer array [index1, index2] of length 2.

You may not use the same element twice. Your solution must use only constant extra space.

Write a function twoSum(numbers: List[int], target: int) -> List[int].

Constraints

•2 <= len(numbers) <= 3 * 10^4
•-1000 <= numbers[i] <= 1000
•numbers is sorted in non-decreasing order
•-1000 <= target <= 1000
•Exactly one solution exists

Examples

Example 1

Input

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

Output

[1, 2]

Explanation

2 + 7 = 9. The indices are 1 and 2 (1-indexed).

Example 2

Input

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

Output

[1, 3]

Explanation

2 + 4 = 6. The indices are 1 and 3 (1-indexed).

Example 3

Input

numbers = [-1, 0], target = -1

Output

[1, 2]

Explanation

-1 + 0 = -1. The indices are 1 and 2 (1-indexed).

Need a Hint?

Use two pointer variables starting at different bounds (e.g. left = 0, right = length - 1) and shrink the search window.

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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