What is the optimal time complexity of solving Combination 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 Combination 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 Combination 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 Combination 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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Combination Sum II

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

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Problem Statement

Easy

Given a collection of candidate numbers (candidates) and a target number (target), find all unique combinations in candidates where the candidate numbers sum to target.

Each number in candidates may only be used once in the combination.

Note: The solution set must not contain duplicate combinations.

Implement a function combinationSum2(candidates: list, target: int) -> list.

Constraints

•1 <= candidates.length <= 100
•1 <= candidates[i] <= 50
•1 <= target <= 30

Examples

Example 1

Input

[10,1,2,7,6,1,5], 8

Output

[[1,1,6],[1,2,5],[1,7],[2,6]]

Explanation

All unique combinations that sum to 8, using each element at most once.

Example 2

Input

[2,5,2,1,2], 5

Output

[[1,2,2],[5]]

Explanation

1+2+2 = 5 and 5 = 5. These are the only unique combinations.

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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