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

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

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Problem Statement

Easy

Given an array of distinct integers candidates and a target integer target, return a list of all unique combinations of candidates where the chosen numbers sum to target. You may return the combinations in any order.

The same number may be chosen from candidates an unlimited number of times. Two combinations are unique if the frequency of at least one of the chosen numbers is different.

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

Constraints

•1 <= candidates.length <= 30
•2 <= candidates[i] <= 40
•All elements of candidates are distinct
•1 <= target <= 40

Examples

Example 1

Input

[2,3,6,7], 7

Output

[[2,2,3],[7]]

Explanation

2 + 2 + 3 = 7 and 7 = 7. These are the only two combinations.

Example 2

Input

[2,3,5], 8

Output

[[2,2,2,2],[2,3,3],[3,5]]

Explanation

2+2+2+2 = 8, 2+3+3 = 8, and 3+5 = 8.

Example 3

Input

[2], 1

Output

[]

Explanation

No combination of 2's can sum to 1.

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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