Find Unique One-Use Combination Sums with Negative Values

Question

The candidate is asked to find unique combinations of numbers that sum up to a specific target value, allowing for negative numbers in the input list.

Codemia · Accepted Answer

The problem requires us to find all unique combinations of numbers from a given list that sum up to a specified target. The input list can contain both positive and negative integers, and each number can only be used once in each combination.

To solve this problem, we can use a backtracking approach. We will explore each number in the list, deciding whether to include it in the current combination or not. We'll keep track of the current sum and the current combination of numbers. If the current sum equals the target, we add the combination to our result set. To ensure uniqueness, we can sort the input list and skip over duplicates during the exploration.

Here is a Python implementation of the described approach:

```python
def combination_sum_unique(nums, target):
    def backtrack(start, path, target):
        if target == 0:
            result.append(path)
            return
        for i in range(start, len(nums)):
            if nums[i] > target:
                break
            if i > start and nums[i] == nums[i - 1]:
                continue
            backtrack(i + 1, path + [nums[i]], target - nums[i])

nums.sort()
    result = []
    backtrack(0, [], target)
    return result
```
This function sorts the input list and uses a helper function to perform backtracking.

The time complexity of this algorithm is O(2^n) in the worst case, where n is the number of elements in the input list. This is due to the potential combinations we explore. The space complexity is O(n) for the recursion stack and the space used to store the results.

When dealing with negative numbers, we must ensure that our algorithm can handle cases where adding a negative number could still lead to valid combinations. For example, if the input list is [-1, 1, 2] and the target is 0, the combinations should include [-1, 1]. We should also consider cases where the target is negative or zero.

Find Unique One-Use Combination Sums with Negative Values

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