Solve Subset Sum And Return All Matching Subsets

Question

The candidate is asked to solve the Subset Sum problem by finding all subsets of a given set that sum up to a specified target value.

Codemia · Accepted Answer

To solve the Subset Sum problem, we can use a backtracking approach to explore all possible subsets of the given set. We will recursively build subsets and check if their sum matches the target. If it does, we will store that subset. This method ensures that we explore all combinations without missing any potential solutions.

Here is a Python implementation of the backtracking approach:

```python
def subset_sum(nums, target):
    result = []
    def backtrack(start, path, remaining):
        if remaining == 0:
            result.append(path)
            return
        for i in range(start, len(nums)):
            if nums[i] > remaining:
                continue
            backtrack(i + 1, path + [nums[i]], remaining - nums[i])
    backtrack(0, [], target)
    return result
```
This function initializes a result list and defines a nested backtracking function to explore subsets.

The time complexity of this backtracking solution is O(2^n), where n is the number of elements in the input set. This is because we generate all possible subsets. The space complexity is O(k), where k is the maximum depth of the recursion stack, which can go up to n in the worst case.

It's important to consider edge cases such as an empty input set or a target sum of zero. In the case of an empty set, the only subset is the empty subset, which sums to zero. If the target is zero, we should return the empty subset as a valid solution.

Interviewers will be looking for clarity in your explanation of the approach, the correctness of your implementation, and your ability to analyze the complexity of your solution. They will also pay attention to how you handle edge cases and your thought process when discussing potential optimizations.

Solve Subset Sum And Return All Matching Subsets

Apple

What the Interviewer Expects

Key Topics to Cover

How to Approach This

Possible Follow-up Questions

Sharpen Your Skills on Codemia

Sample Answer

Approach

Algorithm

Submit Your Answer

Apple Software Engineer Interview Guide

Related Questions

Binary Search on graph

Count kth largest element in array

Find connected components in string

Merge Three Sorted strings

Binary Search on string