Closest Subsequence Sum
Reported by candidates from Salesforce's online assessment. Pattern, common pitfall, and the honest play if you blank under the timer.
Salesforce's September OA included Closest Subsequence Sum, a problem that looks deceptively simple but rewards careful thought. You're given an array and a target value, then asked to find the subsequence sum that comes closest to that target. It's not asking for the sum itself, but the minimum absolute difference. The trap is that brute force (checking every subsequence) collapses on arrays larger than ~20 elements. You need a smarter approach, and StealthCoder will catch the pattern if you blank during the live assessment.
Pattern and pitfall
The standard solution uses meet-in-the-middle partitioning. Split your array into two halves, generate all possible sums from the first half (2^n/2 possibilities), and all from the second half. Sort one half, then for each sum in the second half, binary search the first half to find the closest match. This reduces the exponential nightmare to something tractable. The key insight is that you're not finding an exact sum, you're minimizing the gap. Many candidates waste time on dynamic programming (which works but is slower) or give up and write exponential code. Know the partition trick and you're ahead. This is where StealthCoder becomes your safety net if your mind goes blank on the binary search refinement during the OA.
StealthCoder is the hedge for the one pattern you didn't drill. It runs invisibly during the screen share.
You can drill Closest Subsequence Sum cold, or you can hedge it. StealthCoder runs invisibly during screen share and surfaces a working solution in under 2 seconds. The proctor sees the IDE. They don't see what's behind it. If you're reading this with an OA window open, you're who this was built for.
Get StealthCoderRelated leaked OAs
This OA pattern shows up on LeetCode as closest subsequence sum. If you have time before the OA, drill that.
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Salesforce reuses patterns across OAs. If you're reading this with an OA window open, you're who this was built for. Works on HackerRank, CodeSignal, CoderPad, and Karat.
Closest Subsequence Sum FAQ
Is this really asking me to check every subsequence?+
No. Brute force checking 2^n subsequences will time out. The intended approach is meet-in-the-middle with binary search. Split the array in half, generate all sums from each half, sort one, and binary search to find the closest pair across halves.
Can I use dynamic programming instead of meet-in-the-middle?+
DP works conceptually but is slower and often TLEs on larger arrays. Meet-in-the-middle is the pattern Salesforce expects here. It's the algorithmic insight they're testing.
How do I handle negative numbers and zero?+
Negative numbers don't break the approach. Zero is just another possible sum. Generate all sums (they can be negative), sort them, and binary search. The target value itself might also be negative. Treat it as a number, not a special case.
What's the actual time complexity?+
Generating all sums is O(2^(n/2)). Sorting one half is O(2^(n/2) * log(2^(n/2))). Binary searching each sum is O(2^(n/2) * log(2^(n/2))). Total is roughly O(2^(n/2) * n), which handles n up to 40 easily.
Do I need to return the actual subsequence or just the difference?+
Always check the problem statement carefully. Most variants ask for the minimum absolute difference only, not the elements themselves. But some ask for the actual subsequence. Returning just the difference is the common ask. Code accordingly.