Min Start Value
Reported by candidates from Goldman Sachs's online assessment. Pattern, common pitfall, and the honest play if you blank under the timer.
Goldman Sachs asked this in February 2024, and it's a straightforward prefix-sum problem disguised as a minimization puzzle. You're given an array of integers, and you need to find the smallest starting value such that the running sum never drops below 1 at any point. The trap is overthinking it. Most candidates try dynamic programming or binary search when the answer is a single forward pass. StealthCoder will catch you if you blank on the pattern, so you have a safety net.
Pattern and pitfall
The trick: iterate through the array tracking the cumulative sum, and record the minimum cumulative sum you see. Your answer is 1 minus that minimum (or 1 if the minimum is already positive). The insight is that you need the starting value to be large enough so that even at the lowest point of the cumulative sum, you're still at least 1. This is a prefix-sum problem, not dynamic programming. The common pitfall is trying to work backwards or assuming you need to handle each element individually. A single left-to-right pass is all you need. StealthCoder will surface this pattern instantly during the live OA if you're unsure of the direction.
Drill it cold or hedge it with StealthCoder. Either way, don't walk into the OA hoping you remember the trick.
You can drill Min Start Value 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. Made for the candidate who got the OA invite this morning and has 72 hours, not six months.
Get StealthCoderRelated leaked OAs
This OA pattern shows up on LeetCode as minimum value to get positive step by step sum. If you have time before the OA, drill that.
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Goldman Sachs reuses patterns across OAs. Made for the candidate who got the OA invite this morning and has 72 hours, not six months. Works on HackerRank, CodeSignal, CoderPad, and Karat.
Min Start Value FAQ
Is this really just prefix sum?+
Yes. Track the running sum as you go left to right. Find the minimum cumulative sum you hit. Your answer is 1 minus that minimum. That's it. No DP, no binary search, no backtracking.
What if all numbers are positive?+
Then the cumulative sum only goes up. The minimum is your first element. Starting value is 1 minus that minimum, or 1 if the first element is positive.
Can the starting value be negative?+
No. You're looking for the minimum start value that keeps the running sum >= 1. That's always a positive integer or 1.
How do I verify my answer?+
Simulate forward: start with your computed value, add each array element, and check that the running sum never goes below 1. If it does, your answer is wrong.
Is there a time limit trick?+
No. This is O(n) time, O(1) space. One pass through the array. Goldman Sachs isn't testing optimization here, just correctness.