The Minimum Value to Get Positive Step by Step Sum problem asks you to find the minimum positive starting value such that, when you add each element of the array one by one, the running sum never drops to zero or below. This Minimum Value to Get Positive Step by Step Sum coding problem is a clean prefix sum problem that tests minimum prefix tracking.
Goldman Sachs, Microsoft, Google, IBM, and Dell ask this as a straightforward easy-level problem. It confirms candidates understand prefix sums and can correctly identify the minimum initial value needed to keep all prefix sums positive. The array and prefix sum interview pattern is the core here, and clean implementation separates confident candidates from hesitant ones.
Prefix sum + minimum tracking. Compute running prefix sums of the array. Track the minimum running sum encountered. The required starting value = 1 - min_running_sum (to shift the minimum up to at least 1). If the minimum running sum is already ≥ 1, the starting value is just 1.
Array: [-3, 2, -3, 4, 2]. Starting value = 1.
Running sums with start=1: 1-3=-2 (negative!). Need start value such that even this reaches ≥ 1.
Prefix sums (without start): [-3, -1, -4, 0, 2]. Minimum = -4.
Starting value = 1 - (-4) = 5. Verify: 5-3=2, 2+2=4, 4-3=1, 1+4=5, 5+2=7. All ≥ 1 ✓.
max(1, 1 - min_sum) to ensure positivity.Prefix sum problems often have a simple formula that's easy to derive once you identify the constraint. Here: "all running sums must be ≥ 1" → "start + min_prefix_sum ≥ 1" → "start ≥ 1 - min_prefix_sum." Write the mathematical constraint first, then derive the formula. This approach — constraint → formula → implementation — is faster and less error-prone than working through examples iteratively. Practice applying this systematic approach to all prefix sum optimization problems.