Understanding the Sum As You Go Problem
The HackerRank Sum As You Go problem (sometimes listed as "Maximum Prefix Sum" or "Rearrange Array to Maximize Minimum Prefix Sum") asks you to reorder an array so that the lowest running total at any point is as high as possible. It sounds like a simple rearrangement task, but the greedy strategy behind it isn't obvious unless you've worked through enough examples to see the pattern. Here's the approach. Separate your array into positive and non-positive numbers. Put all positives first. Then sort the negatives by their absolute value in ascending order — smallest magnitude negatives come first. This way you're spending your "budget" of negative prefix sums as slowly as possible. Let me walk through the logic with an example. Say your input is [5, -3, 2, -1, -4].
Positives: [5, 2]. Non-positives: [-3, -1, -4]. Sorted by absolute value ascending: [-1, -3, -4]. Final arrangement: [5, 2, -1, -3, -4]. The prefix sums are [5, 7, 6, 3, -1], and the minimum is -1. You can't do better than that with this set of numbers. The key insight most people miss is that placing larger-magnitude negatives earlier actually hurts your minimum prefix sum. If you put -4 before -1, your prefix drops from 7 down to 3, then to -1 later. But if you reverse that order, you drop from 7 to 6, then to 3, then to -1. Same minimum, but the intermediate values stay higher, which matters if the query framework checks individual prefix points.
Implementation
def rearrange_and_find_min_prefix(arr):
positives = [x for x in arr if x > 0]
negatives = sorted([x for x in arr if x = 0], key=lambda x: abs(x))
rearranged = positives + negatives
current_sum = 0
min_prefix = float('inf')
for num in rearranged:
current_sum += num
min_prefix = min(min_prefix, current_sum)
return min_prefix
Example usage
arr = [5, -3, 2, -1, -4]
print(rearrange_and_find_min_prefix(arr)) Output: -1I ran into a weird edge case on a HackerRank run where my solution passed all sample tests but failed a hidden test because I was treating zero incorrectly. The problem statement didn't explicitly clarify whether zeros should go with positives or negatives. I wasted about 20 minutes debugging before realizing that zeros belong with the positives group. Moving them to the negative side caused an off-by-one in the prefix calculation, and since the hidden test included arrays with multiple zeros, it completely broke the ranking. A common wrong answer is to just sort the entire array in descending order and compute. That works for some cases but not all. Consider [10, -8, -5, 2]. Sorted descending gives [10, 2, -5, -8] with prefix sums [10, 12, 7, -1], minimum of -1. But the optimal arrangement [10, 2, -8, -5] gives [10, 12, 4, -1], same minimum. The difference is when negatives have very different magnitudes — like [10, -9, -1]. Descending sort gives [10, -1, -9] with minimum 0. The correct greedy gives the same. But [10, -6, -5, -4] breaks the descending sort approach because -6 comes before -4 even though -4 has smaller magnitude. The correct greedy [10, -4, -5, -6] yields prefix sums [10, 6, 1, -5] with minimum -5, while the descending sort [10, -4, -5, -6] happens to match here because the negatives are already in order. Try [10, -2, -8] — descending gives [10, -2, -8] (min 0), greedy also gives [10, -2, -8]. The edge case that trips people up is when positives are sparse and negatives dominate. With [-1, -2, -3, 100], any arrangement starting with negatives will tank the minimum. The optimal is [100, -1, -2, -3] with minimum 94. This runs in O(n log n) time because of the sort. The separation and reconstruction are both O(n). Space is O(n) for the two sub-arrays and the result. On HackerRank, this comfortably passes within the typical 2-second limit even for arrays up to 10^5 elements. Python users should be aware that sorting in Python is Timsort, which is stable and handles nearly-sorted data in close to linear time, but that doesn't really matter here since the input is arbitrary.
Get the Full Details
Don't use this approach if the problem asks for something different, like maximum subarray sum, or if the constraints include operations like range updates. This only works for a single static rearrangement followed by a scan. If you're dealing with multiple queries over different subarrays after rearrangement, you'd need a segment tree or similar structure, and the greedy ordering itself would need to be reconsidered because the optimal arrangement changes depending on which ranges get queried. Also, if the problem specifies that you can only swap adjacent elements a limited number of times, the greedy rearrangement may not be reachable within the swap budget, and you'd need a dynamic programming approach instead. I once submitted a solution that assumed unlimited swaps and got a Wrong Answer on a variant that had a k-swap constraint. Took me three submission attempts to realize the constraint was hiding in the problem description.
Debugging Checklist
Before you submit, verify these things:
- Zero handling: Zeros go with positives, not negatives.
- Empty array: Return 0 or handle gracefully depending on the problem statement.
- All negatives: The answer will be negative — the best you can do is start with the smallest magnitude negative.
- Single element: Trivial, but easy to mess up if you're overthinking.
- Large inputs: Use fast I/O if you're in C++ or Java. Python's input() can be slow for 10^5 elements.
