Rearrange Array to Maximize Prefix Score

Rearrange Array to Maximize Prefix Score

What is this problem about?

The Rearrange Array to Maximize Prefix Score problem asks you to find the maximum number of prefix sums that are strictly positive, by rearranging the array optimally. This coding problem uses the greedy insight: sort in descending order to keep prefix sums positive as long as possible. The array, sorting, greedy, and prefix sum interview pattern is demonstrated.

Why is this asked in interviews?

J.P. Morgan, Amazon, and IBM ask this to test greedy reasoning: to maximize the number of positive prefix sums, place the largest elements first. Once the prefix sum goes non-positive, no rearrangement of remaining elements can save it.

Algorithmic pattern used

Sort descending + prefix sum scan. Sort the array in descending order. Compute running prefix sum from left to right. Count how many prefix sums are strictly positive. Stop when prefix sum becomes ≤ 0 (no further positive prefix sums possible).

Example explanation

arr=[2,-1,3,-2,4]. Sort desc: [4,3,2,-1,-2]. Prefix sums: 4, 7, 9, 8, 6. All positive → 5 prefix sums are positive.

arr=[2,-2,-2,-2]. Sort desc: [2,-2,-2,-2]. Prefix: 2, 0, -2, -4. Only first is positive → 1.

Common mistakes candidates make

• Not sorting in descending order.
• Counting all prefix sums without stopping when negative.
• Using ascending sort (gives minimum instead of maximum positive prefix sums).
• Not handling all-negative arrays (answer = 0).

Interview preparation tip

"Maximize positive prefix sums" problems always use descending sort — the greedy choice is to front-load the largest values. The proof: any other ordering will have a smaller prefix at some position k, potentially making it non-positive earlier. Practice similar "greedy prefix optimization" problems: "maximize sum of first k elements," "minimum operations to make all prefix sums non-negative."