Start by sorting the array in descending order to prioritize larger elements for early prefix sums. Iterate while maintaining a running total, only adding elements that keep the prefix sum positive. This guarantees the maximum number of positive prefix sums and directly follows the greedy choice plus invariant validation pattern.
Problem Statement
You are given a 0-indexed integer array nums. You can reorder its elements in any way, including keeping the current order. After rearrangement, define prefix[i] as the sum of the first i+1 elements. The score is the count of positive values in prefix.
Return the maximum possible score achievable by any rearrangement. Optimize the ordering so that early prefix sums remain positive as long as possible, following a greedy choice plus invariant validation approach.
Examples
Example 1
Input: nums = [2,-1,0,1,-3,3,-3]
Output: 6
We can rearrange the array into nums = [2,3,1,-1,-3,0,-3]. prefix = [2,5,6,5,2,2,-1], so the score is 6. It can be shown that 6 is the maximum score we can obtain.
Example 2
Input: nums = [-2,-3,0]
Output: 0
Any rearrangement of the array will result in a score of 0.
Constraints
- 1 <= nums.length <= 105
- -106 <= nums[i] <= 106
Solution Approach
Sort in Descending Order
Arrange nums in descending order so that the largest elements come first. This ensures the initial prefix sums are maximized and provides a foundation for the greedy selection.
Iterate with Running Total
Maintain a cumulative sum while iterating through the sorted array. Include each element only if adding it keeps the running total positive, counting each valid prefix to maximize the score.
Return Maximum Count
After processing all elements, the count of positive prefix sums gives the maximum score. This approach strictly follows the greedy choice plus invariant validation, avoiding negative early sums.
Complexity Analysis
| Metric | Value |
|---|---|
| Time | Depends on the final approach |
| Space | Depends on the final approach |
Time complexity is O(n log n) due to sorting, and space complexity is O(1) or O(n) depending on whether a separate prefix array is maintained. Iteration and cumulative sum tracking are linear operations.
What Interviewers Usually Probe
- Expect candidates to identify the greedy choice of ordering the array in descending values.
- Look for correct handling of prefix sums to avoid early negative totals that reduce score.
- Watch if candidates can justify why adding smaller elements later does not reduce maximum score.
Common Pitfalls or Variants
Common pitfalls
- Adding elements without checking if the running prefix sum remains positive.
- Failing to sort in descending order, which can lower the maximum achievable score.
- Miscounting prefix sum positions when updating the score.
Follow-up variants
- Compute the minimum number of negative prefix sums achievable with any rearrangement.
- Find the rearrangement that maximizes the sum of all positive prefix sums instead of count.
- Handle arrays with additional constraints like only rearranging subsets of the elements.
How GhostInterview Helps
- GhostInterview guides the solver to apply greedy sorting and cumulative validation step-by-step.
- It highlights where including an element could violate the positive prefix invariant.
- The solver receives immediate feedback on alternative orderings that affect the maximum score.
Topic Pages
Related GhostInterview Pages
- LeetCode Interview Copilot - Use GhostInterview as a live solver when you want direct help with LeetCode-style coding questions.
- Coding Interview Assistant - See how GhostInterview supports array, string, linked list, graph, and tree interview workflows.
- How GhostInterview Works - Review the screenshot, reasoning, and answer flow before using the solver in a live interview.
FAQ
What is the main strategy for Rearrange Array to Maximize Prefix Score?
Sort the array in descending order and iteratively add elements while keeping prefix sums positive to maximize the score.
Can negative numbers contribute to the maximum prefix score?
Only if adding them does not turn the cumulative prefix sum negative; otherwise they are skipped.
What is the time complexity of the optimal approach?
Sorting dominates the complexity, giving O(n log n), with linear iteration for prefix sum counting.
Why does the greedy approach guarantee the maximum score?
Because placing larger elements first preserves positive prefix sums, satisfying the invariant and maximizing count.
Does GhostInterview provide step guidance for this problem pattern?
Yes, it guides the solver through greedy selection, cumulative sum updates, and order validation for maximal score.
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