How do you solve Rearrange Array to Maximize Prefix Score on LeetCode?

Rearrange Array to Maximize Prefix Score (LeetCode #2587) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(n log n) time complexity and O(1) space complexity. Key insight: Sorting the array in descending order maximizes the positive contributions to the prefix sums.

What is the time complexity of Rearrange Array to Maximize Prefix Score?

The optimal solution for Rearrange Array to Maximize Prefix Score runs in O(n log n) time and uses O(1) space. The time complexity is dominated by the sorting step, which is O(n log n). The space complexity is O(1) since we are using a constant amount of extra space.

What is the brute force solution for Rearrange Array to Maximize Prefix Score?

The brute force approach for Rearrange Array to Maximize Prefix Score is Brute Force, with O(n²) time complexity and O(n) space complexity. In this approach, we will generate all possible permutations of the array and calculate the prefix sums for each permutation. This will help us find the maximum score by checking how many prefix sums are positive. The optimal Optimal Solution approach improves this to O(n log n).

What algorithm or data structure is used to solve Rearrange Array to Maximize Prefix Score?

Rearrange Array to Maximize Prefix Score uses the following concepts: Array, Greedy, Sorting, Prefix Sum. The recommended patterns to study are: Greedy, Sorting, Prefix Sum.

What are the interview tips for Rearrange Array to Maximize Prefix Score?

Always consider sorting as a first step if the problem involves maximizing or minimizing values. Be clear about how prefix sums work and how they can be influenced by the order of elements. Practice explaining your thought process clearly, as communication is key in interviews.

What are common mistakes when solving Rearrange Array to Maximize Prefix Score?

Failing to sort the array before calculating prefix sums. Not correctly counting positive prefix sums.

#2587

Rearrange Array to Maximize Prefix Score

Medium

ArrayGreedySortingPrefix SumGreedySortingPrefix Sum

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

	Brute Force	Optimal Solution★
Time	O(n²)	O(n log n)
Space	O(n)	O(1)

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Intuition

Time O(n log n)Space O(1)

To maximize the number of positive prefix sums, we should sort the array in descending order. This way, we ensure that larger numbers contribute positively to the prefix sums early on, maximizing the count of positive values.

⚙️

Algorithm

3 steps

1Step 1: Sort the array nums in descending order.
2Step 2: Initialize prefix sum and score to 0.
3Step 3: Iterate through the sorted array, updating the prefix sum and counting positive values.

solution.py11 lines

1# Full working Python code
2
3def maxPrefixScore(nums):
4    nums.sort(reverse=True)
5    prefix_sum = 0
6    score = 0
7    for num in nums:
8        prefix_sum += num
9        if prefix_sum > 0:
10            score += 1
11    return score

ℹ

Complexity note: The time complexity is dominated by the sorting step, which is O(n log n). The space complexity is O(1) since we are using a constant amount of extra space.

1Sorting the array in descending order maximizes the positive contributions to the prefix sums.
2The prefix sum must be tracked to count how many positive values are generated.

Solutions and explanations are original Tejav content. Problem titles © LeetCode — use the LeetCode button above for the full problem statement.