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

The optimal solution has a time complexity of O(n log n).

What data structures are used to solve Rearrange Array to Maximize Prefix Score?

This problem uses Array, Greedy, Sorting, Prefix Sum. Understanding these concepts is essential for solving this Medium problem efficiently.

What are the key insights for solving Rearrange Array to Maximize Prefix Score?

Insight 1: Sorting the numbers in descending order is the key to maximizing the score. By placing larger positive numbers at the beginning, we ensure the prefix sums remain positive for as long as possible. Insight 2: We can stop iterating when the prefix sum becomes non-positive because adding more numbers (whether positive or negative) won't increase the score any further. Any subsequent prefix sum will be less than or equal to zero.

Which companies ask LeetCode 2587. Rearrange Array to Maximize Prefix Score in interviews?

This problem is frequently asked at IBM, J.P. Morgan.

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Rearrange Array to Maximize Prefix Score - LeetCode 2587 Solution

Rearrange Array to Maximize Prefix Score - Complete Solution Guide

Rearrange Array to Maximize Prefix Score is LeetCode problem 2587, a Medium level challenge. This complete guide provides step-by-step explanations, multiple solution approaches, and optimized code in python3, java, cpp, c.

Problem Statement

You are given a 0-indexed integer array nums . You can rearrange the elements of nums to any order (including the given order). Let prefix be the array containing the prefix sums of nums after rearranging it. In other words, prefix[i] is the sum of the elements from 0 to i in nums after rearranging it. The score of nums is the number of positive integers in the array prefix . Return the maximum score you can achieve . Example 1: Input: nums = [2,-1,0,1,-3,3,-3] Output: 6 Explanation: We can rear

Detailed Explanation

The problem asks us to rearrange an array of integers such that the number of positive prefix sums (the score) is maximized. We are given an array `nums` and we can rearrange it in any order. We need to find an arrangement that yields the highest possible score, where the score is the number of positive elements in the array of prefix sums after the rearrangement.

Solution Approach

The solution sorts the input array `nums` in descending order. It then iterates through the sorted array, calculating the prefix sum. For each element, it checks if the prefix sum is positive. If it is, the score is incremented. If the prefix sum becomes non-positive, the loop terminates because adding more elements will not increase the score, since the prefix sums would never recover from becoming non-positive.

Step-by-Step Algorithm

Step 1: Sort the input array `nums` in descending order.
Step 2: Initialize `prefix_sum` to 0 and `score` to 0.
Step 3: Iterate through the sorted `nums` array.
Step 4: Add the current number to `prefix_sum`.
Step 5: If `prefix_sum` is greater than 0, increment `score`.
Step 6: If `prefix_sum` is not greater than 0, break the loop.
Step 7: Return the final `score`.

Key Insights

Insight 1: Sorting the numbers in descending order is the key to maximizing the score. By placing larger positive numbers at the beginning, we ensure the prefix sums remain positive for as long as possible.
Insight 2: We can stop iterating when the prefix sum becomes non-positive because adding more numbers (whether positive or negative) won't increase the score any further. Any subsequent prefix sum will be less than or equal to zero.
Insight 3: We need to use long long for prefix_sum to prevent overflow issues with large input arrays.

Complexity Analysis

Time Complexity: O(n log n)

Space Complexity: O(1)

Topics

This problem involves: Array, Greedy, Sorting, Prefix Sum.

Companies

Asked at: IBM, J.P. Morgan.

Rearrange Array to Maximize Prefix Score | LeetCode 2587

Medium

Array Greedy Sorting Prefix Sum

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

Solution Code

Available in:

import java.util.Arrays;

class Solution {
    public int maxScore(int[] nums) {
        Arrays.sort(nums);
        
        int n = nums.length;
        int[] reversedNums = new int[n];
        for (int i = 0; i < n; i++) {
            reversedNums[i] = nums[n - 1 - i];
        }
        
        long prefix_sum = 0;
        int score = 0;
        
        for (int num : reversedNums) {
            prefix_sum += num;
            if (prefix_sum > 0) {
                score += 1;
            } else {
                break;
            }
        }
        
        return score;
    }
}

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Problem Info

Description

Problem 2587: Rearrange Array to Maximize Prefix Score - Detailed explanation and solution approaches.

Topics

Array Greedy Sorting Prefix Sum

Companies

IBMJ.P. Morgan

Stats

Difficulty:Medium

Languages:4

Companies:2

Problem #:2587

Problem Explanation

💡

Think Before You Code

🤔 Ask Yourself

→What is the input? What output do I need?
→Can I solve a smaller version of this problem first?
→What patterns have I seen in similar problems?

✏️ Try This First

Before looking at the solution, try to solve it on paper with a simple example!

🚀 Try on LeetCode

Solution Approach

📋

Step-by-Step Solution

7 steps

1
Step 1: Sort the input array `nums` in descending order.
2
Step 2: Initialize `prefix_sum` to 0 and `score` to 0.
3
Step 3: Iterate through the sorted `nums` array.
4
Step 4: Add the current number to `prefix_sum`.
5
Step 5: If `prefix_sum` is greater than 0, increment `score`.
6
Step 6: If `prefix_sum` is not greater than 0, break the loop.
7
Step 7: Return the final `score`.

💡

Pro Tip for Students

Try tracing through each step with a small example on paper before coding. Understanding "why" each step happens is more important than memorizing the code!

⚡

Complexity Analysis

⏱️

Time Complexity

O(n log n)

✨ Log-linear - Great for sorting algorithms!

💾

Space Complexity

O(1)

💪 Constant space - Uses same memory regardless of input!

📝

Why?

Sorting dominates the runtime. The iterative part of the algorithm is linear, but the sorting is n log n. The space used to keep track of the prefix sum and score is constant.

📖New to Big O? Click to learn more

Big O Notation - Quick Guide

O(1)Best - Instant

O(log n)Excellent - Binary Search

O(n)Good - One loop

O(n log n)OK - Sorting

O(n²)Slow - Nested loops

O(2ⁿ)Very Slow - Recursion

Alternative Approaches

Brute Force (Permutations)

Generate all possible permutations of the input array, calculate the score for each permutation, and return the maximum score found. This approach is highly inefficient.

Time: O(n! * n), where n is the length of the input array. Generating each permutation takes O(n!) time, and calculating the score for each permutation takes O(n) time.Space: O(n) in the best case (in-place generation), or O(n * n!) for explicit storage of permutations

Trade-offs: The brute-force approach is simple to understand but extremely slow. It's not practical for arrays of any reasonable size. The provided solution is significantly better.

✨

Key Insights

1Insight 1: Sorting the numbers in descending order is the key to maximizing the score. By placing larger positive numbers at the beginning, we ensure the prefix sums remain positive for as long as possible.
2Insight 2: We can stop iterating when the prefix sum becomes non-positive because adding more numbers (whether positive or negative) won't increase the score any further. Any subsequent prefix sum will be less than or equal to zero.
3Insight 3: We need to use long long for prefix_sum to prevent overflow issues with large input arrays.

📚

Key Terms Explained

For Students

Array

A collection of items stored at contiguous memory locations. Like a row of boxes.

Greedy Algorithm

Making the best choice at each step without looking ahead.

Sorting

Arranging elements in a specific order (ascending/descending).

Edge Cases

Edge case 1: All negative numbers. The solution will correctly return 0, as the prefix sum will immediately become negative after the first number.
Edge case 2: All positive numbers. The solution will correctly return the length of the array, as the prefix sum will always be positive.
Edge case 3: Empty array. The problem statement guarantees that the array is not empty, but a robust solution would handle this gracefully, probably returning 0.

⚠️

Common Mistakes to Avoid

✗Common mistake 1: Not sorting the array. This will lead to incorrect scores as positive numbers might be placed after negative numbers, decreasing the length of positive prefixes.

✗Common mistake 2: Using `int` for `prefix_sum`. Given the constraints of `-10^6 <= nums[i] <= 10^6` and `1 <= nums.length <= 10^5`, the `prefix_sum` could exceed the maximum value that an `int` can hold, leading to integer overflow. Using `long long` or `long` (in Java) is important.

✗Common mistake 3: Assuming that all positive numbers must be included in the 'positive prefix' portion. It is acceptable to have a negative number at index *i* such that it causes a prefix sum at index *i* to become negative, as long as the overall *score* is maximized.

✅

Learning Tip

Every mistake is a learning opportunity! When you make an error, understand why it happened before moving on.

🌍

Where is This Used in Real Life?

💼Real-world scenario 1: Optimizing resource allocation. Suppose `nums` represents the potential profit/loss from different projects. Rearranging the project order to maximize the number of cumulatively profitable periods is analogous to maximizing the score.

🏦Real-world scenario 2: Trading strategies. `nums` could represent the daily profit/loss from trades. Rearranging the order of trades (hypothetically, for analysis) to maximize the number of profitable streaks can help evaluate the strategy's robustness.

💡Understanding real-world applications helps you see the "why" behind algorithms. It's not just about passing interviews—these concepts power the apps and websites you use every day!

Author's Notes

💡 Key Insight

When dealing with arrays, always consider if sorting would simplify the problem. Many array problems have O(n) solutions using hash maps or two-pointer technique.

🎯 Interview Tip

If stuck, try working through a small example by hand. The pattern often reveals itself.

⚠️ Watch Out

Off-by-one errors are the most common mistake. Double-check your loop bounds and array indices.

Written by Saswata Mondal

Software Engineer • Algorithms Enthusiast • Interview Coach

👨‍💻

About the Author

👨‍💻

Saswata MondalAuthor400+ LC Problems

B.Tech CSE, IEM Kolkata | LeetCode Rating: 1672 (Top 15%)

Certified: IBM Java Developer, NPTEL Programming in Java

Last updated: August 7, 2024LeetCode Profile GitHub

This solution has been crafted based on my experience solving 400+ LeetCode problems. Each explanation is designed to help you understand the underlying concepts, not just memorize the code.

Community Tips & Insights

I was asked this exact problem at my Google interview. The interviewer wanted me to optimize space complexity.

@InterviewProJul 14

Try solving this without using extra space first. It's a great exercise for understanding the underlying pattern.

@CodeNinjaJul 7

In a real interview, always clarify constraints first. Ask about input size and value ranges.

@TechLeadJun 30

❓

Frequently Asked Questions

When should I use in-place modification vs creating a new array?

Use in-place modification when space complexity matters (O(1) space requirement) and the original array can be modified. Create a new array when you need to preserve the original data or when the problem involves significant restructuring that would complicate in-place logic.

What are common greedy problem patterns?

Activity selection (sort by end time), interval scheduling (sort by start/end), Huffman coding (always combine smallest), fractional knapsack (sort by value/weight ratio), and minimum spanning tree. Look for problems where local decisions don't affect future options.

How much time should I spend on a medium problem in interviews?

In a 45-minute interview, aim for: 5-10 minutes understanding and clarifying, 5-10 minutes discussing approach, 20-25 minutes coding, and 5-10 minutes testing. If stuck after 15 minutes of thinking, verbalize your thought process and ask for hints.

What is the importance of time and space complexity analysis?

Complexity analysis is crucial because: 1) Interviewers always ask about it, 2) It helps you choose between approaches, 3) It demonstrates CS fundamentals. Always state both time and space complexity, and be prepared to explain how you derived them.

What is the optimal approach for "Rearrange Array to Maximize Prefix Score"?

For this medium-level Array problem, the key is to identify the core pattern. Analyze the input constraints to determine acceptable time complexity. Consider whether greedy techniques can optimize the solution. Always handle edge cases and validate your approach with examples before coding.

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