We use cookies (including Google cookies) to personalize ads and analyze traffic. By continuing to use our site, you accept our Privacy Policy.

SimplyLeet
TagsCompaniesDisclaimersPrivacyTermsContactAbout Us

Rearrange Array to Maximize Prefix Score

Number: 2655

Difficulty: Medium

Paid? No

Companies: J.P. Morgan, Amazon, IBM

Problem Description

Given an integer array nums, you are allowed to rearrange its elements in any order. After rearranging, let prefix[i] be the sum of elements from index 0 to i. The score is defined as the number of positive values in the prefix sum array. The goal is to return the maximum possible score by reordering nums.

Key Insights

  • To maximize the number of positive prefix sums, you want the running sum to be as high as possible for as long as possible.
  • Sorting the array in descending order helps to accumulate a larger sum quickly.
  • Once the running sum becomes non-positive after adding an element, further additions (even if they are less negative) might not yield additional positive prefix sums.
  • It suffices to simulate the prefix sum process after sorting to count how many positive prefix sums you obtain.

Space and Time Complexity

Time Complexity: O(n log n) due to sorting the array. Space Complexity: O(n) if accounting for the space needed to sort, though in-place sorting may use O(1) extra space.

Solution

The optimal strategy to maximize the positive prefix count is to sort nums in descending order. By doing this, the largest elements add to the prefix sum first, increasing the chance that subsequent prefix sums remain positive despite any later negative numbers.

Steps:

  1. Sort the array in descending order.
  2. Initialize a running sum to 0 and a counter for positive prefix sums.
  3. Iterate through the sorted array, add each element to the running sum.
  4. If the running sum is positive after adding an element, increment the counter.
  5. Return the counter once the whole array is processed.

This greedy approach works because placing larger numbers first maximizes the cumulative sum, allowing more elements to contribute to a positive prefix sum before the accumulation might drop below or equal to zero.

Code Solutions

# Function to maximize prefix score
def max_prefix_score(nums):
    # Sort the numbers in descending order to maximize the running sum
    nums.sort(reverse=True)
    
    score = 0  # Count of positive prefix sums
    current_sum = 0  # Running prefix sum
    
    # Iterate over the sorted list and update the running sum and score
    for num in nums:
        current_sum += num  # Add current number to the running sum
        if current_sum > 0:
            score += 1  # Increase score if current prefix sum is positive
        else:
            # Even if current_sum becomes non-positive, we continue the loop,
            # as further large negative numbers won't make it positive again.
            pass
    
    return score

# Example usage:
print(max_prefix_score([2, -1, 0, 1, -3, 3, -3]))  # Output should be 6
← Back to All Questions