Rearrange Array to Maximize Prefix Score Solution

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Rearrange Array to Maximize Prefix Score Solution

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:Rearrange Array to Maximize Prefix Score Solution

Input: nums = [2,-1,0,1,-3,3,-3]
Output: 6
Explanation: 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:Rearrange Array to Maximize Prefix Score Solution

Input: nums = [-2,-3,0]
Output: 0
Explanation: Any rearrangement of the array will result in a score of 0.

 

Constraints:Rearrange Array to Maximize Prefix Score Solution

  • 1 <= nums.length <= 105
  • -106 <= nums[i] <= 106

Solution to Rearrange Array to Maximize Prefix Score:

To maximize the score, we want to make sure that the positive numbers in the array are placed at the beginning. Since we can rearrange the elements of the array, we can sort the array in decreasing order and then calculate the prefix sums.

Here’s the algorithm:

  1. Sort the array nums in decreasing order.
  2. Initialize a count variable to 0 and a prefix sum variable to 0.
  3. Iterate over the elements of nums and for each element x, do the following: a. If x is positive, add it to the prefix sum and increment the count. b. If x is non-positive, break out of the loop.
  4. Return the count.

Here’s the Python code that implements the above algorithm:

def max_score(nums):
nums.sort(reverse=True)
count = 0
prefix_sum = 0
for x in nums:
if x > 0:
prefix_sum += x
count += 1
else:
break
return count

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