Apply Operations to Maximize Frequency Score

Problem Description

You are given a 0-indexed integer array nums and an integer k. You can perform the following operation on the array at most k times: choose any index i from the array and increase or decrease nums[i] by 1. The score of the final array is the frequency of the most frequent element in the array. Return the maximum score you can achieve.

Key Insights

• The frequency score is determined by how many times the most frequent element appears after performing up to k operations.
• To maximize the frequency score, we should focus on converting elements into the most frequent number within a given range.
• A binary search or sliding window approach can be utilized to efficiently determine the maximum achievable frequency score.

Space and Time Complexity

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

Solution

To solve this problem, we can use a combination of sorting and a sliding window technique. The steps are as follows:

1. Sort the Array: First, sort the nums array. This allows us to easily analyze how many operations are needed to make elements equal to a specific target.
2. Sliding Window: Use a two-pointer or sliding window approach to find the maximum frequency of elements. For each unique element, calculate how many operations are needed to convert previous elements to match this target.
3. Calculate Operations: For each candidate target, calculate the number of operations required to increase previous elements to the value of the current target.
4. Maximize Frequency: Keep track of the maximum frequency encountered during the traversal.

This approach ensures that we efficiently use our operations to maximize the frequency score.

Code Solutions