Maximum Frequency of an Element After Performing Operations I

Problem Description

You are given an integer array nums and two integers k and numOperations. You must perform an operation numOperations times on nums, where in each operation you select an index i that was not selected in any previous operations and add an integer in the range [-k, k] to nums[i]. Return the maximum possible frequency of any element in nums after performing the operations.

Key Insights

• The goal is to maximize the frequency of any element after modifying nums using the allowed operations.
• We can only choose each index once for the operations.
• The range of modifications allows us to increase or decrease values in the array.
• A sliding window or two-pointer approach can help efficiently calculate possible frequencies by focusing on a target value and the required operations to bring other values to that target.

Space and Time Complexity

Time Complexity: O(n log n) (due to sorting the array) Space Complexity: O(1) (for the pointers and counters)

Solution

To solve this problem, we can use a two-pointer technique combined with sorting. Here’s how the solution works:

1. First, sort the array nums. This allows us to focus on increasing frequencies of values that are already close to each other.
2. Use two pointers to explore the range of numbers and track how many operations are needed to bring all numbers in the current window to the maximum number represented by the right pointer.
3. If the number of operations needed exceeds numOperations, we will move the left pointer to narrow the window.
4. Keep track of the maximum frequency found during this process.

Code Solutions