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:
i that was not selected in any previous operations.[-k, k] to nums[i].Return the maximum possible frequency of any element in nums after performing the operations.
Example 1:
Input: nums = [1,4,5], k = 1, numOperations = 2
Output: 2
Explanation:
We can achieve a maximum frequency of two by:
nums[1], after which nums becomes [1, 4, 5].nums[2], after which nums becomes [1, 4, 4].Example 2:
Input: nums = [5,11,20,20], k = 5, numOperations = 1
Output: 2
Explanation:
We can achieve a maximum frequency of two by:
nums[1].
Constraints:
1 <= nums.length <= 1051 <= nums[i] <= 1090 <= k <= 1090 <= numOperations <= nums.lengthThis approach leverages a sorted array and the sliding window approach to maximize the frequency of elements. The idea is to use the sliding window to keep track of a subarray where you can potentially make all elements equal by performing add operations within the given range [-k, k].
You maintain a window that only expands when the needed operations are within the limit specified by numOperations. This involves checking the operations needed to turn the smallest element in the window into the largest element and adjusting it as necessary to stretch the window.
The C code uses quick-sort to sort the array and then applies a sliding window to calculate the maximum frequency of any number that can be achieved by performing operations. The steps:
left and right to maintain the window.right pointer index and adjust the left pointer accordingly.Python
Java
C#
JavaScript
Time Complexity: O(n log n) due to sorting, where n is the number of elements in the array.
Space Complexity: O(1) because modification is done in place.
This approach focuses on efficiently maximizing the frequency using a greedy strategy with a series of modifications limited by numOperations. It involves selectively manipulating elements to bunch them toward an optimal frequency level after sorting the array.
The process aims to utilize available changes strategically for maximizing occurrences of a particular value obtained.
The C++ code example applies sorting followed by greedy decision making:
k.JavaScript
Time Complexity: O(n log n) due to sort operation as largest part.
Space Complexity: O(1) as changes are internal within the input collection.
| Approach | Complexity |
|---|---|
| Sliding Window Technique | Time Complexity: O(n log n) due to sorting, where n is the number of elements in the array. Space Complexity: O(1) because modification is done in place. |
| Greedy with Frequency Count | Time Complexity: O(n log n) due to sort operation as largest part. Space Complexity: O(1) as changes are internal within the input collection. |
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