Frequency of the Most Frequent Element
Difficulty: Medium
Category: DSA
Topics: Array, Binary Search, Greedy, Sliding Window, Sorting, Prefix Sum
The **frequency** of an element is the number of times it occurs in an array.
You are given an integer array `nums` and an integer `k`. In one operation, you can choose an index of `nums` and increment the element at that index by `1`.
Return _the **maximum possible frequency** of an element after performing **at most** _`k`_ operations_.
**Example 1:**
**Input:** nums = [1,2,4], k = 5
**Output:** 3**
Explanation:** Increment the first element three times and the second element two times to make nums = [4,4,4].
4 has a frequency of 3.
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**Example 2:**
**Input:** nums = [1,4,8,13], k = 5
**Output:** 2
**Explanation:** There are multiple optimal solutions:
- Increment the first element three times to make nums = [4,4,8,13]. 4 has a frequency of 2.
- Increment the second element four times to make nums = [1,8,8,13]. 8 has a frequency of 2.
- Increment the third element five times to make nums = [1,4,13,13]. 13 has a frequency of 2.
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**Example 3:**
**Input:** nums = [3,9,6], k = 2
**Output:** 1
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**Constraints:**
- `1 <= nums.length <= 105`
- `1 <= nums[i] <= 105`
- `1 <= k <= 105`