Rust solution
IntuitionThe problem asks us to find the maximum frequency of a number in the array after performing at most numOperations. We can view the problem as trying to
# Intuition
<!-- Describe your first thoughts on how to solve this problem. -->
The problem asks us to find the maximum frequency of a number in the array after performing at most numOperations. We can view the problem as trying to "cover" each point with a range of k on both sides. We can then add the number of operations required to cover other points to the frequency of each point. The key is to efficiently track the number of points covered by each point.

# Approach
<!-- Describe your approach to solving the problem. -->
We use a sweep line approach. We create a pointsCover map to store the start and end points of the coverage ranges. For each number num in the input array, we increment pointsCover[num - k] and decrement pointsCover[num + k + 1]. We also create a cntPoints map to store the frequency of each number. We then iterate through the sorted points (using a BTreeSet) and maintain a running sum pointsCoverThisPoint of the coverage. For each point, we calculate the maximum possible frequency by adding the number of operations required to cover the other points within the range, limited by numOperations. We update the result res with the maximum frequency found.

# Complexity
- Time complexity: O(1)
<!-- Add your time complexity here, e.g. $$O(n)$$ -->

- Space complexity: O(N)
<!-- Add your space complexity here, e.g. $$O(n)$$ -->

# Code
```rust []
use std::collections::{HashMap, BTreeSet};
use std::cmp::max;

impl Solution {
    pub fn max_frequency(nums: Vec<i32>, k: i32, num_operations: i32) -> i32 {
        let mut points_cover: HashMap<i32, i32> = HashMap::new();
        let mut cnt_points: HashMap<i32, i32> = HashMap::new();
        let mut points: BTreeSet<i32> = BTreeSet::new();

        for &num in &nums {
            *cnt_points.entry(num).or_insert(0) += 1;
            *points_cover.entry(num - k).or_insert(0) += 1;
            *points_cover.entry(num + k + 1).or_insert(0) -= 1;
            points.insert(num);
            points.insert(num - k);
            points.insert(num + k + 1);
        }

        let mut res = 0;
        let mut points_cover_this_point = 0;

        for &point in &points {
            points_cover_this_point += *points_cover.get(&point).unwrap_or(&0);
            res = max(res, *cnt_points.get(&point).unwrap_or(&0) + 
                        (num_operations as i32).min(points_cover_this_point - *cnt_points.get(&point).unwrap_or(&0)));
        }

        res
    }
}
```
['Binary Search', 'Dynamic Programming', 'Greedy', 'Sliding Window', 'Sorting', 'Prefix Sum', 'Rust']