Maximum Frequency of an Element After Performing Operations I

Maximum Frequency of an Element After Performing Operations I

1. What is this problem about?

In this problem, you are given an array of integers and two integers: k and num_operations. In one operation, you can pick an element and change it to any value within the range [nums[i] - k, nums[i] + k]. The goal is to perform at most num_operations to maximize the frequency of some value in the array.

2. Why is this asked in interviews?

Companies like Meta and Amazon ask this to evaluate a candidate's skill in Range-based optimizations and Sliding Window. It requires understanding that the 'best' target value must be either an existing value in the array or a value that is exactly k distance away from some existing values. It tests if you can handle overlap and frequency constraints efficiently.

3. Algorithmic pattern used

The problem utilizes Sorting and Sliding Window (or Binary Search). For a chosen target value V, any element nums[i] can be changed to V if abs(nums[i] - V) <= k. This is equivalent to saying V must fall in the range [nums[i] - k, nums[i] + k]. By sorting the array and using a sliding window, you can count how many elements can reach a specific target value. You then take the minimum of (elements in range) and (original frequency + num_operations).

4. Example explanation

Nums: [1, 5, 9], k = 3, num_operations = 1.

• Target = 4:
  • 1 can become 4 (1+3=4).
  • 5 can become 4 (5-1=4).
  • 9 cannot (9-3=6 > 4).
  • Total in range = 2.
  • We have 1 op. Original frequency of 4 is 0. 0 + 1 = 1.
  • min(2, 0 + 1) = 1.
• Target = 1:
  • 1 is 1.
  • 5 can become 1 (5-4=1, but 4 > k=3, so NO).
  • Total in range = 1. Result = 1. The maximum frequency is 1. (Wait, if k was larger, say k=4, then 1 and 5 could both be 1).

5. Common mistakes candidates make

A common error is not sorting the array, which makes the windowing or range checks very difficult. Another is not properly accounting for the difference between elements that are already the target value and those that need an operation to become the target.

6. Interview preparation tip

For problems involving 'ranges' around points, try visualizing the points on a 1D number line. Often, the solution involves finding the densest cluster of overlapping intervals.