Maximize Element Frequency with Limited Increments

Question

The question asks the candidate to devise a solution that maximizes the frequency of an element in an array by allowing a limited number of increments to other elements.

Codemia · Accepted Answer

To solve the problem of maximizing the frequency of an element in an array with limited increments, we can take the following steps:

1. **Identify the maximum element** in the array, as this will be the target for maximizing frequency.
2. **Count the frequency** of each element in the array.
3. **Sort the elements** based on their values to facilitate the incrementing process.
4. **Iterate through the sorted list**, using the allowed increments to increase the frequency of the maximum element.

The algorithm can be summarized in the following steps:

1. **Count Frequencies**: Use a dictionary to count occurrences of each element.
2. **Sort Elements**: Create a list of unique elements and sort it.
3. **Maximize Frequency**: Starting from the second largest element, use the allowed increments to increase the maximum element's frequency until increments run out or all elements are processed.

Here is a sample Python code implementation:

```python
def maxFrequency(arr, k):
    from collections import Counter
    freq = Counter(arr)
    max_elem = max(arr)
    increments = k
    unique_elements = sorted(freq.keys())

for elem in unique_elements:
        if elem < max_elem:
            needed = (max_elem - elem) * freq[elem]
            if increments >= needed:
                increments -= needed
                freq[max_elem] += freq[elem]
                freq[elem] = 0
            else:
                freq[max_elem] += increments // (max_elem - elem)
                break
    return freq[max_elem]
```

The time complexity of this algorithm is O(n log n) due to the sorting step, where n is the number of unique elements in the array. The space complexity is O(n) as we are using a dictionary to store the frequency counts. This makes the solution efficient for moderate-sized inputs.

Maximize Element Frequency with Limited Increments

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