Maximum Sum of Almost Unique Subarray

Maximum Sum of Almost Unique Subarray

1. What is this problem about?

The Maximum Sum of Almost Unique Subarray problem asks you to find the maximum sum of a contiguous subarray of a fixed length k, with one additional condition: the subarray must contain at least m distinct elements. If no such subarray exists in the given array, you should return 0. It is a variation of the fixed-size sliding window problem, but with a constraint on the diversity of the elements within that window.

2. Why is this asked in interviews?

This "Maximum Sum of Almost Unique Subarray interview question" is commonly asked by Yandex and Amazon. it tests a candidate's ability to manage two different metrics within a sliding window simultaneously: the numerical sum and the count of unique elements. It evaluates whether you can use a hash table (or frequency map) efficiently to update the unique count as the window moves across the array.

3. Algorithmic pattern used

The "Array, Hash Table, Sliding Window interview pattern" is the perfect fit. You maintain a window of size k. As you slide the window from left to right:

1. Add the new element on the right: update the window sum and increment its count in a frequency map.
2. Remove the old element on the left: update the window sum and decrement its count in the map. If the count hits zero, remove the key.
3. After each shift, check the size of the frequency map. If map.size() >= m, update the global maximum sum.

4. Example explanation

Array: [1, 2, 1, 3, 3], k = 3, m = 2.

• Window 1: [1, 2, 1]. Sum = 4. Unique elements: {1, 2}. Count is 2. Since 2 >= 2, Max Sum = 4.
• Window 2: [2, 1, 3]. Sum = 6. Unique elements: {2, 1, 3}. Count is 3. Since 3 >= 2, Max Sum = 6.
• Window 3: [1, 3, 3]. Sum = 7. Unique elements: {1, 3}. Count is 2. Since 2 >= 2, Max Sum = 7. The result is 7.

5. Common mistakes candidates make

In the "Maximum Sum of Almost Unique Subarray coding problem," a common mistake is recalculating the entire sum or re-scanning for unique elements every time the window moves. This results in O(N * k) time complexity, whereas the correct sliding window approach is O(N). Another error is not handling the case where no subarray meets the "m unique" requirement, or incorrectly managing the frequency map (e.g., forgetting to remove a key when its count reaches zero).

6. Interview preparation tip

Get comfortable with the "sliding window with a hash map" pattern. It’s a very common combination. Practice identifying when a problem can be solved by just "adding one and removing one" from a sliding set. For this problem, specifically, pay attention to the constraints on m and k—if m > k, the answer will always be 0 because it's impossible to have more unique elements than total elements in the window. Mentioning this edge case to your interviewer shows great attention to detail.