Maximum Sum of Distinct Subarrays With Length K

Maximum Sum of Distinct Subarrays With Length K

1. What is this problem about?

The Maximum Sum of Distinct Subarrays With Length K problem asks you to find the maximum sum of a contiguous subarray of length k that contains only distinct elements. If a subarray of length k has even one duplicate, it is disqualified. Your goal is to slide through the array and identify the highest sum among all valid, unique-element windows. If no such subarray exists, the answer is 0.

2. Why is this asked in interviews?

This "Maximum Sum of Distinct Subarrays With Length K interview question" is a favorite for high-volume hiring companies like Microsoft, Amazon, and Google. It tests your ability to efficiently manage state in a sliding window. Interviewers want to see if you can track both the running sum and the frequency of elements simultaneously using a hash table or a set. It’s an excellent test of O(N) optimization skills.

3. Algorithmic pattern used

The "Array, Hash Table, Sliding Window interview pattern" is the standard solution. You use a frequency map (hash table) to keep track of the elements currently inside your window of size k. As the window slides:

1. Add the new element: update the sum and increment its count in the map.
2. Remove the oldest element: update the sum and decrement its count in the map.
3. Check validity: If the map's size is exactly k, it means all k elements are distinct. Update your global maximum sum accordingly.

4. Example explanation

Array: [1, 5, 4, 2, 9, 9, 9], k = 3

• Window 1: [1, 5, 4]. Sum = 10. All distinct. Max = 10.
• Window 2: [5, 4, 2]. Sum = 11. All distinct. Max = 11.
• Window 3: [4, 2, 9]. Sum = 15. All distinct. Max = 15.
• Window 4: [2, 9, 9]. Sum = 20. Contains duplicate (9). Not valid.
• Window 5: [9, 9, 9]. Sum = 27. Contains duplicate (9). Not valid. The result is 15.

5. Common mistakes candidates make

In the "Maximum Sum of Distinct Subarrays With Length K coding problem," a common mistake is using a nested loop to check for uniqueness, which leads to O(N*k) time complexity. Another error is not properly updating the hash map when an element is removed—specifically, forgetting to delete the key entirely when its frequency drops to zero. This would cause the "distinct count" check to fail even if the window only contains unique elements.

6. Interview preparation tip

Master the "Sliding Window + Hash Map" template. This combination is incredibly common for subarray problems with constraints. Pay close attention to how you define "distinct." In this problem, the size of the window and the number of keys in the hash map must both equal k. When practicing, try to implement this using the most efficient data structure available in your language (like unordered_map in C++ or dict in Python) to ensure O(N) performance.