Maximum Sum of Almost Unique Subarray

Problem Description

You are given an integer array nums and two positive integers m and k. Return the maximum sum out of all almost unique subarrays of length k of nums. If no such subarray exists, return 0. A subarray of nums is almost unique if it contains at least m distinct elements.

Key Insights

• A subarray is defined as a contiguous sequence of elements within an array.
• An "almost unique" subarray must contain at least m distinct elements.
• We can utilize a sliding window technique to efficiently find subarrays of length k.
• A hash table (or dictionary) can be used to count the distinct elements in the current subarray.

Space and Time Complexity

Time Complexity: O(n)
Space Complexity: O(k)

Solution

To solve the problem, we can employ a sliding window approach. We maintain a window of size k that moves through the array. We utilize a hash table to keep track of the frequency of elements within this window. As we slide the window:

1. When the window reaches size k, we check if the number of distinct elements (tracked using the hash table) is at least m.
2. If it is, we calculate the sum of the current window and update our maximum sum if this sum is greater than the previous maximum.
3. We then slide the window by removing the element that is exiting the window and adding the new element that is entering the window.

Code Solutions