Maximum Sum of Distinct Subarrays With Length K

Look at every contiguous window of exactly k elements in the integer array nums. Among the windows whose values are all distinct, with no value repeated, return the largest sum.

If every window of length k contains a duplicate, the answer is 0.

A brute force check for distinctness takes O(k). Doing this for every window results in O(Nk) or O(Nk^2). We need O(N).

Strategy: Fixed Sliding Window + Frequency Map

1. Window: Maintain a window of size k.
2. Tracking: Use a Hash Map (or frequency array) to count occurrences of each number in the current window.
3. Validity: A full window is distinct exactly when the map holds k different keys (len(counts) == k).
   • If count[num] > 1, we have a duplicate.
4. Updates:
   • Add incoming element: Add it to the sum and increment its count.
   • Remove outgoing element: Subtract it from the sum, decrement its count, and delete the key when the count reaches 0.
   • If the window holds k elements and the map holds k keys, update max_sum.

Watch the window slide: a solid frame marks a full window of different values, and a dashed frame marks one that repeats a value. The counts beside the figure show which value repeats.