My first instinct was two pointers and I think that's right, but I fumbled the pair-counting logic initially.
Clarify the problem and constraints, then propose an efficient solution using a sliding window with a frequency map to track distinct values and count pairs. Explain how to maintain the number of pairs as the window expands and shrinks, and how to count valid subarrays in O(n) time.
Pro tip: Emphasize that each distinct value contributes at most one pair, so the pair count is simply the number of distinct values with frequency ≥ 2. This simplifies the sliding window logic and avoids overcounting.
Confirm the definition of a pair (two equal elements) and that each distinct value contributes at most one pair. Ask about input size, value range, and expected time complexity.
Use two pointers (left and right) to represent a window. Maintain a frequency map of elements in the window and a variable `pairs` counting distinct values with frequency ≥ 2.
Expand right, update frequency and pairs. While pairs ≥ k, add (n - right) to the answer and shrink left, updating frequency and pairs accordingly.
Discuss edge cases like k=0, empty array, or no valid subarrays. State that the algorithm runs in O(n) time and O(n) space for the frequency map.
Walk through a small example to verify correctness, such as array [1,2,1,2,1] and k=2, showing how the window and pairs change.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.