Subarrays with K Different Integers / visualized

You cannot slide a window for exactly k distinct values. The predicate is not monotone: at distinct == k, extending to the right can jump to k+1, and there is no shrink rule that lands you back — shrinking from the left can drop you to k−1 in the same move. But distinct ≤ s is monotone: once a window holds too many values, removing from the left only ever removes values, and they never come back on their own. So atMost(s) is windowable, and exactly(k) = atMost(k) − atMost(k−1). Run the same O(n) window twice and subtract. Inside each pass a valid window [l..r] banks r − l + 1 subarrays at once — one per suffix ending at r. The trap lives in the map: a count that falls to zero must have its key deleted, or size() never falls and the loop never ends.