4 articles
Count smaller elements to the right of every index using a Binary Indexed Tree (Fenwick Tree) with coordinate compression. The cleanest O(n log n) solution every interviewer expects.
Track the tallest stack height as squares fall onto a number line. The textbook problem for segment trees with lazy propagation, range max queries, and range-assign updates.
Count subarray sums in [lower, upper] using merge sort or Fenwick tree on prefix sums. The flagship Hard problem connecting prefix sums, divide-and-conquer counting, and BIT range queries.
Count all longest increasing subsequences with DP in O(n^2) or with a segment tree on values for O(n log n). The classic crossover problem between DP and range-query data structures.