When to Use

Look for these signals in the problem:

• "Range sum/min/max query" with updates: Segment tree handles both in $O(\log n)$.
• "Count elements" in range satisfying condition: Segment tree with custom aggregation function.
• "Update range, query point": Lazy propagation variant handles range updates.
• "Merge sort based" counting: Segment tree on value space counts inversions, smaller numbers, etc.
• Dynamic order statistics: Segment tree tracks count of elements for rank queries.