A logistics report has four independent lookup requirements. Shipment weights have sparse numeric labels but a known catalog. Recorded weights need mutable multiplicities and kth selection. A frozen scan batch needs distinct-code counts across many submitted windows. A fixed rectangular capacity grid needs rectangle totals. Build each index only after writing a plain reference: sorted unique keys for ranks, a sorted multiset list for kth values, a set over each scan slice for distinct counts, and a nested rectangle sum for the grid. Run the same requests through both paths. Preserve duplicates in records even though the rank catalog removes duplicate keys. State which requests can arrive online and which must be collected before reordering.
Project: audit ranks, windows, and grid reports
Acceptance trace
For weights 4700, -35, 4700, 82000, 19, require rank two for 4700 and two recorded weights below 4700. The third recorded weight is 4700 before and after one copy is removed. For scan codes D47, D19, D47, D61, D19, D83, D47, require window counts four, two, zero, four for [1, 6), [0, 3), [3, 3), [2, 7). For the three-by-four capacity grid in the lesson, require 147 for rows [0, 2) by columns [1, 3), and 495 for the whole grid. Check the results in the original request order even if the window processor rearranges work.
Expected output
rank-4700=2 third-weight=4700 distinct=[4, 2, 0, 4]
center-capacity=147 full-capacity=495Boundary and cost review
Test an empty key catalog, an empty frequency index, duplicate weights, a removal larger than recorded multiplicity, windows of length zero, a query with an excluded stop at the array length, an empty grid, and a ragged grid. Rebuild when an unseen weight enters the catalog or when the frozen scan codes or grid values change. Compare memory costs before selecting an index: the rank catalog stores distinct keys, the frequency tree stores one slot per known key, Mo ordering stores all requests, and the prefix grid stores an additional border. A report that needs one small query may need no index at all.
Common Mistakes
- Do not use rank differences as measurement differences.
- Do not select the kth key from distinct keys while ignoring multiplicity.
- Do not return offline window answers in processing order.
- Do not forget the rectangle overlap correction.