Project: audit ordered ranks, grid corrections, and majority windows

Acceptance trace

Split depot keys at 47 to obtain [19,29] and [47,61,83]. The third key after removal of 61 is 47. An alert index initially ranks 47 at position two, then removes 29. A heat-grid rectangle rises from 176 to 200 after one sensor correction. A majority query over the first five readings returns 47, while the last four have no majority. Reproduce these results with direct sorted lists, matrix slices, and occurrence counts before accepting index output.

Failure and cost review

Generate duplicate insertions and random removals, then compare ordered treap rank selection and split partitions with sorted sets. Mutate the skip list repeatedly while checking every rank and select against that set. Replace grid values at corners and padded boundaries; compare half-open rectangles with direct sums, including empty windows. Check majority candidates against a direct frequency count, especially when one value appears exactly half the time. Record expected logarithmic bounds separately from strict worst-case claims for randomized structures.

Common Mistakes

• Do not reuse consumed treap roots as snapshots.
• Do not leave skip-list spans stale after removal.
• Do not add a new grid value on top of the old cell.
• Do not return a majority candidate without exact verification.

Connected lessons

• Ordered treaps: split, join, and select depot keys
• Span skip lists: rank and select without a full scan
• Two-dimensional segment trees: correct sensors and sum rectangles
• Range-majority indexes: verify a candidate before returning it
• Projects
• Quizzes
• Data Structures