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Project: audit capacity ranges and warehouse indexes

Last updated: 5 Oct 202624 min read
project
IntermediateBy AITrove Editorial

A warehouse console adjusts capacity estimates across intervals, answers reporting-chain questions, totals quantities in rectangular storage zones, and keeps an asset-ID set. Each index has a separate invariant. The segment tree postpones work only on fully covered intervals; the reporting table is valid only for one fixed rooted tree; the two-dimensional Fenwick grid converts assignments into differences; and a Robin Hood table preserves probe order when deleting a key. Compare outputs against an array, a plain parent map, a matrix scan, and a Python set.

Acceptance trace

Start capacity values 61, 47, 83, 26, 52, 19. Subtract 7 over [1, 5), add 20 over [3, 6), and require a minimum of 39 in [2, 6). Build a reporting tree where E-19 manages E-26 and E-47, E-26 manages E-52 and E-61, and E-47 manages E-83; the common manager for E-52 and E-83 is E-19. Put 47 units at grid cell (1, 2), 61 at (2, 3), and 19 at (3, 4). Rectangle [1, 3) by [2, 4) sums to 108 before replacing the first quantity with 26, then 87. Insert five colliding asset IDs into seven slots, delete 26, and confirm 33 remains findable.

Expected output

Output
range-minimum=39 common-manager=E-19
rectangle-before=108 rectangle-after=87
asset-33-present=true live=19,33,47,54

Cost and boundary review

Lazy range updates and minimum queries take O(log N) time over a fixed array. Binary lifting spends O(N log N) preprocessing and answers common-ancestor requests in O(log N). A dense two-dimensional Fenwick grid spends O(RC) memory and O(log R log C) time per assignment or rectangle. The fixed-capacity hash set has O(C) worst-case probes and can reject insertion when full. Test invalid bounds and malformed trees explicitly. These examples are local single-process models; none supplies transactional atomicity, live topology edits, or synchronized readers.

Common Mistakes

  • Do not lose a deferred update during partial descent.
  • Do not use a stale ancestor table after moving an employee.
  • Do not omit an inclusion-exclusion corner.
  • Do not leave a hash deletion hole before displaced keys.

Connected lessons

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