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Project: audit dispatch order and dense depot links

Last updated: 5 Oct 202622 min read
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IntermediateBy AITrove Editorial

A local dispatch board must rotate through depots, show four views of a task tree, compare shared neighbors in a small dense depot graph, and answer asset rank questions. Keep the operation contracts distinct. The circular ring changes who is first by moving one tail reference. Tree orders use stacks or a queue but do not modify the task nodes. Bitset rows represent a fixed vertex mapping. The AVL node stores both height and subtree count, and each rotation has to repair both. Validate every mutation against a simpler independent representation.

Ring and task views

Append D-19, D-47, and D-61 to a ring. Rotate once, remove the front, and require D-47 as the removed depot with D-61 then D-19 remaining. Continue until empty and verify the singleton transition on the way. Build a task tree rooted at T-47, with T-19 and T-61 as its children and T-07 and T-26 beneath T-19. Record pre-, in-, post-, and level-order sequences. State whether any of those sequences is guaranteed to be sorted when the tree is not a search tree.

Dense links and ordered assets

Connect D-19 to D-26 and D-47, then connect D-61 to those same two depots. The first and last depots share two neighbors. Delete one link and assert both corresponding row bits clear; the shared count becomes one. Insert assets 47, 19, 61, 52, and 83 into a size-augmented AVL tree. Select zero-based ordinal 2 and rank key 58, then delete 47 and select every remaining ordinal. Audit height, subtree size, search ordering, and balance after each edit.

Acceptance trace

Output
Ring removal after one rotation: D-47
Tree in-order: T-07, T-19, T-26, T-47, T-61
Shared neighbors before deletion: 2; after deletion: 1
Select ordinal 2: 52; rank 58: 3

Cost and boundary review

Ring append, one-step rotation, and head removal take O(1) work, while a complete snapshot walks N members. Each tree traversal visits N task nodes and retains O(N) output. A bitset graph spends O(V²) bits for V depots before object overhead; Python row operations may touch O(V/W) machine words. An AVL tree keeps O(log N) height, so rank, select, insertion, and deletion follow logarithmic paths. Explain why repeated select is O(N log N) for all keys and why a static bitset vertex mapping is unsuitable for frequent vertex additions. Keep thread safety outside this project's contract.

Common Mistakes

  • Do not break the ring's singleton self-link or traverse until None.
  • Do not confuse post-order with level-order when clearing tasks.
  • Do not update only one endpoint in an undirected bitset graph.
  • Do not refresh AVL height while leaving subtree size stale.
  • Do not claim a traversal result is sorted without a search-tree invariant.

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