Project: audit member moves, cut depots, bottlenecks, and set families

Acceptance trace

Start with shipment groups {1,3,5} and {2,4}; after moving shipment 3 into the latter, their sizes and ID sums become (2,6) and (3,9). A road graph with two triangles and two bridges has articulation depots 2, 3, and 5. The minimum maximum edge on the route from depot 0 to 2 is 29, while depot 5 is unreachable from 0 in a separate weighted example. A four-set dispatch family includes cold plus insured but rejects cold alone. Check each trace against a direct model with the stated snapshot.

Failure and cost review

Fuzz merge and move operations against explicit group labels; test a move of a member whose old DSU node is a root. Compare articulation vertices with component counts after removing each vertex from small graphs. Compare bottleneck queries with an all-pairs minimax oracle, including disconnected vertices and repeated edge weights. Enumerate every subset of a small item universe to check diagram membership and count. Reject parallel roads in the simple block-cut model and unknown items in the set family. Do not claim any of the static graph or family indexes repair themselves after their inputs change.

Common Mistakes

• Do not reparent a live DSU node during a logical member move.
• Do not apply the non-root articulation rule to a DFS root.
• Do not confuse bottleneck maximum with path-weight sum.
• Do not treat a skipped zero-suppressed item as a wildcard.

Connected lessons

• Moveable disjoint sets: transfer one shipment without splitting its old tree
• Block-cut indexes: separate articulation depots from cyclic road blocks
• Kruskal reconstruction trees: answer route bottlenecks through merge ancestors
• Zero-suppressed diagrams: share sparse dispatch set families
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