Day 4: a dataset where greedy provably misses the optimum (closes #37) - #59
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The heuristic-vs-exact lesson had nothing on screen behind it: every shipped dataset agrees with greedy. The theater cannot supply a counterexample -- 0 of 240 single-capacity edits and 0 of 4,335 two-lane interior edits diverge -- so this instance is authored at the measured floor of 6 nodes and 8 lanes. Baseline 140; exhaustive reaches 0 at k=2 by taking both lanes into t; greedy opens with the damage-80 s->A and stalls at 30. Both load-bearing JSON edge orderings are now pinned by tests. A sweep of all 40,320 trap orderings confirms 66.7% preserve the divergence and that the pinned condition selects exactly that set; a sweep of all 5,040 Day 2 orderings confirms the pinned precedences are exactly the 25% that demonstrate cancellation.
Both review axes caught the same thing: the edge-order pin explained greedy's tie-break as first-in-file, but the candidate scan iterated a set of indices, which is ascending only incidentally for small contiguous values. Sort the scan so the datasets' edge order is something the solver guarantees, and assert greedy's opening lane so the tie-break is pinned by behaviour rather than assumed. Also pin that k=1 falls short at 60 (otherwise 'exhaustive reaches 0 at k=2' says nothing), name the optimal pair C->t/D->t rather than counting it, assert the lane count so a duplicate lane cannot hide in the capacity map, and give the two datasets' edge-order reads a single home.
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Closes #37.
Day 4 claims a budget interdictor who always takes the most damaging single lane can end up strictly worse than one that searches — but every shipped dataset agreed with greedy, so the claim had nothing on screen behind it. This adds
data/greedy_trap.json, authored at the measured 6-node / 8-lane floor.The optimal blockade contains neither of the damage-80 lanes greedy reaches for — greedy fails when the best blockade isn't where the biggest single lane is.
Both load-bearing edge orderings are pinned
Verified by exhaustive sweep, not by assertion:
textbook_maxflow.json): of 5,040 orderings, exactly 1,260 (25%) demonstrate cancellation and 2,520 (50%) collapse to a two-iteration trace that silently restores the bug the dataset was replaced to fix. The pinned precedences (s->Abefores->C,A->BbeforeA->D) match the cancelling set on all 5,040 — zero disagreements.Both are silent if broken: the files still load and still draw.
Review follow-up
The review caught that the tie-break docstring claimed "first-in-file" while the solver iterated a set of indices — ascending only incidentally for small contiguous values.
budget_interdictionnow scanssorted(remaining), so file order is a guarantee rather than an accident, and the test asserts greedy's opening lane so the tie-break is pinned by behaviour.Registry pickup and the
data/-parameterised suites required no code or test edits. 216 tests pass.