Fix DirectedHamiltonianVerifier missing closing-edge check - #507
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The verifier checked consecutive edges in a certificate but never required the walk to close back to its starting vertex, and had an off-by-one in its coverage check that happened to mask the gap for exact-length certificates. Ports the closure fix already applied to the undirected HamiltonianVerifier in b719fda, adapted for directed edges (no reverse-edge fallback), and removes an unused pairCheck2 left over from that copy.
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Trosper3
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Sep 1, 2026
Superseded by the fix+test file already open in PR #507 (fixes the missing closing-edge check and adds fuller test coverage vs. this PR's 3-test format smoke check). Keeping the instanceFormat/certificateFormat declaration changes; only dropping the file that would otherwise collide on merge.
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Summary
DirectedHamiltonianVerifierchecked consecutive edges in a certificate but never required the walk to close back to its starting vertex — the loop wasfor (i = 0; i < order.Count - 1; i++), so the last listed node's closing edge back to the start was never checked. An off-by-one in the coverage check happened to mask this for exact-length certificates, but an (n+1)-length certificate that visits every node via valid edges without ever returning to the start was incorrectly accepted.HamiltonianVerifieralready had this exact bug fixed inb719fda("Fix TSP and Hamiltonian verifiers missing closing-edge check") — only the directed verifier still had the hole, so this PR ports that same fix, adapted for directed edges (no reverse-edge fallback, since direction matters here).pairCheck2variable left over from copying the undirected verifier (issue's "Bug 3").Closes #255
Test plan
dotnet test --filter "...DIRECTEDHAMILTONIAN_Tests"— 8/8 passed (new test file; no prior tests existed for this problem)dotnet build --configuration Release(gates ondotnet format --verify-no-changes) — cleandotnet test(full suite) — 906/906 passed