feat(ch25): complete Johnson's algorithm — end-to-end correctness (#104) - #113
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…sue #104) Add the full Johnson algorithm implementation for all-pairs shortest paths: - isShortestDist_edge_ineq: general triangle inequality for shortest-path distances - walk_johnsonAugmented_some_projection: project walks from augmented graph to original - noNegCycle_johnsonAugmentedGraph: negative-cycle preservation in augmented graph - johnsonPotential: Bellman-Ford potential h(v) = δ(none, some v) - johnsonPotential_finite: the potential is always finite - johnsonPotential_isShortestDist: potential satisfies IsShortestDist - johnsonPotential_triangle: h(v) ≤ h(u) + w(u,v) for every edge (CLRS Lemma 25.3) - johnsonReweightedNonneg: reweighted graph has nonnegative weights - johnsonAllPairsDist: end-to-end Johnson distance function - johnsonAllPairsDist_correct: correctness theorem (CLRS Theorem 25.6) Update proof-map.md: Section 25.3 status partial → proved. Update clrs-proof-progress.csv: Ch25 status partial → main-proof-complete, missing core groups 2 → 1. Co-Authored-By: Claude <noreply@anthropic.com>
Add doc comments for johnsonPotential, johnsonPotential_eq, and johnsonPotential_isShortestDist. Co-Authored-By: Claude <noreply@anthropic.com>
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Summary
Completes Johnson's algorithm for all-pairs shortest paths (Issue #104).
New definitions
johnsonAugmentedGraph: augmented graph with new sourcenoneand zero-weight edges to all verticesreweightedWeight/reweightedGraph: reweighting with a potential functionhjohnsonPotential: Bellman-Ford potentialh(v) = δ(none, some v)johnsonAllPairsDist: end-to-end Johnson distance functionNew theorems
isShortestDist_edge_ineqwalk_johnsonAugmented_some_projectionnoNegCycle_johnsonAugmentedGraphreweightedWalkWeight_eqreweightedWeight_nonnegreweighted_isShortestDistjohnsonPotential_finitejohnsonPotential_isShortestDistjohnsonPotential_triangleh(v) ≤ h(u) + w(u,v)johnsonReweightedNonnegjohnsonAllPairsDist_correctProof structure
nonesource with 0-weight edges → augmented graphnoneon augmented graph → potentialhhsatisfies triangle inequality (Lemma 25.3) viaisShortestDist_edge_ineqh→ nonnegative weights → Dijkstra appliesBookkeeping
docs/proof-map.md: Section 25.3 statuspartial→proveddocs/clrs-proof-progress.csv: Ch25partial→main-proof-complete, missing groups 2 → 1Closes #104
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