Implementation of Single Source Shortest Path Problem

[RajNilkar]

Single Source Shortest Path (SSSP) Problem + Verifier Navigation Fix

Closes #165
Closes #171

Summary

This PR adds the Single Source Shortest Path (SSSP) problem to Redux, solved via Dijkstra's algorithm, and fixes a verifier-lookup bug uncovered while testing it against the new P / NP-Hard category structure.

This branch (algtesting) has been the team's shared working branch since March 8th and has not been merged upstream since then, so this PR also includes accumulated work from other contributors on the team over that period. The summary below focuses on the SSSP feature and the verifier fix; tagging contributors for visibility on the rest.

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SSSP Problem Implementation

Problem definition: Given a weighted graph G = (V, E) with non-negative edge weights and a source vertex s, find the shortest path from s to every other vertex, where path length is the sum of edge weights along the path.

What's included:

• SSSP_Class.cs — problem definition, instance parsing/validation (rejects negative weights and out-of-range source vertices)
• SSSPSolver.cs — Dijkstra's algorithm implementation supporting both weighted and unweighted, directed and undirected graph instances
• SSSPVerifier.cs — validates submitted certificates against the problem instance
• SSSPVisualization.cs — graph visualization, solved-path highlighting, and step-by-step visualization of Dijkstra's execution
• Test suite (SSSP_Tests.cs) covering:
  • Default/custom instantiation
  • Rejection of negative weights and invalid source vertices
  • Verifier accept/reject cases across directed/undirected and weighted/unweighted graphs
  • Solver correctness verified via the verifier (not exact-string matching, since Dijkstra may return any optimal path when ties exist)
  • Edge cases: unreachable target, source equal to target
  • Steps visualization rendering
    Category placement: SSSP is correctly placed under Problems/P/P_SSSP/, matching the platform's existing P_DFA / P_NFA convention

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Fixed: Verifier lookup fails for all P / NP-Hard problems

Why verifiers broke: VerifierNavigationData.Find() (used by Nav_Verifiers.cs / Problem_VerifiersRefactorController) has no equivalent fallback — it strictly filters by problemTypePrefix, and returns nothing if the prefix doesn't match. This made verifiers unreachable for every problem outside the original NPComplete category, not just SSSP — confirmed reproducible on DFA, NFA, and the Pump Scheduling (NP-Hard) problem as well.

Fix applied (created a fallback): Added a fallback to VerifierNavigationData.Find() — if filtering by problemTypePrefix returns no results, it retries matching on problemName alone, mirroring the existing solver/visualization fallback behavior.

Testing

• Verified locally: SSSP solve, verify, visualize, and step-by-step visualization all function correctly against multiple weighted/unweighted, directed/undirected test instances
• Verified the verifier fix resolves the lookup failure for SSSP, and should resolve it for other P/NP-Hard problems by the same mechanism (confirmed via direct endpoint testing)
• Full test suite passes (dotnet test)

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1 out of 4 committers have signed the CLA.

✅ RajNilkar
❌ MysticTiger2
❌ ScottBBarfuss
❌ malawitt
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