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# Solvers in Action

The 12 Celestial Transformers — running live in your browser.

Each solver below generates random problem instances and solves them in real-time. Watch the algorithm work, see the speed, and understand how each transformer maps to a specific NP-complete problem class.

B2 🗺️ Travelling Salesman Problem TSP Find the shortest route visiting every city exactly once. Nearest-neighbour heuristic with 2-opt improvement. B1 🧩 Boolean Satisfiability SAT Determine if a boolean formula has a satisfying assignment. DPLL algorithm with unit propagation. B5 🛡️ Vertex Cover VC Find smallest set of vertices that touches every edge. Greedy approximation algorithm. B4 🎨 Graph Coloring GC Assign colours to vertices so no adjacent vertices share a colour. Greedy sequential algorithm. B6 📦 Set Cover SC Find smallest collection of sets that covers all elements. Greedy approximation. B8 🔗 Hamiltonian Path HP Find a path visiting every vertex exactly once. Backtracking with forward checking. B3 ⚖️ Subset Sum SS Find a subset that sums to a target value. Meet-in-the-middle algorithm. B7 💎 Max Clique MC Find the largest complete subgraph. Branch and bound with colour-based pruning. B10 🧩 Exact Cover EC Find a collection of sets that covers each element exactly once. Algorithm X with dancing links. B9 🌳 Steiner Tree ST Find shortest network connecting required points, optionally using intermediate points. Dynamic programming. B11 ⚡ Resonant Collector RC Find optimal frequency resonance points. Wave propagation simulation. B72 👁️ Observer — The Watcher OBS Watches all 72 bands for pattern anomalies. Doesn't solve — observes.