Computational Complexity

Hamiltonian Path & Cycle

The problem of finding a path that visits every vertex exactly once. This is an NP-Complete problem, typically solved using backtracking with exponential time complexity O(N!).

ComplexityNP-Complete

TechniqueBacktracking

Try Interactive Simulator

Vertex Visit

Unlike Eulerian paths (edges), Hamiltonian paths must cover all vertices exactly once.

Backtracking Search

The algorithm explores every possible permutation of vertices until it finds a valid sequence or exhausts all options.

🖱️ Click to Add • ↔️ Drag to Move • ⌨️ Shift+Drag to Join

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Computational Complexity

Hamiltonian Path & Cycle

The problem of finding a path that visits every vertex exactly once. This is an NP-Complete problem, typically solved using backtracking with exponential time complexity O(N!).

ComplexityNP-Complete

TechniqueBacktracking

Try Interactive Simulator

Vertex Visit

Unlike Eulerian paths (edges), Hamiltonian paths must cover all vertices exactly once.

Backtracking Search

The algorithm explores every possible permutation of vertices until it finds a valid sequence or exhausts all options.

🖱️ Click to Add • ↔️ Drag to Move • ⌨️ Shift+Drag to Join

Hamiltonian Path Cycle

Hamiltonian Path Cycle

Hamiltonian Path & Cycle

Vertex Visit

Backtracking Search

Hamiltonian Path & Cycle

Vertex Visit

Backtracking Search