Add Hamiltonian Path in R

[nachiket2005]

Overview

The hamiltonianPath function attempts to construct a valid Hamiltonian Path by recursively adding vertices to a path while ensuring adjacency and non-repetition constraints.
If the input adjacency matrix does not contain a Hamiltonian Path, the algorithm reports that no valid path was found.

This implementation provides a clear, educational example of graph backtracking and can be extended to find Hamiltonian Cycles as well.

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Features

• Implements a backtracking-based Hamiltonian Path search
• Accepts input as an adjacency matrix (n × n)
• Verifies adjacency and uniqueness at each recursive step
• Prints the Hamiltonian Path when found
• Returns logical TRUE if a path exists, otherwise FALSE
• Includes a sample graph and example usage block for demonstration

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Complexity

• Time Complexity: O(n!) in the worst case (backtracking over all vertex permutations)
• Space Complexity: O(n) for recursion stack and path storage