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

[Copilot]

Pull Request Overview

This PR adds two new algorithm implementations to the repository: a Hamiltonian Path search using backtracking and a Fast Fourier Transform (FFT) using the Cooley-Tukey recursive approach. Both implementations include comprehensive documentation and example usage.

Key Changes:

• Adds a backtracking-based Hamiltonian Path algorithm for finding paths that visit each vertex exactly once in an undirected graph
• Adds a recursive FFT implementation with automatic zero-padding for non-power-of-two inputs
• Includes detailed documentation files explaining usage, complexity, and implementation notes for both algorithms

Reviewed Changes

Copilot reviewed 4 out of 4 changed files in this pull request and generated 5 comments.

File	Description
graph_algorithms/hamiltonian_path.r	Implements Hamiltonian Path search using backtracking with adjacency matrix input
mathematics/fast_fourier_transform.r	Implements Cooley-Tukey FFT algorithm with power-of-two padding
documentation/hamiltonian_path.md	Documents the Hamiltonian Path implementation including usage and complexity analysis
documentation/fast_fourier_transform.md	Documents the FFT implementation including usage examples and complexity notes

[siriak]

We don't add documentation in a separate file, please remove it