Add - traveling Salesman algorithm

[Erennn7]

PR: Traveling Salesman Problem (TSP) using Bitmask Dynamic Programming in R

This PR introduces a fully documented implementation of the Traveling Salesman Problem (TSP) in R using Bitmask Dynamic Programming (DP).
The algorithm efficiently finds the shortest possible route that visits each city exactly once and returns to the starting city, making it suitable for small-to-medium numbers of cities.

Overview

The tsp_bitmask_dp function applies Bitmask DP to track visited cities using binary masks.
Instead of enumerating all permutations (which is factorial in time complexity), the algorithm leverages memoization and bitwise operations to reduce redundant computations, achieving O(n² * 2^n) performance.

Key features include:

• Recursive DP with memoization for minimum travel cost
• Optional path reconstruction using a separate function (tsp_bitmask_with_path)
• Handles arbitrary distance matrices
• Demonstrates the optimal TSP route and total cost

This approach is ideal for applications such as:

• Route optimization and logistics
• Network and circuit design
• Scheduling and planning problems
• Microchip and genome sequencing tasks

Complexity

• Time Complexity: O(n² * 2^n), where n = number of cities
• Space Complexity: O(n * 2^n) for memoization table

Notes

• Works efficiently for small n (typically n ≤ 20)
• For larger instances, consider heuristic or approximation algorithms like Nearest Neighbor, 2-opt, Christofides algorithm, or metaheuristics (Genetic Algorithms, Simulated Annealing)

[Copilot]

Pull Request Overview

This PR adds a new implementation of the Traveling Salesman Problem (TSP) using Bitmask Dynamic Programming in R. The algorithm efficiently finds the shortest route visiting all cities exactly once and returning to the starting city, suitable for small-to-medium problem sizes (n ≤ 20).

Key Changes:

• Implements TSP using bitmask DP with O(n² × 2^n) time complexity
• Provides both cost-only and path reconstruction variants
• Includes three example use cases demonstrating the algorithm

[Erennn7]

@siriak please have a look

[Copilot]

Pull Request Overview

Copilot reviewed 1 out of 1 changed files in this pull request and generated 4 comments.