Add-Prims's Algorithm for MST

[Erennn7]

PR: Prim's Algorithm for Minimum Spanning Tree (MST)

This PR introduces a fully documented implementation of Prim's Algorithm in R, designed to compute the Minimum Spanning Tree (MST) of a connected, weighted, undirected graph. The algorithm efficiently grows the MST by repeatedly adding the minimum-weight edge connecting the already included vertices to a new vertex.

Overview

Prim's algorithm operates as follows:

• Start from an arbitrary vertex.
• Repeatedly select the smallest edge connecting a vertex in the MST to a vertex outside the MST.
• Add the selected edge and vertex to the MST.
• Continue until all vertices are included.

The implementation supports both adjacency matrix and edge list representations, includes input validation, and provides formatted MST output.

Features

• Computes the MST of connected, weighted, undirected graphs.
• Handles edge cases like disconnected graphs with appropriate warnings.
• Outputs MST edges, total weight, and parent array.
• Includes helper functions for printing MST and constructing adjacency matrices from edge lists.
• Multiple examples provided: basic graphs, complete graphs, edge-list graphs, and disconnected graphs.
• Comparison notes with Kruskal's algorithm for educational purposes.

Complexity

• Time Complexity:
  • O(V²) with adjacency matrix (simple implementation)
  • O((V + E) log V) with priority queue (optimized, not implemented here)
• Space Complexity: O(V) for key, parent, and visited arrays

Applications

• Network design (telecommunications, computer networks)
• Circuit design and electrical grids
• Clustering algorithms in machine learning
• Transportation and logistics planning
• Approximation algorithms for NP-hard problems

Demonstration

Run the included examples to see Prim's Algorithm in action:

# Example: Basic 5-vertex graph
graph <- matrix(c(
  0, 2, 0, 6, 0,
  2, 0, 3, 8, 5,
  0, 3, 0, 0, 7,
  6, 8, 0, 0, 9,
  0, 5, 7, 9, 0
), nrow = 5, byrow = TRUE)

mst <- prim_mst(graph)
print_mst(mst, graph)

[Copilot]

Pull Request Overview

This PR adds a comprehensive implementation of Prim's algorithm for computing the Minimum Spanning Tree (MST) of weighted, undirected graphs in R. The implementation includes input validation, helper functions, and multiple examples demonstrating various use cases.

• Introduces prim_mst() function with O(V²) adjacency matrix implementation
• Adds utility functions for MST visualization and graph construction from edge lists
• Provides five detailed examples covering basic graphs, edge lists, disconnected graphs, and complete graphs

[Erennn7]

✅ Updated Prim’s MST R implementation
• Fixed roxygen2 documentation syntax: removed colons after @param names for prim_mst(), print_mst(), and create_graph_from_edges() functions.
• No functional changes were made; all examples, logic, and outputs remain unchanged.
• This ensures documentation is compatible with standard roxygen2 processing and avoids warnings/errors when generating Rd files.

[Erennn7]

@siriak please have a look

[Copilot]

Pull Request Overview

Copilot reviewed 1 out of 1 changed files in this pull request and generated 3 comments.

[Copilot]

Pull Request Overview

Copilot reviewed 1 out of 1 changed files in this pull request and generated 2 comments.