Bron kerbosch max cliques

[ArpitaHanjagi]

Algorithm: Bron–Kerbosch

Purpose: Finds all maximal cliques in an undirected graph.

Theory: Uses recursive backtracking with three sets:

R – currently growing clique

P – potential vertices to add

X – vertices already processed

Time Complexity: Exponential in worst case; optimal for sparse graphs.

Space Complexity: O(V + E) for adjacency list.

Input: Undirected graph as adjacency list.

Output: List of all maximal cliques.

[Copilot]

Pull Request Overview

This PR implements the Bron-Kerbosch algorithm for finding all maximal cliques in an undirected graph, along with an extensive collection of graph algorithms and dynamic programming solutions in R.

Key changes:

• Implementation of Bron-Kerbosch algorithm for maximal clique detection
• Addition of 15+ graph algorithms (DFS, BFS, Dijkstra, Floyd-Warshall, Prim, Kruskal, etc.)
• Addition of multiple dynamic programming algorithms (LIS, LCS, Knapsack, Coin Change, etc.)
• Addition of machine learning documentation and empty directory structures

Reviewed Changes

Copilot reviewed 138 out of 218 changed files in this pull request and generated 3 comments.

Show a summary per file

File	Description
graph_algorithms/bron_kerbosch_max_cliques.r	Implements Bron-Kerbosch algorithm for finding maximal cliques
graph_algorithms/*.r	Multiple graph algorithm implementations (DFS, BFS, Dijkstra, Floyd-Warshall, Prim, Kruskal, topological sort, etc.)
dynamic_programming/*.r	Dynamic programming algorithms (LIS, LCS, Knapsack, Coin Change, Matrix Chain, etc.)
kruskal_mst.r	Duplicate Kruskal implementation in root directory
documentation/.md/.html	Machine learning documentation files with error outputs
machine_learning/README.md	Tutorial links for ML in R
data_mining/.gitignore	Empty .gitignore file

[siriak]

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