Gomory hu tree

[ArpitaHanjagi]

Algorithm: Gomory-Hu Tree

Purpose: Represents all-pairs minimum cuts in an undirected weighted graph as a tree.

Theory:

Each edge in the tree corresponds to a minimum cut between its endpoints.

Any min-cut between two vertices in the original graph is the minimum weight on the path connecting them in the tree.

Time Complexity: O(V * max-flow) (depends on the max-flow algorithm used).

Space Complexity: O(V + E).

Input: Weighted undirected graph as adjacency list.

Output: Parent array and edge weights representing the Gomory-Hu tree.

[Copilot]

Pull Request Overview

This pull request adds the Gomory-Hu Tree algorithm implementation to the repository, along with numerous other graph algorithms, dynamic programming solutions, and documentation files. The Gomory-Hu Tree algorithm constructs a tree representing all-pairs minimum cuts in an undirected weighted graph.

Key changes:

• Added Gomory-Hu Tree algorithm implementation
• Added multiple graph algorithms (Kruskal's MST, Prim's MST, Dijkstra, BFS/DFS, Floyd-Warshall, etc.)
• Added dynamic programming algorithms (0/1 Knapsack, LCS, LIS, etc.)
• Added machine learning documentation and examples

Reviewed Changes

Copilot reviewed 140 out of 220 changed files in this pull request and generated 2 comments.

Show a summary per file

File	Description
Desktop/open-source/R/graph_algorithms/gomory_hu_tree.r	Implements Gomory-Hu Tree algorithm with placeholder min-cut function
Desktop/open-source/R/graph_algorithms/kruskal_mst.r	Implements Kruskal's MST algorithm with Union-Find
Desktop/open-source/R/graph_algorithms/prim_mst.r	Implements Prim's MST algorithm
Desktop/open-source/R/graph_algorithms/dijkstra_shortest_path.r	Implements Dijkstra's algorithm with priority queue
Desktop/open-source/R/dynamic_programming/0/1_knapsack_problem.r	Implements 0/1 Knapsack problem solution
Desktop/open-source/R/dynamic_programming/coin_change.r	Implements coin change problem solution
Desktop/open-source/R/documentation/*.md	Machine learning algorithm documentation files

[siriak]

You have changed 220 files, check your changes