Dinics algo

[Prathameshk2024]

• Finds maximum flow in a flow network from source to sink
• Uses blocking flows approach for efficient computation
• Builds level graphs using BFS (Breadth-First Search)
• Finds augmenting paths using DFS (Depth-First Search)
• Handles residual graph with forward and reverse edges
• Computes minimum cut and cut edges
• Supports bipartite matching and multi-source/sink problems
• Time complexity: O(V² × E), Space complexity: O(V + E)
• Includes network creation, edge addition, and flow validation
• Demonstrates 5 test cases: simple networks, bipartite matching, complex paths, bottlenecks, and multi-source/sink scenarios

[Copilot]

Pull Request Overview

This pull request adds Dinic's Maximum Flow Algorithm implementation to the repository, along with several other graph algorithms. The PR focuses on providing a comprehensive implementation of the maximum flow problem using Dinic's algorithm with blocking flows approach.

• Implements Dinic's maximum flow algorithm with BFS level graph construction and DFS blocking flow finding
• Adds supporting algorithms including graph coloring, bidirectional BFS, and Viterbi algorithm
• Provides extensive test cases and examples demonstrating various network flow scenarios

Reviewed Changes

Copilot reviewed 5 out of 5 changed files in this pull request and generated 1 comment.

Show a summary per file

File	Description
graph_algorithms/dinics_max_flow.r	Main implementation of Dinic's algorithm with network creation, flow computation, and minimum cut functions
graph_algorithms/graph_coloring.r	Graph coloring algorithms using backtracking, greedy, and Welsh-Powell approaches
graph_algorithms/bidirectional_bfs.r	Bidirectional breadth-first search implementation for shortest path finding
dynamic_programming/viterbi.r	Viterbi algorithm for Hidden Markov Model decoding
et --soft HEAD~1	Git log output file that should not be included in the repository

Comments suppressed due to low confidence (1)

et --soft HEAD~1:1

• This file appears to be Git log output and should not be included in the repository. Only algorithm implementations and related documentation should be committed.

�[33mcommit 7d4b7af52036b21abf54435f14250ef170351389�[m�[33m (�[m�[1;36mHEAD�[m�[33m -> �[m�[1;32mGraph_colouring�[m�[33m)�[m

[Prathameshk2024]

@siriak

[Copilot]

Pull Request Overview

Copilot reviewed 4 out of 4 changed files in this pull request and generated 2 comments.

Comments suppressed due to low confidence (1)

et --soft HEAD~1:1

• This file appears to be an accidentally committed git log output. It should be removed from the repository as it contains no algorithmic implementation and was likely created due to a typo in a git command (appears to be 'git reset --soft HEAD~1' with 'res' missing).

�[33mcommit 7d4b7af52036b21abf54435f14250ef170351389�[m�[33m (�[m�[1;36mHEAD�[m�[33m -> �[m�[1;32mGraph_colouring�[m�[33m)�[m