Hopcroft karp max matching

[ArpitaHanjagi]

Algorithm: Hopcroft-Karp

Purpose: Computes the maximum matching in a bipartite graph, i.e., the largest set of edges where no two edges share a vertex.

Theory:

Uses the concept of augmenting paths: a path that alternates between unmatched and matched edges, starting and ending at unmatched vertices.

By finding shortest augmenting paths and augmenting along multiple disjoint paths in one phase, it minimizes the number of iterations.

Relies on BFS to layer the graph and find distances to unmatched vertices, and DFS to actually augment paths.

Efficiency: Faster than naive augmenting path algorithms because it increases matching size by multiple paths per iteration.

Time Complexity: O(E × √V)

Space Complexity: O(V + E)

Input: Bipartite graph as an adjacency list from the left partition to the right partition.

Output: Maximum matching size and the matched vertex pairs.

[Copilot]

Pull Request Overview

This pull request introduces a substantial collection of algorithms and data structures to the R repository, primarily focused on graph algorithms, dynamic programming, and machine learning implementations. The PR appears to be part of expanding TheAlgorithms/R with comprehensive algorithmic implementations.

Key changes:

• Addition of 10+ graph algorithms including Hopcroft-Karp, Dijkstra, Floyd-Warshall, and various MST algorithms
• Implementation of 6+ dynamic programming solutions covering classic problems like knapsack, LCS, and coin change
• Addition of mathematics algorithms including bisection method and Armstrong number checking
• Inclusion of machine learning implementations (gradient boosting) and documentation files

Reviewed Changes

Copilot reviewed 138 out of 214 changed files in this pull request and generated 2 comments.

Show a summary per file

File	Description
graph_algorithms/hopcroft_karp_max_matching.r	Implements Hopcroft-Karp algorithm for maximum bipartite matching
graph_algorithms/dijkstra_shortest_path.r	Dijkstra's algorithm with priority queue implementation
graph_algorithms/floyd_warshall.r	All-pairs shortest path algorithm with R6 class structure
dynamic_programming/subset_sum.r	Subset sum problem with both standard and optimized solutions
dynamic_programming/longest_increasing_subsequence.r	LIS algorithm with O(n²) and O(n log n) variants
machine_learning/gradient_boosting.r	Complete gradient boosting regressor implementation
mathematics/bisection_method.r	Root-finding algorithm implementation
mathematics/armstrong_number.r	Armstrong number checking function

[siriak]

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