Hierholzer eulerian

[ArpitaHanjagi]

Algorithm: Hierholzer’s Algorithm

Purpose: Finds an Eulerian circuit in a graph, visiting every edge exactly once.

Theory: Starts at any vertex and follows edges to form a cycle; additional cycles are merged until all edges are used. Works for undirected graphs with all vertices of even degree or directed graphs with in-degree = out-degree.

Time Complexity: O(E)

Space Complexity: O(V + E)

Input: Graph as an adjacency list.

Output: Eulerian circuit as a sequence of vertices.

[Copilot]

Pull Request Overview

This PR adds Hierholzer's Algorithm implementation for finding Eulerian circuits in graphs, along with extensive additions across multiple algorithm categories including graph algorithms, dynamic programming, machine learning, and mathematics.

Key changes:

• Implementation of Hierholzer's algorithm for Eulerian circuit detection
• Addition of multiple graph algorithms (Dijkstra, Floyd-Warshall, Bellman-Ford, DFS, BFS, Kruskal, Prim, Topological Sort, Kosaraju, Hopcroft-Karp, Hamiltonian Cycle, Bridge Detection)
• Implementation of dynamic programming algorithms (0/1 Knapsack, Coin Change, LCS, LIS, Matrix Chain Multiplication, Minimum Path Sum, Subset Sum)
• Machine learning implementations (Gradient Boosting, documentation for various ML algorithms)
• Mathematics algorithms (Armstrong Number, Amicable Numbers, Bisection Method)

Reviewed Changes

Copilot reviewed 139 out of 215 changed files in this pull request and generated 5 comments.

Show a summary per file

File	Description
graph_algorithms/hierholzer_eulerian.r	Implements Hierholzer's algorithm for finding Eulerian circuits
graph_algorithms/dijkstra_shortest_path.r	Implements Dijkstra's shortest path algorithm with priority queue
graph_algorithms/floyd_warshall.r	Implements Floyd-Warshall all-pairs shortest path with R6 classes
graph_algorithms/bellman_ford_shortest_path.r	Implements Bellman-Ford algorithm with negative cycle detection
graph_algorithms/depth_first_search.r	Implements DFS in both recursive and iterative versions
graph_algorithms/breadth_first_search.r	Implements BFS with shortest path finding capabilities
graph_algorithms/kruskal_mst.r	Implements Kruskal's MST algorithm using union-find
graph_algorithms/prim_mst.r	Implements Prim's MST algorithm
graph_algorithms/topological_sort.r	Implements Kahn's algorithm for topological sorting
graph_algorithms/kosaraju_scc.r	Implements Kosaraju's algorithm for strongly connected components
graph_algorithms/hopcroft_karp_max_matching.r	Implements Hopcroft-Karp for maximum bipartite matching
graph_algorithms/hamilitonian_cycle.r	Implements backtracking algorithm for Hamiltonian cycle detection
graph_algorithms/bridge_detector.r	Implements Tarjan's algorithm for bridge detection
machine_learning/gradient_boosting.r	Implements gradient boosting regressor using R6 classes
machine_learning/README.md	Adds machine learning tutorial resources
dynamic_programming/0/1_knapsack_problem.r	Implements 0/1 knapsack with DP
dynamic_programming/coin_change.r	Implements coin change problem solution
dynamic_programming/longest_common_subsequence.r	Implements LCS algorithm with multiple variants
dynamic_programming/longest_increasing_subsequence.r	Implements LIS with O(n²) and O(n log n) solutions
dynamic_programming/matrix_chain_multiplication.r	Implements matrix chain multiplication optimization
dynamic_programming/minimum_path_sum.r	Implements minimum path sum in grid
dynamic_programming/subset_sum.r	Implements subset sum problem with DP
mathematics/armstrong_number.r	Implements Armstrong number checker
mathematics/amicable_numbers.r	Implements amicable number verification
mathematics/bisection_method.r	Implements bisection method for root finding
kruskal_mst.r	Duplicate of graph_algorithms/kruskal_mst.r in wrong location
documentation/*.md/*.html	Documentation and example files for various ML algorithms

[siriak]

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