Added edmonds_blossom_algorithm.py #12053
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| BlossomData class with reduced parameters. | ||
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| def __init__(self, aux_data: BlossomAuxData, u: int, v: int, lca: int) -> None: |
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# Conflicts: # graphs/edmonds_blossom_algorithm.py
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# Conflicts: # graphs/edmonds_blossom_algorithm.py
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| BlossomData class with reduced parameters. | ||
| """ | ||
|
|
||
| def __init__(self, aux_data: BlossomAuxData, u: int, v: int, lca: int) -> None: |
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Describe your change:
This PR implements the Edmonds' Blossom Algorithm in the EdmondsBlossomAlgorithm class, which efficiently finds the maximum matching in general graphs, including those with odd-length cycles. The implementation includes methods for handling augmenting paths, updating matchings, and contracting blossoms.
Maximum Matching: Introduces the maximumMatching method, which takes a list of edges and the total number of vertices as input and returns a list of matched pairs of vertices.
Augmenting Path Search: Utilizes a breadth-first search (BFS) approach to locate augmenting paths within the graph, ensuring that it can handle complex graph structures effectively.
Blossom Contraction: Implements mechanisms for contracting blossoms to manage odd-length cycles, which is a key aspect of the algorithm's efficiency.
Detailed Comments: Each method and critical section of the code are thoroughly commented to ensure clarity and understanding of the algorithm's functionality.
Checklist: