Add Hopcroft-Karp algorithm for maximum bipartite matching - #15293
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Add Hopcroft-Karp algorithm for maximum bipartite matching#15293Clear20-22 wants to merge 4 commits into
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| # distance_map stores the BFS level/distance from free vertices in U | ||
| distance_map: dict[T | None, float] = {} | ||
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| def breadth_first_search() -> bool: |
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As there is no test file in this pull request nor any test function or class in the file graphs/hopcroft_karp.py, please provide doctest for the function breadth_first_search
| # Termination condition: True if an augmenting path was found, False otherwise | ||
| return distance_map[None] != math.inf | ||
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| def depth_first_search(left_vertex: T | None) -> bool: |
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As there is no test file in this pull request nor any test function or class in the file graphs/hopcroft_karp.py, please provide doctest for the function depth_first_search
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🟡 Changes recommended
The implementation has unresolved correctness and recursion-limit issues.
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Pull request overview
Adds a generic Hopcroft–Karp algorithm for maximum cardinality matching in unweighted bipartite graphs.
Changes:
- Implements BFS layering and DFS augmentation.
- Adds validation, documentation, reference link, and doctests.
File summaries
| File | Summary | Findings |
|---|---|---|
graphs/hopcroft_karp.py |
New Hopcroft–Karp implementation. | Critical (3 votes): None sentinel can collide with valid vertices. Moderate (3 votes): recursive DFS can exceed Python’s recursion limit. |
Review details
- Files reviewed: 1/1 changed files
- Comments generated: 2
- Review effort level: Lite
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| # pair_right[v] stores the vertex in U matched to v in V (or None if free) | ||
| pair_right: dict[T, T | None] = dict.fromkeys(right_vertices) | ||
| # distance_map stores the BFS level/distance from free vertices in U | ||
| distance_map: dict[T | None, float] = {} |
| # Augmentation Condition: Only step forward along the layered DAG | ||
| if distance_map.get(matched_left, math.inf) == distance_map[ | ||
| left_vertex | ||
| ] + 1.0 and depth_first_search(matched_left): |
…tinel, iterative DFS, and tests
algorithms-keeper
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Sep 12, 2026
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Describe your change
Add the Hopcroft–Karp algorithm ($O(|E|\sqrt{|V|})$ time using alternating BFS layering and DFS augmenting paths.
graphs/hopcroft_karp.py) for finding maximum cardinality matchings in unweighted bipartite graphs inChecklist