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Merge remote-tracking branch 'origin/master'

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# Conflicts:
#	graphs/edmonds_blossom_algorithm.py
This commit is contained in:
Tarun Vishwakarma 2024-10-14 12:15:05 +05:30
commit b8571bcffc
1 changed files with 30 additions and 16 deletions
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46
graphs/edmonds_blossom_algorithm.py
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@ -5,8 +5,9 @@ UNMATCHED = -1 # Constant to represent unmatched vertices
class EdmondsBlossomAlgorithm:
@staticmethod
def maximum_matching(edges: list[tuple[int, int]], vertex_count: int) \
-> list[tuple[int, int]]:
def maximum_matching(
edges: list[tuple[int, int]], vertex_count: int
) -> list[tuple[int, int]]:
"""
Finds the maximum matching in a general graph using Edmonds' Blossom Algorithm.
@ -84,10 +85,16 @@ class EdmondsBlossomAlgorithm:
EdmondsBlossomAlgorithm.contract_blossom(
BlossomData(
BlossomAuxData(
queue, parent, base, in_blossom,
match, in_queue
queue,
parent,
base,
in_blossom,
match,
in_queue,
),
current_vertex, neighbor, base_vertex
current_vertex,
neighbor,
base_vertex,
)
)
@ -100,8 +107,9 @@ class EdmondsBlossomAlgorithm:
return matching_result
@staticmethod
def update_matching(match: list[int],
parent: list[int], current_vertex: int) -> None:
def update_matching(
match: list[int], parent: list[int], current_vertex: int
) -> None:
"""
Updates the matching along the augmenting path found.
@ -160,7 +168,7 @@ class EdmondsBlossomAlgorithm:
current_vertex_v = parent[current_vertex_v]
@staticmethod
def contract_blossom(blossom_data: 'BlossomData') -> None:
def contract_blossom(blossom_data: "BlossomData") -> None:
"""
Contracts a blossom in the graph, modifying the base array
and marking the vertices involved.
@ -176,9 +184,9 @@ class EdmondsBlossomAlgorithm:
current_vertex_u = blossom_data.vertex_u
while blossom_data.aux_data.base[current_vertex_u] != blossom_data.lca:
base_u = blossom_data.aux_data.base[current_vertex_u]
match_base_u = blossom_data.aux_data.base[blossom_data.aux_data.match
[current_vertex_u]
]
match_base_u = blossom_data.aux_data.base[
blossom_data.aux_data.match[current_vertex_u]
]
blossom_data.aux_data.in_blossom[base_u] = True
blossom_data.aux_data.in_blossom[match_base_u] = True
current_vertex_u = blossom_data.aux_data.parent[
@ -188,9 +196,9 @@ class EdmondsBlossomAlgorithm:
current_vertex_v = blossom_data.vertex_v
while blossom_data.aux_data.base[current_vertex_v] != blossom_data.lca:
base_v = blossom_data.aux_data.base[current_vertex_v]
match_base_v = blossom_data.aux_data.base[blossom_data.aux_data.match
[current_vertex_v]
]
match_base_v = blossom_data.aux_data.base[
blossom_data.aux_data.match[current_vertex_v]
]
blossom_data.aux_data.in_blossom[base_v] = True
blossom_data.aux_data.in_blossom[match_base_v] = True
current_vertex_v = blossom_data.aux_data.parent[
@ -212,8 +220,13 @@ class BlossomAuxData:
"""
def __init__(
self, queue: deque, parent: list[int], base: list[int], in_blossom: list[bool],
match: list[int], in_queue: list[bool]
self,
queue: deque,
parent: list[int],
base: list[int],
in_blossom: list[bool],
match: list[int],
in_queue: list[bool],
) -> None:
self.queue = queue
self.parent = parent
@ -243,3 +256,4 @@ class BlossomData:
self.vertex_u = vertex_u
self.vertex_v = vertex_v
self.lca = lca