mirror of
https://github.com/TheAlgorithms/Python.git
synced 2024-11-30 16:31:08 +00:00
1d457be29d
* matching algorithm for min vertex cover problem * fixed hint on row 37 * changed variable names * provided doctest for get_edges function * Removed dict.keys() iteration * Update matching_min_vertex_cover.py Co-authored-by: Christian Clauss <cclauss@me.com>
63 lines
2.1 KiB
Python
63 lines
2.1 KiB
Python
"""
|
|
* Author: Manuel Di Lullo (https://github.com/manueldilullo)
|
|
* Description: Approximization algorithm for minimum vertex cover problem.
|
|
Matching Approach. Uses graphs represented with an adjacency list
|
|
|
|
URL: https://mathworld.wolfram.com/MinimumVertexCover.html
|
|
URL: https://www.princeton.edu/~aaa/Public/Teaching/ORF523/ORF523_Lec6.pdf
|
|
"""
|
|
|
|
|
|
def matching_min_vertex_cover(graph: dict) -> set:
|
|
"""
|
|
APX Algorithm for min Vertex Cover using Matching Approach
|
|
@input: graph (graph stored in an adjacency list where each vertex
|
|
is represented as an integer)
|
|
@example:
|
|
>>> graph = {0: [1, 3], 1: [0, 3], 2: [0, 3, 4], 3: [0, 1, 2], 4: [2, 3]}
|
|
>>> matching_min_vertex_cover(graph)
|
|
{0, 1, 2, 4}
|
|
"""
|
|
# chosen_vertices = set of chosen vertices
|
|
chosen_vertices = set()
|
|
# edges = list of graph's edges
|
|
edges = get_edges(graph)
|
|
|
|
# While there are still elements in edges list, take an arbitrary edge
|
|
# (from_node, to_node) and add his extremity to chosen_vertices and then
|
|
# remove all arcs adjacent to the from_node and to_node
|
|
while edges:
|
|
from_node, to_node = edges.pop()
|
|
chosen_vertices.add(from_node)
|
|
chosen_vertices.add(to_node)
|
|
for edge in edges.copy():
|
|
if from_node in edge or to_node in edge:
|
|
edges.discard(edge)
|
|
return chosen_vertices
|
|
|
|
|
|
def get_edges(graph: dict) -> set:
|
|
"""
|
|
Return a set of couples that represents all of the edges.
|
|
@input: graph (graph stored in an adjacency list where each vertex is
|
|
represented as an integer)
|
|
@example:
|
|
>>> graph = {0: [1, 3], 1: [0, 3], 2: [0, 3], 3: [0, 1, 2]}
|
|
>>> get_edges(graph)
|
|
{(0, 1), (3, 1), (0, 3), (2, 0), (3, 0), (2, 3), (1, 0), (3, 2), (1, 3)}
|
|
"""
|
|
edges = set()
|
|
for from_node, to_nodes in graph.items():
|
|
for to_node in to_nodes:
|
|
edges.add((from_node, to_node))
|
|
return edges
|
|
|
|
|
|
if __name__ == "__main__":
|
|
import doctest
|
|
|
|
doctest.testmod()
|
|
|
|
# graph = {0: [1, 3], 1: [0, 3], 2: [0, 3, 4], 3: [0, 1, 2], 4: [2, 3]}
|
|
# print(f"Matching vertex cover:\n{matching_min_vertex_cover(graph)}")
|