mirror of
https://github.com/TheAlgorithms/Python.git
synced 2024-10-06 13:49:30 +00:00
908cb4f1e7
* added complete graph generator function * added doctest, type hints, wikipedia explanation * added return type hint for function complete_graph * added descriptive name for the parameter: n * random graph generator with doctest and type hints * added Greedy min vertex algorithm * pre-commit hook(s) made changes * Delete complete_graph_generator.py * Delete random_graph_generator.py * fixed doctest * updated commit following highligths * fixed following pre-commit highlights * modified variables names
66 lines
2.3 KiB
Python
66 lines
2.3 KiB
Python
"""
|
|
* Author: Manuel Di Lullo (https://github.com/manueldilullo)
|
|
* Description: Approximization algorithm for minimum vertex cover problem.
|
|
Greedy Approach. Uses graphs represented with an adjacency list
|
|
|
|
URL: https://mathworld.wolfram.com/MinimumVertexCover.html
|
|
URL: https://cs.stackexchange.com/questions/129017/greedy-algorithm-for-vertex-cover
|
|
"""
|
|
|
|
import heapq
|
|
|
|
|
|
def greedy_min_vertex_cover(graph: dict) -> set:
|
|
"""
|
|
Greedy APX Algorithm for min Vertex Cover
|
|
@input: graph (graph stored in an adjacency list where each vertex
|
|
is represented with an integer)
|
|
@example:
|
|
>>> graph = {0: [1, 3], 1: [0, 3], 2: [0, 3, 4], 3: [0, 1, 2], 4: [2, 3]}
|
|
>>> greedy_min_vertex_cover(graph)
|
|
{0, 1, 2, 4}
|
|
"""
|
|
# queue used to store nodes and their rank
|
|
queue = []
|
|
|
|
# for each node and his adjacency list add them and the rank of the node to queue
|
|
# using heapq module the queue will be filled like a Priority Queue
|
|
# heapq works with a min priority queue, so I used -1*len(v) to build it
|
|
for key, value in graph.items():
|
|
# O(log(n))
|
|
heapq.heappush(queue, [-1 * len(value), (key, value)])
|
|
|
|
# chosen_vertices = set of chosen vertices
|
|
chosen_vertices = set()
|
|
|
|
# while queue isn't empty and there are still edges
|
|
# (queue[0][0] is the rank of the node with max rank)
|
|
while queue and queue[0][0] != 0:
|
|
# extract vertex with max rank from queue and add it to chosen_vertices
|
|
argmax = heapq.heappop(queue)[1][0]
|
|
chosen_vertices.add(argmax)
|
|
|
|
# Remove all arcs adjacent to argmax
|
|
for elem in queue:
|
|
# if v haven't adjacent node, skip
|
|
if elem[0] == 0:
|
|
continue
|
|
# if argmax is reachable from elem
|
|
# remove argmax from elem's adjacent list and update his rank
|
|
if argmax in elem[1][1]:
|
|
index = elem[1][1].index(argmax)
|
|
del elem[1][1][index]
|
|
elem[0] += 1
|
|
# re-order the queue
|
|
heapq.heapify(queue)
|
|
return chosen_vertices
|
|
|
|
|
|
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"Minimum vertex cover:\n{greedy_min_vertex_cover(graph)}")
|