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Kruskal's algorithm
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""" | |
Kruskal's algorithm | |
Pure Python implementation by Danilo J. S. Bellini | |
""" | |
import pytest | |
def kruskal_sets(graph): | |
nodes = frozenset.union(*graph) | |
sets = {node: {node} for node in nodes} | |
for edge in sorted(graph, key=graph.__getitem__): | |
set1, set2 = map(sets.__getitem__, edge) | |
if set1 is not set2: | |
set_union = set1.union(set2) | |
for node in set_union: | |
sets[node] = set_union | |
yield edge | |
def kruskal_union_find(graph): | |
nodes = frozenset.union(*graph) | |
parent = {node: node for node in nodes} | |
rank = {node: 0 for node in nodes} | |
for edge in sorted(graph, key=graph.__getitem__): | |
node1, node2 = edge | |
while parent[node1] != node1: # Path compression optimization | |
node1 = parent[node1] = parent[parent[node1]] | |
while parent[node2] != node2: | |
node2 = parent[node2] = parent[parent[node2]] | |
root1, root2 = sorted([node1, node2], key=rank.__getitem__) | |
if root1 != root2: | |
parent[root1] = root2 | |
if rank[root1] == rank[root2]: # Weighted union optimization | |
rank[root2] += 1 | |
yield edge | |
def kruskal_networkx(graph): | |
import networkx as nx | |
nxgraph = nx.Graph(tuple(edge) + ({"weight": weight},) | |
for edge, weight in graph.items()) | |
for node1, node2, data in nx.minimum_spanning_edges(nxgraph): | |
yield frozenset((node1, node2)) | |
@pytest.mark.parametrize("kruskal", [kruskal_sets, kruskal_union_find, | |
kruskal_networkx]) | |
def test_kruskal(kruskal): | |
graph = {frozenset(("A", "B")): 5, | |
frozenset(("A", "C")): 4, | |
frozenset(("A", "D")): 3, | |
frozenset(("A", "E")): 2, | |
frozenset(("B", "C")): 1, | |
frozenset(("B", "D")): 2, | |
frozenset(("B", "E")): 4, | |
frozenset(("C", "D")): 3, | |
frozenset(("C", "E")): 5, | |
frozenset(("D", "E")): 4} | |
expected = {frozenset(("B", "C")), | |
frozenset(("A", "E")), | |
frozenset(("B", "D")), | |
frozenset(("A", "D"))} | |
assert set(kruskal(graph)) == expected |
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