def MST_Kruskal(g):
"""Compute a minimum spanning tree of a graph using Kruskal's algorithm.
Return a list of edges that comprise the MST.
The elements of the graph's edges are assumed to be weights.
"""
tree = [] # list of edges in spanning tree
pq = HeapPriorityQueue() # entries are edges in G, with weights as key
forest = Partition() # keeps track of forest clusters
position = {} # map each node to its Partition entry
for v in g.vertices():
position[v] = forest.make_group(v)
for e in g.edges():
pq.add(e.element(), e) # edge's element is assumed to be its weight
size = g.vertex_count()
while len(tree) != size - 1 and not pq.is_empty():
# tree not spanning and unprocessed edges remain
weight, edge = pq.remove_min()
u, v = edge.endpoints() # (self._origin, self._destination)
# line 65 ~ 69 are used for cycle checking.
a = forest.find(position[u])
b = forest.find(position[v])
if a != b:
tree.append(edge)
forest.union(a, b)
return tree
def MST_Kruskal(g):
"""Compute a minimum spanning tree of a graph using Kruskal's algorithm.
Return a list of edges that comprise the MST.
The elements of the graph's edges are assumed to be weights.
"""
tree = [] # list of edges in spanning tree
pq = HeapPriorityQueue() # entries are edges in G, with weights as key
forest = Partition() # keeps track of forest clusters
position = {} # map each node to its Partition entry
for v in g.vertices():
position[v] = forest.make_group(v)
for e in g.edges():
pq.add(e.element(), e) # edge's element is assumed to be its weight
size = g.vertex_count()
while len(tree) != size - 1 and not pq.is_empty():
# tree not spanning and unprocessed edges remain
weight,edge = pq.remove_min()
u,v = edge.endpoints()
a = forest.find(position[u])
b = forest.find(position[v])
if a != b:
tree.append(edge)
forest.union(a,b)
return tree
def min_span_tree(self):
"""Use the Kruskal's algorithm to find the minimum spanning tree."""
result = []
forest = Partition(self.nodes)
# greedily pick lighter edges first
sorted_edges = sorted(self.edges, key=lambda edge: edge.weight)
for edge in sorted_edges:
start, end = edge.pair
# Add the edge to the tree if its nodes belong to different groups
if forest.find(start) != forest.find(end):
result.append(edge)
forest.union(start, end)
# the mst must have (self.node_count - 1) edges
if len(result) == self.node_count - 1:
break
return result
