def maximum_k(node_list=[], node_length=24, maximum_spacing=3):
""" Input:
list of nodes (edges defined implictly by Hamming distances between nodes)
Output:
max number of clusters with specified maximum spacing
Method:
BRUTE FORCE
For each node iterate through all permuations of possible n-bit differences from 1 up to max_spacing - 1.
For example, for max_spacing = 3, node length 24 bits, the number of permutations is (24 C 1) + (24 C 2) = 300.
"""
node_set = set(node_list)
node_list = list(node_set)
union_find = UnionFind(nodes=node_list)
bitmasks = get_bitmasks(node_length)
for node1 in node_list:
for i in xrange(1, maximum_spacing):
for permutation in combinations(xrange(node_length), i):
node2 = node1
for pos in permutation:
node2 ^= bitmasks[pos]
if node2 in node_set:
if union_find.find(node1) != union_find.find(node2):
union_find.union(node1, node2)
return len(set(union_find.leader_lookup.values()))
def kruskal(node_list, edge_list):
edge_list.sort()
mst = defaultdict(dict) # minimum spanning tree
union_find = UnionFind(nodes=node_list)
for edge in edge_list:
weight, node1, node2 = edge
if union_find.find(node1) != union_find.find(node2):
union_find.union(node1, node2)
mst[node1][node2] = weight
mst[node2][node1] = weight
else:
continue
return mst
def maximum_spacing(node_list=[], edge_list=[], k=0):
""" Returns maximum spacing between k clusters"""
edge_order = []
# mst = defaultdict(dict)
union_find = UnionFind(nodes=node_list)
edge_list.sort()
for edge in edge_list:
weight, node1, node2 = edge
if union_find.find(node1) != union_find.find(node2):
union_find.union(node1, node2)
# mst[node1][node2] = weight
# mst[node2][node1] = weight
edge_order.append(edge)
else:
continue
return edge_order[-(k - 1)][0]
class KruskalGraph(WeightedGraph):
edges = []
spanning_tree = []
components = {}
union = None
def __init__(self, graph={}, directed=False, *args, **kwargs):
super(KruskalGraph, self).__init__(graph, directed, *args, **kwargs)
self.union = UnionFind()
# find and insert edges
for vertex, edges in self.graph.items():
self.components[vertex] = Node(vertex)
for edge, weight in edges.items():
self._add_edge(vertex, edge, weight)
# sort edges
self.edges = sorted(self.edges, key=lambda edges: edges[2])
def build(self):
"""
Build the MST using Kruskal's Algorithm.
"""
for x, y, weight in self.edges:
x_root = self.union.find(self.components[x])
y_root = self.union.find(self.components[y])
if x_root != y_root:
self.spanning_tree.append((x, y, weight))
self.union.union(x_root, y_root)
def show(self):
for edge in self.spanning_tree:
print edge[0], edge[1], edge[2]
def _add_edge(self, x, y, weight):
edge = (x, y, weight)
reverse_edge = (y, x, weight)
if edge not in self.edges and reverse_edge not in self.edges:
self.edges.append((x, y, weight))