106 lines
3.2 KiB
Python
106 lines
3.2 KiB
Python
|
"""
|
||
|
|
Union-find data structure.
|
||
|
|
"""
|
||
|
|
|
||
|
|
from networkx.utils import groups
|
||
|
|
|
||
|
|
|
||
|
|
class UnionFind:
|
||
|
|
"""Union-find data structure.
|
||
|
|
|
||
|
|
Each unionFind instance X maintains a family of disjoint sets of
|
||
|
|
hashable objects, supporting the following two methods:
|
||
|
|
|
||
|
|
- X[item] returns a name for the set containing the given item.
|
||
|
|
Each set is named by an arbitrarily-chosen one of its members; as
|
||
|
|
long as the set remains unchanged it will keep the same name. If
|
||
|
|
the item is not yet part of a set in X, a new singleton set is
|
||
|
|
created for it.
|
||
|
|
|
||
|
|
- X.union(item1, item2, ...) merges the sets containing each item
|
||
|
|
into a single larger set. If any item is not yet part of a set
|
||
|
|
in X, it is added to X as one of the members of the merged set.
|
||
|
|
|
||
|
|
Union-find data structure. Based on Josiah Carlson's code,
|
||
|
|
https://code.activestate.com/recipes/215912/
|
||
|
|
with significant additional changes by D. Eppstein.
|
||
|
|
http://www.ics.uci.edu/~eppstein/PADS/UnionFind.py
|
||
|
|
|
||
|
|
"""
|
||
|
|
|
||
|
|
def __init__(self, elements=None):
|
||
|
|
"""Create a new empty union-find structure.
|
||
|
|
|
||
|
|
If *elements* is an iterable, this structure will be initialized
|
||
|
|
with the discrete partition on the given set of elements.
|
||
|
|
|
||
|
|
"""
|
||
|
|
if elements is None:
|
||
|
|
elements = ()
|
||
|
|
self.parents = {}
|
||
|
|
self.weights = {}
|
||
|
|
for x in elements:
|
||
|
|
self.weights[x] = 1
|
||
|
|
self.parents[x] = x
|
||
|
|
|
||
|
|
def __getitem__(self, object):
|
||
|
|
"""Find and return the name of the set containing the object."""
|
||
|
|
|
||
|
|
# check for previously unknown object
|
||
|
|
if object not in self.parents:
|
||
|
|
self.parents[object] = object
|
||
|
|
self.weights[object] = 1
|
||
|
|
return object
|
||
|
|
|
||
|
|
# find path of objects leading to the root
|
||
|
|
path = [object]
|
||
|
|
root = self.parents[object]
|
||
|
|
while root != path[-1]:
|
||
|
|
path.append(root)
|
||
|
|
root = self.parents[root]
|
||
|
|
|
||
|
|
# compress the path and return
|
||
|
|
for ancestor in path:
|
||
|
|
self.parents[ancestor] = root
|
||
|
|
return root
|
||
|
|
|
||
|
|
def __iter__(self):
|
||
|
|
"""Iterate through all items ever found or unioned by this structure."""
|
||
|
|
return iter(self.parents)
|
||
|
|
|
||
|
|
def to_sets(self):
|
||
|
|
"""Iterates over the sets stored in this structure.
|
||
|
|
|
||
|
|
For example::
|
||
|
|
|
||
|
|
>>> partition = UnionFind("xyz")
|
||
|
|
>>> sorted(map(sorted, partition.to_sets()))
|
||
|
|
[['x'], ['y'], ['z']]
|
||
|
|
>>> partition.union("x", "y")
|
||
|
|
>>> sorted(map(sorted, partition.to_sets()))
|
||
|
|
[['x', 'y'], ['z']]
|
||
|
|
|
||
|
|
"""
|
||
|
|
# Ensure fully pruned paths
|
||
|
|
for x in self.parents.keys():
|
||
|
|
_ = self[x] # Evaluated for side-effect only
|
||
|
|
|
||
|
|
yield from groups(self.parents).values()
|
||
|
|
|
||
|
|
def union(self, *objects):
|
||
|
|
"""Find the sets containing the objects and merge them all."""
|
||
|
|
# Find the heaviest root according to its weight.
|
||
|
|
roots = iter(
|
||
|
|
sorted(
|
||
|
|
{self[x] for x in objects}, key=lambda r: self.weights[r], reverse=True
|
||
|
|
)
|
||
|
|
)
|
||
|
|
try:
|
||
|
|
root = next(roots)
|
||
|
|
except StopIteration:
|
||
|
|
return
|
||
|
|
|
||
|
|
for r in roots:
|
||
|
|
self.weights[root] += self.weights[r]
|
||
|
|
self.parents[r] = root
|