# Source code for networkx.utils.union_find

```
# Copyright 2016-2019 NetworkX developers.
# Copyright (C) 2004-2019 by
# Aric Hagberg <hagberg@lanl.gov>
# Dan Schult <dschult@colgate.edu>
# Pieter Swart <swart@lanl.gov>
# All rights reserved.
# BSD license.
"""
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,
http://aspn.activestate.com/ASPN/Cookbook/Python/Recipe/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']]
"""
# TODO In Python 3.3+, this should be `yield from ...`.
for block in groups(self.parents).values():
yield block
[docs] def union(self, *objects):
"""Find the sets containing the objects and merge them all."""
roots = [self[x] for x in objects]
# Find the heaviest root according to its weight.
heaviest = max(roots, key=lambda r: self.weights[r])
for r in roots:
if r != heaviest:
self.weights[heaviest] += self.weights[r]
self.parents[r] = heaviest
```