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