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authorS. Solomon Darnell2025-03-28 21:52:21 -0500
committerS. Solomon Darnell2025-03-28 21:52:21 -0500
commit4a52a71956a8d46fcb7294ac71734504bb09bcc2 (patch)
treeee3dc5af3b6313e921cd920906356f5d4febc4ed /.venv/lib/python3.12/site-packages/networkx/utils/union_find.py
parentcc961e04ba734dd72309fb548a2f97d67d578813 (diff)
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+"""
+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 = []
+ root = self.parents[object]
+ while root != object:
+ path.append(object)
+ object = root
+ root = self.parents[object]
+
+ # 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:
+ _ = 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