Add union_find from PADS

diff --git a/union_find.py b/union_find.py
new file mode 100644 (file)
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+++ b/union_find.py
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+"""UnionFind.py
+
+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.
+"""
+
+
+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.
+    """
+
+    def __init__(self):
+        """Create a new empty union-find structure."""
+        self.weights = {}
+        self.parents = {}
+
+    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 union(self, *objects):
+        """Find the sets containing the objects and merge them all."""
+        roots = [self[x] for x in objects]
+        heaviest = max([(self.weights[r], r) for r in roots])[1]
+        for r in roots:
+            if r != heaviest:
+                self.weights[heaviest] += self.weights[r]
+                self.parents[r] = heaviest