Merge pull request TheAlgorithms#186 from gilbertoalexsantos/union-find

Created Union-Find algorithm

Author: harshildarji

data_structures/UnionFind/__init__.py

@@ -0,0 +1,77 @@
+from union_find import UnionFind
+import unittest
+
+
+class TestUnionFind(unittest.TestCase):
+    def test_init_with_valid_size(self):
+        uf = UnionFind(5)
+        self.assertEqual(uf.size, 5)
+
+    def test_init_with_invalid_size(self):
+        with self.assertRaises(ValueError):
+            uf = UnionFind(0)
+
+        with self.assertRaises(ValueError):
+            uf = UnionFind(-5)
+
+    def test_union_with_valid_values(self):
+        uf = UnionFind(10)
+
+        for i in range(11):
+            for j in range(11):
+                uf.union(i, j)
+
+    def test_union_with_invalid_values(self):
+        uf = UnionFind(10)
+
+        with self.assertRaises(ValueError):
+            uf.union(-1, 1)
+
+        with self.assertRaises(ValueError):
+            uf.union(11, 1)
+
+    def test_same_set_with_valid_values(self):
+        uf = UnionFind(10)
+
+        for i in range(11):
+            for j in range(11):
+                if i == j:
+                    self.assertTrue(uf.same_set(i, j))
+                else:
+                    self.assertFalse(uf.same_set(i, j))
+
+        uf.union(1, 2)
+        self.assertTrue(uf.same_set(1, 2))
+
+        uf.union(3, 4)
+        self.assertTrue(uf.same_set(3, 4))
+
+        self.assertFalse(uf.same_set(1, 3))
+        self.assertFalse(uf.same_set(1, 4))
+        self.assertFalse(uf.same_set(2, 3))
+        self.assertFalse(uf.same_set(2, 4))
+
+        uf.union(1, 3)
+        self.assertTrue(uf.same_set(1, 3))
+        self.assertTrue(uf.same_set(1, 4))
+        self.assertTrue(uf.same_set(2, 3))
+        self.assertTrue(uf.same_set(2, 4))
+
+        uf.union(4, 10)
+        self.assertTrue(uf.same_set(1, 10))
+        self.assertTrue(uf.same_set(2, 10))
+        self.assertTrue(uf.same_set(3, 10))
+        self.assertTrue(uf.same_set(4, 10))
+
+    def test_same_set_with_invalid_values(self):
+        uf = UnionFind(10)
+
+        with self.assertRaises(ValueError):
+            uf.same_set(-1, 1)
+
+        with self.assertRaises(ValueError):
+            uf.same_set(11, 0)
+
+
+if __name__ == '__main__':
+    unittest.main()

data_structures/UnionFind/tests_union_find.py

@@ -0,0 +1,87 @@
+class UnionFind():
+    """
+    https://en.wikipedia.org/wiki/Disjoint-set_data_structure
+
+    The union-find is a disjoint-set data structure
+
+    You can merge two sets and tell if one set belongs to
+    another one.
+
+    It's used on the Kruskal Algorithm
+    (https://en.wikipedia.org/wiki/Kruskal%27s_algorithm)
+
+    The elements are in range [0, size]
+    """
+    def __init__(self, size):
+        if size <= 0:
+            raise ValueError("size should be greater than 0")
+
+        self.size = size
+
+        # The below plus 1 is because we are using elements
+        # in range [0, size]. It makes more sense.
+
+        # Every set begins with only itself
+        self.root = [i for i in range(size+1)]
+
+        # This is used for heuristic union by rank
+        self.weight = [0 for i in range(size+1)]
+
+    def union(self, u, v):
+        """
+        Union of the sets u and v.
+        Complexity: log(n).
+        Amortized complexity: < 5 (it's very fast).
+        """
+
+        self._validate_element_range(u, "u")
+        self._validate_element_range(v, "v")
+
+        if u == v:
+            return
+
+        # Using union by rank will guarantee the
+        # log(n) complexity
+        rootu = self._root(u)
+        rootv = self._root(v)
+        weight_u = self.weight[rootu]
+        weight_v = self.weight[rootv]
+        if weight_u >= weight_v:
+            self.root[rootv] = rootu
+            if weight_u == weight_v:
+                self.weight[rootu] += 1
+        else:
+            self.root[rootu] = rootv
+
+    def same_set(self, u, v):
+        """
+        Return true if the elements u and v belongs to
+        the same set
+        """
+
+        self._validate_element_range(u, "u")
+        self._validate_element_range(v, "v")
+
+        return self._root(u) == self._root(v)
+
+    def _root(self, u):
+        """
+        Get the element set root.
+        This uses the heuristic path compression
+        See wikipedia article for more details.
+        """
+
+        if u != self.root[u]:
+            self.root[u] = self._root(self.root[u])
+
+        return self.root[u]
+
+    def _validate_element_range(self, u, element_name):
+        """
+        Raises ValueError if element is not in range
+        """
+        if u < 0 or u > self.size:
+            msg = ("element {0} with value {1} "
+                   "should be in range [0~{2}]")\
+                  .format(element_name, u, self.size)
+            raise ValueError(msg)