Add Union-Find data structure (yangshun#65)

* Union-Find implementation

* Example usage

utilities/python/union_find.py

@@ -0,0 +1,50 @@
+## Union-Find data structure
+## https://en.wikipedia.org/wiki/Disjoint-set_data_structure
+
+parents = [0, 1, 2, 3, 4, 5, 6] # parent[i] is the parent of i
+weights = [1, 1, 1, 1, 1, 1, 1]
+
+def find_root(parents, p):
+    '''Average: O(log n)'''
+    root = p
+    while parents[root] != root:
+        root = parents[root]
+    # Flatten tree
+    while parents[p] != p:
+        parents[p], p = root, parents[p]
+    return root
+
+def union(parents, p, q):
+    '''Average: O(log n)'''
+    p = find_root(parents, p)
+    q = find_root(parents, q)
+    # Link the smaller node to the larger node
+    if weights[p] > weights[q]:
+        parents[q] = p
+        weights[p] += weights[q]
+    else:
+        parents[p] = q
+        weights[q] += weights[p]
+
+
+
+# Start with all elements separate
+# -> [0], [1], [2], [3], [4], [5], [6]
+print(find_root(parents, 2) == 2)
+
+# Merge 1, 2, 3 and 4, 5, 6
+# -> [0], [1, 2, 3], [4, 5, 6]
+union(parents, 1, 2)
+union(parents, 2, 3)
+union(parents, 4, 5)
+union(parents, 4, 6)
+
+# Roots of 1, 2, 3 and 4, 5, 6 are the same
+print(find_root(parents, 0))
+print(list(find_root(parents, i) for i in (1, 2, 3)))
+print(list(find_root(parents, i) for i in (4, 5, 6)))
+
+# Merge 2, 4
+# -> [0], [1, 2, 3, 4, 5, 6]
+union(parents, 2, 4)
+print(list(find_root(parents, i) for i in (1, 2, 3, 4, 5, 6)))