Add Union-Find (Disjoint Set) with path compression

Author: cureprotocols

Diff for: data_structures/disjoint_set/union_find.py

@@ -0,0 +1,56 @@
+"""
+Union-Find (Disjoint Set Union) with Path Compression and Union by Rank
+
+Use Case:
+- Efficient structure to manage disjoint sets
+- Useful in network connectivity, Kruskal's MST, and clustering
+
+Time Complexity:
+- Nearly constant: O(α(n)) where α is the inverse Ackermann function
+
+Author: Michael Alexander Montoya
+"""
+
+class UnionFind:
+    def __init__(self, size):
+        self.parent = list(range(size))
+        self.rank = [0] * size
+
+    def find(self, node):
+        if self.parent[node] != node:
+            self.parent[node] = self.find(self.parent[node])  # Path compression
+        return self.parent[node]
+
+    def union(self, x, y):
+        rootX = self.find(x)
+        rootY = self.find(y)
+
+        if rootX == rootY:
+            return False  # Already connected
+
+        # Union by rank
+        if self.rank[rootX] < self.rank[rootY]:
+            self.parent[rootX] = rootY
+        elif self.rank[rootX] > self.rank[rootY]:
+            self.parent[rootY] = rootX
+        else:
+            self.parent[rootY] = rootX
+            self.rank[rootX] += 1
+
+        return True
+
+
+# Example usage
+if __name__ == "__main__":
+    uf = UnionFind(10)
+
+    uf.union(1, 2)
+    uf.union(2, 3)
+    uf.union(4, 5)
+
+    print("1 and 3 connected:", uf.find(1) == uf.find(3))  # True
+    print("1 and 5 connected:", uf.find(1) == uf.find(5))  # False
+
+    uf.union(3, 5)
+
+    print("1 and 5 connected after union:", uf.find(1) == uf.find(5))  # True