Added Union-Find Data Structure

Data-Structures/Union-Find.cpp

@@ -0,0 +1,96 @@
+/*
+Implements Unioun Find operations
+Complexity: O(logN) amortized is O(1)
+*/
+#include <bits/stdc++.h>
+using namespace std;
+
+class UnionFind
+{
+private:
+    int numberOfComponents;
+    vector<int> parent;
+    vector<int> size;
+
+public:
+    UnionFind(int n)
+    {
+        numberOfComponents = n;
+        parent = vector<int>(n);
+        size = vector<int>(n);
+
+        for (int i = 0; i < n; i++)
+        {
+            parent[i] = i;
+            size[i] = 1;
+        }
+    }
+
+    //returns root node of the component where p belongs
+    int find(int n)
+    {
+        int root = n;
+
+        //find root of this component
+        while (parent[root] != root)
+        {
+            root = parent[root];
+        }
+
+        //path-compression i.e. making all nodes in the route to point directly to the root
+        while (parent[n] != n)
+        {
+            int temp = parent[n];
+            parent[n] = root;
+            n = temp;
+        }
+        return root;
+    }
+
+    //unites two components of n1 and n2
+    void unite(int n1, int n2)
+    {
+        int root1 = find(n1);
+        int root2 = find(n2);
+
+        if (root1 == root2) //if belong to same component then no need to unite
+            return;
+        if (size[root1] < size[root2])
+        {
+            size[root2] += size[root1];
+            parent[root1] = root2;
+        }
+        else
+        {
+            size[root1] += size[root2];
+            parent[root2] = root1;
+        }
+        //number of components decrease by one
+        numberOfComponents--;
+    }
+
+    //returns number of different components
+    int getNumberOfComponents()
+    {
+        return numberOfComponents;
+    }
+
+    //returns true if n1 and n2 belong to same component and false otherwise
+    bool isConnected(int n1, int n2)
+    {
+        return find(n1) == find(n2);
+    }
+};
+
+// int main()
+// {
+//     UnionFind uf(10);
+//     cout << uf.find(5) << endl;
+//     cout << uf.getNumberOfComponents() << endl;
+//     uf.unite(6, 5);
+//     cout << uf.find(5) << endl;
+//     cout << uf.getNumberOfComponents() << endl;
+//     cout << uf.isConnected(1, 2) << endl;
+
+//     return 0;
+// }