diff --git a/tree/virtual_tree.cpp b/old_impl/tree/virtual_tree.cpp
similarity index 100%
rename from tree/virtual_tree.cpp
rename to old_impl/tree/virtual_tree.cpp
diff --git a/tree/lca.hpp b/tree/lca.hpp
index e8ed4d6..fb40238 100644
--- a/tree/lca.hpp
+++ b/tree/lca.hpp
@@ -6,7 +6,7 @@ class LCAUtils {
     int max_log, dfs_time;
     vector<vector<int>> par_up;
 
-    void dfs_lca(int u, int pr, int &dfs_time) {
+    void dfs_lca(int u, int pr, int& dfs_time) {
         in_time[u] = ++dfs_time;
         par_up[u][0] = pr;
         for(int i = 1; i < max_log; i++) {
@@ -27,7 +27,13 @@ class LCAUtils {
     vector<int> in_time, out_time;
     vector<vector<int>> adj;
 
-    LCAUtils() {}
+    LCAUtils() : n(0) {}
+    LCAUtils(int _n) { init(_n); }
+    LCAUtils(int _n, const vector<vector<int>>& _adj, int root = 0) {
+        init(_n);
+        adj = _adj;
+        prepare(root);
+    }
 
     void init(int _n) {
         n = _n;
diff --git a/tree/lca_sparse_table.hpp b/tree/lca_sparse_table.hpp
index 0dcfa32..583c125 100644
--- a/tree/lca_sparse_table.hpp
+++ b/tree/lca_sparse_table.hpp
@@ -29,6 +29,13 @@ class LCAUtilsRMQ {
     int n;
     vector<vector<int>> adj;
 
+    LCAUtilsRMQ() { n = 0; }
+    LCAUtilsRMQ(int _n) { init(_n); }
+    LCAUtilsRMQ(int _n, const vector<vector<int>>& _adj) {
+        init(_n);
+        adj = _adj;
+    }
+
     void add_edge(int u, int v) {
         adj[u].push_back(v);
         adj[v].push_back(u);
@@ -37,13 +44,13 @@ class LCAUtilsRMQ {
     void init(int _n) {
         n = _n;
         order.clear();
-        adj.assign(n + 1, {});
+        adj.assign(n, {});
     }
 
-    void prepare(int root = 1) {
+    void prepare(int root = 0) {
         order.clear();
-        pos.resize(n + 1);
-        dep.resize(n + 1);
+        pos.resize(n);
+        dep.resize(n);
         pre_dfs(root);
         rmq.init(order);
     }
diff --git a/tree/virtual_tree.hpp b/tree/virtual_tree.hpp
new file mode 100644
index 0000000..ed2260a
--- /dev/null
+++ b/tree/virtual_tree.hpp
@@ -0,0 +1,59 @@
+#include <bits/stdc++.h>
+#include <coding_library/tree/lca.hpp>
+using namespace std;
+
+class VirtualTree : public LCAUtils {
+  public:
+    VirtualTree() : LCAUtils() {}
+    VirtualTree(int n) : LCAUtils(n) {}
+    VirtualTree(int n, const vector<vector<int>>& adj, int root = 0)
+        : LCAUtils(n, adj, root) {
+        prepare(root);
+    }
+
+    void add_edge(int u, int v) { LCAUtils::add_edge(u, v); }
+
+    pair<vector<vector<int>>, vector<int>> build(const vector<int>& vertices) {
+        if(vertices.empty()) {
+            return {{}, {}};
+        }
+
+        vector<int> vec = vertices;
+        sort(vec.begin(), vec.end(), [&](int u, int v) {
+            return in_time[u] < in_time[v];
+        });
+        vec.erase(unique(vec.begin(), vec.end()), vec.end());
+
+        for(int i = (int)vec.size() - 1; i > 0; i--) {
+            vec.push_back(lca(vec[i - 1], vec[i]));
+        }
+
+        sort(vec.begin(), vec.end(), [&](int u, int v) {
+            return in_time[u] < in_time[v];
+        });
+        vec.erase(unique(vec.begin(), vec.end()), vec.end());
+
+        vector<vector<int>> virtual_adj(vec.size());
+
+        stack<int> s;
+        s.push(0);
+        for(int i = 1; i < (int)vec.size(); i++) {
+            while(!upper(vec[s.top()], vec[i])) {
+                int u = s.top();
+                s.pop();
+                int v = s.top();
+                virtual_adj[v].push_back(u);
+            }
+            s.push(i);
+        }
+
+        while(s.size() > 1) {
+            int u = s.top();
+            s.pop();
+            int v = s.top();
+            virtual_adj[v].push_back(u);
+        }
+
+        return {virtual_adj, vec};
+    }
+};