Added virtual-tree.cpp (#83)

* Added tarjan for scc.

* Added virtual-tree.cpp.

* Added virtual-tree.cpp to wf-tracker.

* Fix comment bug.

Author: abner-vidal3

content/graphs/trees/virtual-tree.cpp

@@ -0,0 +1,64 @@
+/*
+ *Description:* Computes the virtual tree given the nodes in $O(K log V)$, uses binary lifting and works for directed and undirected graphs.
+ *Status:* Tested
+*/
+struct virtual_tree {
+  int n,timer,lg;
+  vector<int> tin,tout,dep;
+  vector<vector<int>> up,adj_vt;
+  void dfs(int u, int p, vector<vector<int>> & adj){
+    tin[u] = ++timer;
+    up[u][0] = p;
+    for (int i = 1; i <= lg; i++)
+      up[u][i] = up[up[u][i-1]][i-1];
+    for (int v : adj[u]){
+      if (v == p) continue;
+      dep[v] = dep[u]+1;
+      dfs(v,u,adj);
+    }
+    tout[u] = timer;
+  }
+  bool is_ancestor(int u, int v) { 
+    return (tin[u] <= tin[v] && tout[u] >= tout[v]); 
+  }
+  int lca(int u, int v){
+    if (is_ancestor(u,v)) return u;
+    if (is_ancestor(v,u)) return v;
+    for (int i = lg; i >= 0; i--)
+      if (!is_ancestor(up[u][i],v))
+        u = up[u][i];
+    return up[u][0];
+  }
+  virtual_tree(vector<vector<int>> & adj, int logn = 20){
+    n = adj.size(); timer = 0; lg = logn;
+    tin.resize(n); tout.resize(n); dep.resize(n,0);
+    up.assign(n,vector<int>(lg+1));
+    adj_vt.resize(n); dfs(0,0,adj);
+  }
+  // builds the virtual tree in adj_vt, and returns the root
+  int build(vector<int> nodes){
+    assert(!nodes.empty());
+    auto cmp = [&](int u, int v){ return (tin[u] < tin[v]); };
+    sort(nodes.begin(),nodes.end(),cmp);
+    int k = nodes.size();
+    for (int i = 1; i < k; i++)
+      nodes.push_back(lca(nodes[i-1],nodes[i]));
+    sort(nodes.begin(),nodes.end(),cmp);
+    nodes.erase(unique(nodes.begin(),nodes.end()),nodes.end());
+    for (int v : nodes) adj_vt[v].clear();
+    vector<int> st = {nodes[0]};
+    for (int i = 1; i < nodes.size(); i++){
+      int u = nodes[i];
+      while (st.size() >= 2 && !is_ancestor(st.back(),u)){
+        adj_vt[st[st.size()-2]].push_back(st.back());
+        st.pop_back();
+      } 
+      st.push_back(u);
+    }
+    while (st.size() >= 2){
+      adj_vt[st[st.size()-2]].push_back(st.back());
+      st.pop_back();
+    }
+    return nodes[0];
+  }
+};

tracker-wf.yaml

@@ -17,6 +17,7 @@ content:
     - lca-rmq.cpp
     - hld.cpp
     - centroid-decomposition.cpp
+    - virtual-tree.cpp
   - connectivity:
     - tarjan.cpp
     - tarjan-scc.cpp

tracker.yaml

@@ -135,6 +135,7 @@ content:
     - hld.cpp
     - ahld.cpp
     - centroid-decomposition.cpp
+    - virtual-tree.cpp
   - shortest-paths:
     - floyd-warshall.cpp
     - dijkstra.cpp