From 47fcbd601116f318a89a432d985d4ecf0cebff41 Mon Sep 17 00:00:00 2001
From: subcrip <contact@subc.rip>
Date: Thu, 5 Sep 2024 23:27:47 +0800
Subject: [PATCH] Add graph/virtual_tree.cc

---
 graph/virtual_tree.cc | 53 +++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 53 insertions(+)
 create mode 100644 graph/virtual_tree.cc

diff --git a/graph/virtual_tree.cc b/graph/virtual_tree.cc
new file mode 100644
index 0000000..361a619
--- /dev/null
+++ b/graph/virtual_tree.cc
@@ -0,0 +1,53 @@
+// BUG: unchecked code
+struct virtual_tree {
+    int n, root;
+    vector<vector<pil>> e;
+    LCA lca;
+    vector<int> dfn;
+    vector<ll> ps;
+    virtual_tree(const vector<vector<pil>>& e, int root) : n(e.size() - 1), root(root), e(e), lca(vector<vector<int>> {{}, {}}), dfn(n + 1), ps(n + 1) {
+        vector<vector<int>> ch(n + 1);
+        for (int u = 0; u <= n; ++u) {
+            for (auto&& [v, w] : e[u]) {
+                ch[u].emplace_back(v);
+            }
+        }
+        lca = LCA(ch);
+        int t = 0;
+        auto dfs = [&] (auto dfs, int v, int pa) -> void {
+            dfn[v] = ++t;
+            for (auto&& [u, w] : e[v]) {
+                if (u == pa) continue;
+                ps[u] = ps[v] + w;
+                dfs(dfs, u, v);
+            }
+        };
+        dfs(dfs, root, 0);
+    }
+    // returned vertex number starts from 0
+    vector<vector<pil>> generate(vector<int> pivots) {
+        int m = pivots.size();
+        if (m == 0) return {};
+        sort_by_key(pivots.begin(), pivots.end(), expr(dfn[v], int v));
+        vector<int> a;
+        for (int i = 0; i < m - 1; ++i) {
+            int v = pivots[i];
+            int u = lca.query(pivots[i], pivots[i + 1]);
+            a.emplace_back(v);
+            a.emplace_back(u);
+        }
+        a.emplace_back(pivots[m - 1]);
+        sort_by_key(a.begin(), a.end(), expr(dfn[v], int v));
+        m = unique(a.begin(), a.end()) - a.begin();
+        unordered_map<int, int, safe_hash> mp;
+        for (int i = 0;  i < m; ++i) {
+            mp[a[i]] = i;
+        }
+        vector<vector<pil>> ret(m);
+        for (int i = 0; i < m - 1; ++i) {
+            int l = lca.query(a[i], a[i + 1]);
+            edgew(ret, mp[l], i + 1, ps[a[i + 1]] - ps[l]);
+        }
+        return ret;
+    }
+};