From 6bbb6e4f59f6bb5deda478343cbf47916971f6d4 Mon Sep 17 00:00:00 2001
From: Baoshuo Ren <i@baoshuo.ren>
Date: Wed, 8 Dec 2021 19:48:49 +0800
Subject: [PATCH] =?UTF-8?q?P4092=20[HEOI2016/TJOI2016]=E6=A0=91?=
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R64569666
---
 Luogu/P4092/P4092.cpp | 153 ++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 153 insertions(+)
 create mode 100644 Luogu/P4092/P4092.cpp

diff --git a/Luogu/P4092/P4092.cpp b/Luogu/P4092/P4092.cpp
new file mode 100644
index 00000000..77fe4ce2
--- /dev/null
+++ b/Luogu/P4092/P4092.cpp
@@ -0,0 +1,153 @@
+#include <iostream>
+#include <vector>
+
+using std::cin;
+using std::cout;
+using std::endl;
+
+const int N = 100005;
+
+int n, q, u, v;
+char op;
+std::vector<int> g[N];
+
+// Heavy Path Decomposition
+int cnt, id[N], rid[N], fa[N], dep[N], son[N], siz[N], top[N];
+void dfs1(int, int);
+void dfs2(int, int);
+void modify_path(int);
+int query_path(int);
+
+// Segment Tree
+void pushup(int);
+void build(int, int, int);
+void modify(int, int, int);
+int query(int, int, int);
+
+int main() {
+    cin >> n >> q;
+    for (int i = 1; i < n; i++) {
+        cin >> u >> v;
+        g[u].push_back(v);
+        g[v].push_back(u);
+    }
+    dfs1(1, 1);
+    dfs2(1, 1);
+    build(1, 1, n);
+    modify_path(1);
+    while (q--) {
+        cin >> op >> u;
+        if (op == 'C') {
+            modify_path(u);
+        } else {
+            cout << query_path(u) << endl;
+        }
+    }
+    return 0;
+}
+
+// === Heavy Path Decomposition ===
+
+void dfs1(int u, int f) {
+    fa[u] = f;
+    siz[u] = 1;
+    dep[u] = dep[f] + 1;
+    for (int v : g[u]) {
+        if (v == f) continue;
+        dfs1(v, u);
+        siz[u] += siz[v];
+        if (siz[son[u]] < siz[v]) son[u] = v;
+    }
+}
+
+void dfs2(int u, int t) {
+    id[u] = ++cnt;
+    top[u] = t;
+    if (!son[u]) return;
+    dfs2(son[u], t);
+    for (int v : g[u]) {
+        if (v == fa[u]) continue;
+        if (v == son[u]) continue;
+        dfs2(v, v);
+    }
+}
+
+inline void modify_path(int u) {
+    modify(1, id[u], u);
+}
+
+int query_path(int u) {
+    while (top[u] != 1) {
+        int t = query(1, id[top[u]], id[u]);
+        if (t != -1) return t;
+        u = fa[top[u]];
+    }
+    int t = query(1, 1, id[u]);
+    if (t == -1) return 1;
+    return t;
+}
+
+// === Segment Tree ===
+
+struct node {
+    int l, r, d;
+
+    node()
+        : l(0), r(0), d(-1) {}
+    node(int _l, int _r)
+        : l(_l), r(_r), d(-1) {}
+} tr[N << 2];
+
+inline void pushup(int u) {
+    node &root = tr[u], &left = tr[u << 1], &right = tr[u << 1 | 1];
+    if (left.d != -1 && right.d != -1) {
+        if (dep[left.d] > dep[right.d]) {
+            root.d = left.d;
+        } else {
+            root.d = right.d;
+        }
+    } else if (left.d != -1) {
+        root.d = left.d;
+    } else if (right.d != -1) {
+        root.d = right.d;
+    } else {
+        root.d = -1;
+    }
+}
+
+void build(int u, int l, int r) {
+    tr[u] = node(l, r);
+    if (l == r) return;
+    int mid = l + r >> 1;
+    build(u << 1, l, mid);
+    build(u << 1 | 1, mid + 1, r);
+}
+
+void modify(int u, int x, int k) {
+    if (tr[u].l == tr[u].r) {
+        tr[u].d = k;
+        return;
+    }
+    int mid = tr[u].l + tr[u].r >> 1;
+    if (x <= mid) {
+        modify(u << 1, x, k);
+    } else {
+        modify(u << 1 | 1, x, k);
+    }
+    pushup(u);
+}
+
+int query(int u, int l, int r) {
+    if (l <= tr[u].l && tr[u].r <= r) return tr[u].d;
+    int mid = tr[u].l + tr[u].r >> 1;
+    int left = -1, right = -1;
+    if (l <= mid) left = query(u << 1, l, r);
+    if (r > mid) right = query(u << 1 | 1, l, r);
+    if (left != -1 && right != -1) {
+        if (dep[left] > dep[right]) return left;
+        return right;
+    }
+    if (left != -1) return left;
+    if (right != -1) return right;
+    return -1;
+}