From d130e48f04976f2649f1f6aef61e61bf6a1eea3b Mon Sep 17 00:00:00 2001
From: Baoshuo Ren <i@baoshuo.ren>
Date: Sun, 5 Dec 2021 00:01:10 +0800
Subject: [PATCH] =?UTF-8?q?918.=20=E8=BD=AF=E4=BB=B6=E5=8C=85=E7=AE=A1?=
 =?UTF-8?q?=E7=90=86=E5=99=A8?=
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https://www.acwing.com/problem/content/submission/code_detail/9213754/
---
 AcWing/918/918.cpp | 152 +++++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 152 insertions(+)
 create mode 100644 AcWing/918/918.cpp

diff --git a/AcWing/918/918.cpp b/AcWing/918/918.cpp
new file mode 100644
index 00000000..7b37e2c3
--- /dev/null
+++ b/AcWing/918/918.cpp
@@ -0,0 +1,152 @@
+#include <bits/stdc++.h>
+
+using std::cin;
+using std::cout;
+using std::endl;
+
+const int N = 100005;
+
+int n, q, a, x;
+std::string op;
+std::vector<int> g[N];
+
+// Heavy Path Decomposition
+int cnt, id[N], fa[N], dep[N], son[N], siz[N], top[N];
+void dfs1(int, int);
+void dfs2(int, int);
+void modify_path(int, int, int);
+void modify_tree(int, int);
+
+// Segment Tree
+void pushup(int);
+void pushdown(int);
+void build(int, int, int);
+void modify(int, int, int, int);
+int query(int, int, int);
+
+int main() {
+    cin >> n;
+    for (int i = 2; i <= n; i++) {
+        cin >> x;
+        x++;
+        g[x].push_back(i);
+        g[i].push_back(x);
+    }
+    dfs1(1, 1);
+    dfs2(1, 1);
+    build(1, 1, n);
+    cin >> q;
+    while (q--) {
+        cin >> op >> x;
+        x++;
+        int before = query(1, 1, n);
+        if (op == "install") {
+            if (!query(1, id[x], id[x])) {
+                modify_path(1, x, 1);
+            }
+        } else {
+            if (query(1, id[x], id[x])) {
+                modify_tree(x, 0);
+            }
+        }
+        int after = query(1, 1, n);
+        cout << std::abs(before - after) << endl;
+    }
+    return 0;
+}
+
+// === Heavy Path Decomposition ===
+
+void dfs1(int u, int f) {
+    dep[u] = dep[f] + 1;
+    fa[u] = f;
+    siz[u] = 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);
+    }
+}
+
+void modify_path(int u, int v, int d) {
+    while (top[u] != top[v]) {
+        if (dep[top[u]] < dep[top[v]]) std::swap(u, v);
+        modify(1, id[top[u]], id[u], d);
+        u = fa[top[u]];
+    }
+    if (dep[u] < dep[v]) std::swap(u, v);
+    modify(1, id[v], id[u], d);
+}
+
+void modify_tree(int u, int d) {
+    modify(1, id[u], id[u] + siz[u] - 1, d);
+}
+
+// === Segment Tree ===
+
+struct node {
+    int l, r, s, d;
+
+    node()
+        : l(0), r(0), s(0), d(-1) {}
+    node(int _l, int _r)
+        : l(_l), r(_r), s(0), d(-1) {}
+} tr[N << 2];
+
+inline void pushup(int u) {
+    tr[u].s = tr[u << 1].s + tr[u << 1 | 1].s;
+}
+
+inline void pushdown(int u) {
+    auto &root = tr[u], &left = tr[u << 1], &right = tr[u << 1 | 1];
+    if (root.d == -1) return;
+    left.s = (left.r - left.l + 1) * root.d;
+    left.d = root.d;
+    right.s = (right.r - right.l + 1) * root.d;
+    right.d = root.d;
+    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 l, int r, int d) {
+    if (l <= tr[u].l && tr[u].r <= r) {
+        tr[u].s = (tr[u].r - tr[u].l + 1) * d;
+        tr[u].d = d;
+        return;
+    }
+    int mid = tr[u].l + tr[u].r >> 1;
+    pushdown(u);
+    if (l <= mid) modify(u << 1, l, r, d);
+    if (r > mid) modify(u << 1 | 1, l, r, d);
+    pushup(u);
+}
+
+int query(int u, int l, int r) {
+    if (l <= tr[u].l && tr[u].r <= r) return tr[u].s;
+    int mid = tr[u].l + tr[u].r >> 1;
+    int sum = 0;
+    pushdown(u);
+    if (l <= mid) sum += query(u << 1, l, r);
+    if (r > mid) sum += query(u << 1 | 1, l, r);
+    return sum;
+}