From 9b2b21aec6f31602fe465dc4a5cc93965a5b9f91 Mon Sep 17 00:00:00 2001
From: Baoshuo <i@baoshuo.ren>
Date: Wed, 29 Jun 2022 21:03:59 +0800
Subject: [PATCH] =?UTF-8?q?P3690=20=E3=80=90=E6=A8=A1=E6=9D=BF=E3=80=91?=
 =?UTF-8?q?=E5=8A=A8=E6=80=81=E6=A0=91=EF=BC=88Link=20Cut=20Tree=EF=BC=89?=
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https://www.luogu.com.cn/record/78096467
---
 Luogu/P3690/P3690.cpp | 226 ++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 226 insertions(+)
 create mode 100644 Luogu/P3690/P3690.cpp

diff --git a/Luogu/P3690/P3690.cpp b/Luogu/P3690/P3690.cpp
new file mode 100644
index 00000000..a35d82c9
--- /dev/null
+++ b/Luogu/P3690/P3690.cpp
@@ -0,0 +1,226 @@
+#include <iostream>
+#include <algorithm>
+#include <cstdlib>
+#include <stack>
+
+using std::cin;
+using std::cout;
+const char endl = '\n';
+
+const int N = 1e5 + 5;
+
+// Link-Cut Tree
+class LinkCutTree {
+  private:
+    std::stack<bool> st;
+
+    struct node {
+        int p,  // 父亲节点
+            l,  // 左儿子
+            r;  // 右儿子
+        int pre;
+        int val,   // 节点值
+            sum;   // 异或和
+        int key;   // 权值
+        bool rev;  // 翻转标记
+
+        node()
+            : p(0), l(0), r(0), pre(0), val(0), sum(0), key(rand()), rev(false) {}
+    } tr[N];
+
+    void pushup(int u) {
+        // 计算异或和
+        tr[u].sum = tr[tr[u].l].sum ^ tr[u].val ^ tr[tr[u].r].sum;
+
+        // 标记父亲节点
+        if (tr[u].l) tr[tr[u].l].p = u;
+        if (tr[u].r) tr[tr[u].r].p = u;
+    }
+
+    void pushdown(int u) {
+        if (!tr[u].rev) return;
+
+        tr[u].rev = false;
+        std::swap(tr[u].l, tr[u].r);
+        tr[tr[u].l].rev ^= 1;
+        tr[tr[u].r].rev ^= 1;
+    }
+
+    std::pair<int, int> split(int u) {
+        if (st.empty()) {
+            pushdown(u);
+            auto t = std::make_pair(u, tr[u].r);
+            tr[u].r = 0;
+            pushup(u);
+
+            return t;
+        }
+
+        bool d = st.top() ^ tr[u].rev;
+        st.pop();
+
+        pushdown(u);
+
+        if (d) {
+            auto t = split(tr[u].l);
+            tr[u].l = t.second;
+            pushup(u);
+
+            return std::make_pair(t.first, u);
+        }
+
+        auto t = split(tr[u].r);
+        tr[u].r = t.first;
+        pushup(u);
+
+        return std::make_pair(u, t.second);
+    }
+
+    // 合并
+    int merge(int x, int y) {
+        if (!x || !y) return x | y;
+
+        if (tr[x].key < tr[y].key) {
+            pushdown(x);
+            tr[x].r = merge(tr[x].r, y);
+            pushup(x);
+            return x;
+        }
+
+        pushdown(y);
+        tr[y].l = merge(x, tr[y].l);
+        pushup(y);
+        return y;
+    }
+
+    // 是否是根节点
+    bool isRoot(int u) {
+        return !tr[u].p || (tr[tr[u].p].l != u && tr[tr[u].p].r != u);
+    }
+
+    // 查找根节点
+    int findRoot(int u) {
+        while (!st.empty()) st.pop();
+        while (!isRoot(u)) {
+            // pushdown(u);
+            st.push(tr[tr[u].p].l == u);
+            u = tr[u].p;
+        }
+        return u;
+    }
+
+    int findLeft(int u) {
+        u = findRoot(u);
+        pushdown(u);
+        while (tr[u].l) {
+            u = tr[u].l;
+            pushdown(u);
+        }
+        return u;
+    }
+
+    int access(int u) {
+        int lst = 0;
+
+        while (u) {
+            auto t = split(findRoot(u));
+            tr[findLeft(lst)].pre = 0;
+            lst = merge(t.first, lst);
+            tr[findLeft(t.second)].pre = u;
+            u = tr[findLeft(lst)].pre;
+        }
+
+        return lst;
+    }
+
+    void makeRoot(int u) {
+        tr[access(u)].rev ^= 1;
+    }
+
+  public:
+    int getRoot(int u) {
+        return findLeft(access(u));
+    }
+
+    void link(int x, int y) {
+        makeRoot(x);
+        tr[x].pre = y;
+    }
+
+    void cut(int x, int y) {
+        makeRoot(x);
+        access(y);
+        access(x);
+        tr[y].pre = 0;
+    }
+
+    int query(int x, int y) {
+        makeRoot(x);
+        access(y);
+
+        auto t = split(findRoot(y));
+        int res = tr[t.first].sum;
+        merge(t.first, t.second);
+
+        return res;
+    }
+
+    void change(int u, int val) {
+        makeRoot(u);
+        auto t = split(findRoot(u));
+        tr[u].val = val;
+        merge(t.first, t.second);
+    }
+
+    void set(int u, int val) {
+        tr[u].sum = tr[u].val = val;
+    }
+} lct;
+
+int n, m;
+
+int main() {
+    std::ios::sync_with_stdio(false);
+    cin.tie(nullptr);
+
+    cin >> n >> m;
+
+    for (int i = 1, x; i <= n; i++) {
+        cin >> x;
+
+        lct.set(i, x);
+    }
+
+    while (m--) {
+        int op, x, y;
+
+        cin >> op >> x >> y;
+
+        switch (op) {
+            case 0: {
+                cout << lct.query(x, y) << endl;
+
+                break;
+            }
+            case 1: {
+                if (lct.getRoot(x) != lct.getRoot(y)) {
+                    lct.link(x, y);
+                }
+
+                break;
+            }
+            case 2: {
+                lct.cut(x, y);
+
+                break;
+            }
+            case 3: {
+                lct.change(x, y);
+
+                break;
+            }
+        }
+    }
+
+    return 0;
+}