From 62ad2d855d3195e49ef64e3a4b72d1852d722ad2 Mon Sep 17 00:00:00 2001
From: Baoshuo <i@baoshuo.ren>
Date: Fri, 15 Jul 2022 18:00:27 +0800
Subject: [PATCH] =?UTF-8?q?P2387=20[NOI2014]=20=E9=AD=94=E6=B3=95=E6=A3=AE?=
 =?UTF-8?q?=E6=9E=97?=
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https://www.luogu.com.cn/record/79706820
---
 Luogu/P2387/P2387.cpp | 237 ++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 237 insertions(+)
 create mode 100644 Luogu/P2387/P2387.cpp

diff --git a/Luogu/P2387/P2387.cpp b/Luogu/P2387/P2387.cpp
new file mode 100644
index 00000000..4dbf368f
--- /dev/null
+++ b/Luogu/P2387/P2387.cpp
@@ -0,0 +1,237 @@
+#include <iostream>
+#include <algorithm>
+#include <limits>
+#include <stack>
+
+using std::cin;
+using std::cout;
+const char endl = '\n';
+
+const int N = 50005,
+          M = 1e5 + 5;
+
+class LinkCutTree {
+  private:
+    struct node {
+        size_t l, r, f;
+        int v, m;
+        unsigned id;
+        bool rev;
+
+        node()
+            : l(0), r(0), f(0), v(0), m(std::numeric_limits<int>::min()), id(0), rev(false) {}
+
+        node(int _v, size_t _f, unsigned _id)
+            : l(0), r(0), f(_f), v(_v), m(_v), id(_id), rev(false) {}
+
+        size_t &child(unsigned x) {
+            return !x ? l : r;
+        }
+    } tr[N + M];
+
+    inline void pushup(size_t u) {
+        tr[u].m = tr[u].v;
+        tr[u].id = u;
+
+        if (tr[u].l && tr[u].m < tr[tr[u].l].m) {
+            tr[u].m = tr[tr[u].l].m;
+            tr[u].id = tr[tr[u].l].id;
+        }
+
+        if (tr[u].r && tr[u].m < tr[tr[u].r].m) {
+            tr[u].m = tr[tr[u].r].m;
+            tr[u].id = tr[tr[u].r].id;
+        }
+    }
+
+    inline void pushdown(const size_t &u) {
+        if (!tr[u].rev) return;
+
+        std::swap(tr[u].l, tr[u].r);
+        tr[tr[u].l].rev = !tr[tr[u].l].rev;
+        tr[tr[u].r].rev = !tr[tr[u].r].rev;
+        tr[u].rev = false;
+    }
+
+    unsigned relation(const size_t &u) {
+        return u == tr[tr[u].f].l ? 0 : 1;
+    }
+
+    bool isRoot(const size_t &u) {
+        return tr[tr[u].f].l != u && tr[tr[u].f].r != u;
+    }
+
+    void rotate(size_t u) {
+        size_t p = tr[u].f;
+        unsigned x = relation(u);
+
+        if (!isRoot(p)) {
+            tr[tr[p].f].child(relation(p)) = u;
+        }
+        tr[u].f = tr[p].f;
+
+        if (tr[u].child(x ^ 1)) {
+            tr[tr[u].child(x ^ 1)].f = p;
+        }
+        tr[p].child(x) = tr[u].child(x ^ 1);
+
+        tr[u].child(x ^ 1) = p;
+        tr[p].f = u;
+
+        pushup(p);
+        pushup(u);
+    }
+
+    void splay(size_t u) {
+        std::stack<size_t> st;
+
+        size_t cur = u;
+        st.push(cur);
+        while (!isRoot(cur)) {
+            st.push(tr[cur].f);
+            cur = tr[cur].f;
+        }
+
+        while (!st.empty()) {
+            pushdown(st.top());
+            st.pop();
+        }
+
+        while (!isRoot(u)) {
+            if (isRoot(tr[u].f)) {
+                rotate(u);
+            } else if (relation(u) == relation(tr[u].f)) {
+                rotate(tr[u].f);
+                rotate(u);
+            } else {
+                rotate(u);
+                rotate(u);
+            }
+        }
+    }
+
+    void access(size_t u) {
+        for (size_t f = 0; u; u = tr[f = u].f) {
+            splay(u);
+            tr[u].r = f;
+            pushup(u);
+        }
+    }
+
+    void makeRoot(const size_t &u) {
+        access(u);
+        splay(u);
+        tr[u].rev = !tr[u].rev;
+    }
+
+    size_t findRoot(size_t u) {
+        access(u);
+        splay(u);
+
+        while (tr[u].l) {
+            u = tr[u].l;
+        }
+
+        return u;
+    }
+
+  public:
+    void set(int p, int v) {
+        tr[p].m = tr[p].v = v;
+    }
+
+    int query(int x, int y) {
+        split(x, y);
+
+        return tr[y].m;
+    }
+
+    void split(const size_t &x, const size_t &y) {
+        makeRoot(x);
+        access(y);
+        splay(y);
+    }
+
+    void link(const int &x, const int &y) {
+        makeRoot(x);
+
+        if (findRoot(y) != x) {
+            tr[x].f = y;
+        }
+    }
+
+    void cut(int x, int y) {
+        split(x, y);
+
+        if (tr[y].l == x) {
+            tr[y].l = 0;
+            tr[x].f = 0;
+        }
+    }
+
+    bool isConnected(const int &x, const int &y) {
+        makeRoot(x);
+
+        return x == findRoot(y);
+    }
+
+    const unsigned &id(const int x) {
+        return tr[x].id;
+    }
+
+    const int &max(const int &x) {
+        return tr[x].m;
+    }
+} lct;
+
+int n, m, ans = std::numeric_limits<int>::max();
+
+struct node {
+    int x, y, a, b;
+} q[M];
+
+int main() {
+    std::ios::sync_with_stdio(false);
+    cin.tie(nullptr);
+
+    cin >> n >> m;
+
+    for (int i = 1; i <= m; i++) {
+        cin >> q[i].x >> q[i].y >> q[i].a >> q[i].b;
+    }
+
+    std::sort(q + 1, q + m + 1, [](const node &a, const node &b) {
+        return a.a == b.a ? a.b < b.b : a.a < b.a;
+    });
+
+    for (int i = 1; i <= m; i++) {
+        lct.set(i + n, q[i].b);
+
+        if (q[i].x == q[i].y) continue;
+
+        if (lct.isConnected(q[i].x, q[i].y)) {
+            lct.split(q[i].x, q[i].y);
+
+            int x = lct.id(q[i].y), y = lct.max(q[i].y);
+            int a = q[x - n].x, b = q[x - n].y;
+
+            if (y > q[i].b) {
+                lct.cut(a, x);
+                lct.cut(x, b);
+                lct.link(q[i].x, i + n);
+                lct.link(i + n, q[i].y);
+            }
+        } else {
+            lct.link(q[i].x, i + n);
+            lct.link(i + n, q[i].y);
+        }
+
+        if (lct.isConnected(1, n)) {
+            ans = std::min(ans, lct.query(1, n) + q[i].a);
+        }
+    }
+
+    cout << (ans == std::numeric_limits<int>::max() ? -1 : ans) << endl;
+
+    return 0;
+}