From 62ad2d855d3195e49ef64e3a4b72d1852d722ad2 Mon Sep 17 00:00:00 2001 From: Baoshuo 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?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit 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 +#include +#include +#include + +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::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 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::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::max() ? -1 : ans) << endl; + + return 0; +}