mirror of
https://git.sb/baoshuo/OI-codes.git
synced 2024-12-12 15:26:26 +00:00
263 lines
5.8 KiB
C++
263 lines
5.8 KiB
C++
#include <iostream>
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#include <algorithm>
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#include <limits>
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#include <numeric>
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#include <queue>
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#include <stack>
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#include <tuple>
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#include <utility>
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using std::cin;
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using std::cout;
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const char endl = '\n';
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const int N = 1e5 + 5,
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M = 3e5 + 5;
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int n, m, a[N + M];
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long long res, ans = std::numeric_limits<long long>::max();
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std::tuple<int, int, int> edges[M];
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bool vis[M];
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class LinkCutTree {
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private:
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struct node {
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size_t lchild, rchild, father;
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int max1, max2;
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bool reversed;
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node()
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: lchild(0),
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rchild(0),
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father(0),
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max1(0),
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max2(0),
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reversed(false) {}
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size_t& child(const unsigned& x) {
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return !x ? lchild : rchild;
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}
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} tr[N + M];
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void pushup(const size_t& u) {
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tr[u].max1 = a[u];
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if (tr[u].max1 < tr[tr[u].lchild].max1) {
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tr[u].max2 = tr[u].max1;
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tr[u].max1 = tr[tr[u].lchild].max1;
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} else if (tr[u].max1 > tr[tr[u].lchild].max1) {
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tr[u].max2 = std::max(tr[u].max2, tr[tr[u].lchild].max1);
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}
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if (tr[u].max1 < tr[tr[u].rchild].max1) {
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tr[u].max2 = tr[u].max1;
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tr[u].max1 = tr[tr[u].rchild].max1;
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} else if (tr[u].max1 > tr[tr[u].rchild].max1) {
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tr[u].max2 = std::max(tr[u].max2, tr[tr[u].rchild].max1);
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}
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tr[u].max2 = std::max({tr[u].max2, tr[tr[u].lchild].max2, tr[tr[u].rchild].max2});
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}
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void pushdown(const size_t& u) {
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if (!tr[u].reversed) return;
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std::swap(tr[u].lchild, tr[u].rchild);
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tr[tr[u].lchild].reversed = !tr[tr[u].lchild].reversed;
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tr[tr[u].rchild].reversed = !tr[tr[u].rchild].reversed;
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tr[u].reversed = false;
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}
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bool relation(const size_t& u) {
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return u == tr[tr[u].father].lchild ? 0 : 1;
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}
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bool is_root(const size_t& u) {
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return tr[tr[u].father].lchild != u && tr[tr[u].father].rchild != u;
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}
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void rotate(const size_t& u) {
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size_t p = tr[u].father;
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bool x = relation(u);
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if (!is_root(p)) tr[tr[p].father].child(relation(p)) = u;
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tr[u].father = tr[p].father;
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if (tr[u].child(x ^ 1)) tr[tr[u].child(x ^ 1)].father = p;
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tr[p].child(x) = tr[u].child(x ^ 1);
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tr[u].child(x ^ 1) = p;
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tr[p].father = u;
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pushup(p);
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pushup(u);
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}
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void splay(size_t u) {
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std::stack<size_t> st;
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size_t cur = u;
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st.emplace(cur);
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while (!is_root(cur)) {
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st.emplace(tr[cur].father);
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cur = tr[cur].father;
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}
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while (!st.empty()) {
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pushdown(st.top());
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st.pop();
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}
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while (!is_root(u)) {
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if (is_root(tr[u].father)) {
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rotate(u);
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} else if (relation(u) == relation(tr[u].father)) {
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rotate(tr[u].father);
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rotate(u);
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} else {
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rotate(u);
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rotate(u);
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}
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}
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}
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void access(size_t u) {
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for (size_t f = 0; u; u = tr[f = u].father) {
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splay(u);
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tr[u].rchild = f;
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pushup(u);
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}
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}
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void make_root(const size_t& u) {
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access(u);
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splay(u);
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tr[u].reversed = !tr[u].reversed;
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}
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size_t find_root(size_t u) {
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access(u);
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splay(u);
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while (tr[u].lchild) {
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u = tr[u].lchild;
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}
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return u;
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}
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void split(const size_t& x, const size_t& y) {
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make_root(x);
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access(y);
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splay(y);
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}
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public:
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bool check(const int& x, const int& y) {
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return find_root(x) == find_root(y);
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}
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std::pair<int, int> query(const int& x, const int& y) {
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split(x, y);
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return {tr[y].max1, tr[y].max2};
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}
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void link(const int& x, const int& y) {
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make_root(x);
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if (find_root(y) != x) {
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tr[x].father = y;
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}
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}
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void cut(const int& x, const int& y) {
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split(x, y);
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if (tr[y].lchild == x) {
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tr[y].lchild = tr[x].father = 0;
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}
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}
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} lct;
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struct DSU : private std::vector<int> {
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DSU(const int& _n)
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: std::vector<int>(_n + 1) {
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std::iota(begin(), end(), 0);
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}
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int find(const int& x) {
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return x == at(x) ? x : at(x) = find(at(x));
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}
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bool check(const int& x, const int& y) {
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return find(x) == find(y);
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}
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void merge(int x, int y) {
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x = find(x);
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y = find(y);
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if (x != y) at(x) = y;
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}
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};
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int main() {
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std::ios::sync_with_stdio(false);
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cin.tie(nullptr);
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cin >> n >> m;
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for (int i = 1; i <= m; ++i) {
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int u, v, w;
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cin >> u >> v >> w;
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edges[i] = {u, v, w};
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}
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std::sort(edges + 1, edges + m + 1, [](const std::tuple<int, int, int>& a, const std::tuple<int, int, int>& b) {
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return std::get<2>(a) < std::get<2>(b);
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});
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DSU dsu(n);
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for (int i = 1; i <= m; i++) {
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int u = std::get<0>(edges[i]),
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v = std::get<1>(edges[i]),
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x = dsu.find(u),
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y = dsu.find(v),
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w = std::get<2>(edges[i]);
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a[n + i] = w;
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if (x != y) {
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dsu.merge(x, y);
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lct.link(u, i + n);
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lct.link(i + n, v);
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res += w;
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vis[i] = true;
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}
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}
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for (int i = 1; i <= m; i++) {
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if (vis[i]) continue;
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int u, v, w;
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std::tie(u, v, w) = edges[i];
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auto max = lct.query(u, v);
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if (w > max.first) {
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ans = std::min(ans, static_cast<long long>(w) - max.first);
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} else {
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ans = std::min(ans, static_cast<long long>(w) - max.second);
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}
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}
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cout << res + ans << endl;
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return 0;
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}
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