mirror of
https://git.sb/baoshuo/OI-codes.git
synced 2024-12-25 19:12:02 +00:00
305 lines
6.3 KiB
C++
305 lines
6.3 KiB
C++
#include <iostream>
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#include <algorithm>
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#include <iterator>
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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 <vector>
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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 = 5e5 + 5;
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const int INF = 0x3f3f3f3f;
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int n, m, fa[N], ans[N];
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std::tuple<int, int, int, int> edges[N];
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std::vector<int> g[N];
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std::vector<std::tuple<int, int, int>> qs;
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int dep[N], siz[N], son[N], top[N];
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std::priority_queue<
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std::pair<int, int>,
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std::vector<std::pair<int, int>>,
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std::greater<std::pair<int, int>>>
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q[N];
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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 val, max;
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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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val(0),
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max(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 << 1];
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void pushup(const size_t& u) {
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tr[u].max = std::max({tr[u].val, tr[tr[u].lchild].max, tr[tr[u].rchild].max});
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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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int query(const int& x, const int& y) {
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split(x, y);
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return tr[y].max;
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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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void set(const int& x, const int& y) {
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tr[x].max = tr[x].val = y;
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}
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} lct;
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int find(const int& x) {
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return fa[x] == x ? x : fa[x] = find(fa[x]);
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}
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void dfs1(int u, int f) {
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dep[u] = dep[f] + 1;
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siz[u] = 1;
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fa[u] = f;
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for (int v : g[u]) {
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if (v == f) continue;
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dfs1(v, u);
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siz[u] += siz[v];
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if (siz[son[u]] < siz[v]) son[u] = v;
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}
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}
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void dfs2(int u, int t) {
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top[u] = t;
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if (!son[u]) return;
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dfs2(son[u], t);
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for (int v : g[u]) {
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if (v == fa[u]) continue;
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if (v == son[u]) continue;
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dfs2(v, v);
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}
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}
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int lca(int u, int v) {
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while (top[u] != top[v]) {
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if (dep[top[u]] < dep[top[v]]) std::swap(u, v);
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u = fa[top[u]];
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}
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return dep[u] < dep[v] ? u : v;
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}
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void dfs3(int u) {
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for (int v : g[u]) {
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if (v == fa[u]) continue;
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dfs3(v);
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if (q[v].size() > q[u].size()) std::swap(q[u], q[v]);
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while (!q[v].empty()) {
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if (dep[q[v].top().second] <= dep[u]) q[u].emplace(q[v].top());
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q[v].pop();
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}
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}
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while (!q[u].empty() && dep[q[u].top().second] > dep[u]) q[u].pop();
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if (u > n && !q[u].empty()) ans[u - n] = q[u].top().first;
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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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std::iota(fa, fa + N, 0);
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std::fill(std::begin(ans), std::end(ans), -1);
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cin >> n >> m;
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for (int i = 1, u, v, w; i <= m; i++) {
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cin >> u >> v >> w;
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edges[i] = {u, v, w, i};
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}
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std::sort(edges + 1, edges + 1 + m, [&](const std::tuple<int, int, int, int>& a, const std::tuple<int, 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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for (int i = 1; i <= m; i++) {
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int u, v, w, id;
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std::tie(u, v, w, id) = edges[i];
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int x = find(u),
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y = find(v);
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lct.set(id + n, w);
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if (x != y) {
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fa[x] = y;
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lct.link(u, id + n);
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lct.link(id + n, v);
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g[u].emplace_back(id + n);
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g[v].emplace_back(id + n);
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g[id + n].emplace_back(u);
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g[id + n].emplace_back(v);
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} else {
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ans[id] = lct.query(v, u) - 1;
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qs.emplace_back(u, v, w - 1);
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}
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}
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std::fill(std::begin(fa), std::end(fa), 0);
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dfs1(1, 0);
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dfs2(1, 1);
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for (auto o : qs) {
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int u, v, w;
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std::tie(u, v, w) = o;
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int x = lca(u, v);
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if (u != x) q[u].emplace(w, x);
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if (v != x) q[v].emplace(w, x);
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}
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dfs3(1);
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std::copy_n(ans + 1, m, std::ostream_iterator<int>(cout, " "));
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cout << endl;
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return 0;
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}
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