0
1
mirror of https://git.sb/baoshuo/OI-codes.git synced 2024-12-25 19:32:12 +00:00
OI-codes/Codeforces/827/D/D.cpp

305 lines
6.3 KiB
C++

#include <iostream>
#include <algorithm>
#include <iterator>
#include <numeric>
#include <queue>
#include <stack>
#include <tuple>
#include <vector>
using std::cin;
using std::cout;
const char endl = '\n';
const int N = 5e5 + 5;
const int INF = 0x3f3f3f3f;
int n, m, fa[N], ans[N];
std::tuple<int, int, int, int> edges[N];
std::vector<int> g[N];
std::vector<std::tuple<int, int, int>> qs;
int dep[N], siz[N], son[N], top[N];
std::priority_queue<
std::pair<int, int>,
std::vector<std::pair<int, int>>,
std::greater<std::pair<int, int>>>
q[N];
class LinkCutTree {
private:
struct node {
size_t lchild, rchild, father;
int val, max;
bool reversed;
node()
: lchild(0),
rchild(0),
father(0),
val(0),
max(0),
reversed(false) {}
size_t& child(const unsigned& x) {
return !x ? lchild : rchild;
}
} tr[N << 1];
void pushup(const size_t& u) {
tr[u].max = std::max({tr[u].val, tr[tr[u].lchild].max, tr[tr[u].rchild].max});
}
void pushdown(const size_t& u) {
if (!tr[u].reversed) return;
std::swap(tr[u].lchild, tr[u].rchild);
tr[tr[u].lchild].reversed = !tr[tr[u].lchild].reversed;
tr[tr[u].rchild].reversed = !tr[tr[u].rchild].reversed;
tr[u].reversed = false;
}
bool relation(const size_t& u) {
return u == tr[tr[u].father].lchild ? 0 : 1;
}
bool is_root(const size_t& u) {
return tr[tr[u].father].lchild != u && tr[tr[u].father].rchild != u;
}
void rotate(const size_t& u) {
size_t p = tr[u].father;
bool x = relation(u);
if (!is_root(p)) tr[tr[p].father].child(relation(p)) = u;
tr[u].father = tr[p].father;
if (tr[u].child(x ^ 1)) tr[tr[u].child(x ^ 1)].father = p;
tr[p].child(x) = tr[u].child(x ^ 1);
tr[u].child(x ^ 1) = p;
tr[p].father = u;
pushup(p);
pushup(u);
}
void splay(size_t u) {
std::stack<size_t> st;
size_t cur = u;
st.emplace(cur);
while (!is_root(cur)) {
st.emplace(tr[cur].father);
cur = tr[cur].father;
}
while (!st.empty()) {
pushdown(st.top());
st.pop();
}
while (!is_root(u)) {
if (is_root(tr[u].father)) {
rotate(u);
} else if (relation(u) == relation(tr[u].father)) {
rotate(tr[u].father);
rotate(u);
} else {
rotate(u);
rotate(u);
}
}
}
void access(size_t u) {
for (size_t f = 0; u; u = tr[f = u].father) {
splay(u);
tr[u].rchild = f;
pushup(u);
}
}
void make_root(const size_t& u) {
access(u);
splay(u);
tr[u].reversed = !tr[u].reversed;
}
size_t find_root(size_t u) {
access(u);
splay(u);
while (tr[u].lchild) {
u = tr[u].lchild;
}
return u;
}
void split(const size_t& x, const size_t& y) {
make_root(x);
access(y);
splay(y);
}
public:
bool check(const int& x, const int& y) {
return find_root(x) == find_root(y);
}
int query(const int& x, const int& y) {
split(x, y);
return tr[y].max;
}
void link(const int& x, const int& y) {
make_root(x);
if (find_root(y) != x) {
tr[x].father = y;
}
}
void cut(const int& x, const int& y) {
split(x, y);
if (tr[y].lchild == x) {
tr[y].lchild = tr[x].father = 0;
}
}
void set(const int& x, const int& y) {
tr[x].max = tr[x].val = y;
}
} lct;
int find(const int& x) {
return fa[x] == x ? x : fa[x] = find(fa[x]);
}
void dfs1(int u, int f) {
dep[u] = dep[f] + 1;
siz[u] = 1;
fa[u] = f;
for (int v : g[u]) {
if (v == f) continue;
dfs1(v, u);
siz[u] += siz[v];
if (siz[son[u]] < siz[v]) son[u] = v;
}
}
void dfs2(int u, int t) {
top[u] = t;
if (!son[u]) return;
dfs2(son[u], t);
for (int v : g[u]) {
if (v == fa[u]) continue;
if (v == son[u]) continue;
dfs2(v, v);
}
}
int lca(int u, int v) {
while (top[u] != top[v]) {
if (dep[top[u]] < dep[top[v]]) std::swap(u, v);
u = fa[top[u]];
}
return dep[u] < dep[v] ? u : v;
}
void dfs3(int u) {
for (int v : g[u]) {
if (v == fa[u]) continue;
dfs3(v);
if (q[v].size() > q[u].size()) std::swap(q[u], q[v]);
while (!q[v].empty()) {
if (dep[q[v].top().second] <= dep[u]) q[u].emplace(q[v].top());
q[v].pop();
}
}
while (!q[u].empty() && dep[q[u].top().second] > dep[u]) q[u].pop();
if (u > n && !q[u].empty()) ans[u - n] = q[u].top().first;
}
int main() {
std::ios::sync_with_stdio(false);
cin.tie(nullptr);
std::iota(fa, fa + N, 0);
std::fill(std::begin(ans), std::end(ans), -1);
cin >> n >> m;
for (int i = 1, u, v, w; i <= m; i++) {
cin >> u >> v >> w;
edges[i] = {u, v, w, i};
}
std::sort(edges + 1, edges + 1 + m, [&](const std::tuple<int, int, int, int>& a, const std::tuple<int, int, int, int>& b) {
return std::get<2>(a) < std::get<2>(b);
});
for (int i = 1; i <= m; i++) {
int u, v, w, id;
std::tie(u, v, w, id) = edges[i];
int x = find(u),
y = find(v);
lct.set(id + n, w);
if (x != y) {
fa[x] = y;
lct.link(u, id + n);
lct.link(id + n, v);
g[u].emplace_back(id + n);
g[v].emplace_back(id + n);
g[id + n].emplace_back(u);
g[id + n].emplace_back(v);
} else {
ans[id] = lct.query(v, u) - 1;
qs.emplace_back(u, v, w - 1);
}
}
std::fill(std::begin(fa), std::end(fa), 0);
dfs1(1, 0);
dfs2(1, 1);
for (auto o : qs) {
int u, v, w;
std::tie(u, v, w) = o;
int x = lca(u, v);
if (u != x) q[u].emplace(w, x);
if (v != x) q[v].emplace(w, x);
}
dfs3(1);
std::copy_n(ans + 1, m, std::ostream_iterator<int>(cout, " "));
cout << endl;
return 0;
}