#include <set>
#include <cstdio>
#include <vector>
#include <utility>
#include <iterator>
#include <algorithm>
using namespace std;
struct Item {
int posde = (int)-1e9;
int negde = (int)-1e9;
int ans = (int)-1e9;
} sp_split[19][500006];
Item f(const Item a, const Item b) {
Item ret = { max(a.posde, b.posde), max(a.negde, b.negde), max(a.ans, b.ans) };
ret.ans = max(ret.ans, a.posde + b.negde);
return ret;
}
int n, m;
vector<int> tree[500006], child[500006];
vector<pair<int, int>> adj[500006];
int depth[500006], sp[19][500006], sp_dist[19][500006];
multiset<int> lt_depth[500006], lt_dist[500006];
int max_depth[500006], rev_max_depth[500006], dist[500006], rev_dist[500006];
int prev_dist[500006], prev_depth[500006][2];
int query_sp_half(int Ap, int x) {
int ret = prev_depth[x][0] - depth[x];
if (Ap == -1) return ret;
for (int t = 18; t >= 0; t--) if (sp[t][x] != -1 && depth[sp[t][x]] >= depth[Ap]) {
ret = max(ret, sp_split[t][x].negde);
x = sp[t][x];
}
return max(ret, sp_split[0][x].negde);
}
int query_sp_res(int Ap, int x) {
Item ret = { prev_depth[x][0] + depth[x], prev_depth[x][0] - depth[x], (int)-1e9 };
for (int t = 18; t >= 0; t--) if (sp[t][x] != -1 && depth[sp[t][x]] >= depth[Ap]) {
ret = f(sp_split[t][x], ret);
x = sp[t][x];
}
return f(sp_split[0][x], ret).ans;
}
int dfs_dist(int x) {
vector<int> v;
max_depth[x] = 0;
dist[x] = 0;
for (auto &i: child[x]) {
v.push_back(dfs_dist(i) + 1);
max_depth[x] = max(max_depth[x], v.back());
dist[x] = max(dist[x], dist[i]);
}
int v0 = max_element(v.begin(), v.end()) - v.begin();
int X = v[v0];
if (!v.empty()) v[v0] = 0;
int v1 = max_element(v.begin(), v.end()) - v.begin();
v[v0] = X;
if (!v.empty()) dist[x] = max(dist[x], v[v0]);
if ((int)v.size() > 1) dist[x] = max(dist[x], v[v0] + v[v1]);
return max_depth[x];
}
void dfs_rev_dist(int x) {
multiset<int> v, u, w;
v.insert(rev_max_depth[x]);
u.insert(rev_dist[x]);
for (auto &i: child[x]) {
v.insert(max_depth[i] + 1);
u.insert(dist[i]);
}
for (auto &i: child[x]) {
v.erase(v.find(max_depth[i] + 1));
u.erase(u.find(dist[i]));
if (!u.empty()) rev_dist[i] = *u.rbegin();
if (!v.empty()) rev_dist[i] = max(rev_dist[i], rev_max_depth[i] = *v.rbegin() + 1);
if ((int)v.size() > 1) rev_dist[i] = max(rev_dist[i], *v.rbegin() + *prev(prev(v.end())));
v.insert(max_depth[i] + 1);
u.insert(dist[i]);
}
for (auto &i: child[x]) dfs_rev_dist(i);
}
void dfs_f_dist(int x) {
for (auto &i: child[x]) {
lt_dist[x].erase(lt_dist[x].find(dist[i]));
sp_dist[0][i] = (lt_dist[x].empty() ? 0 : *lt_dist[x].rbegin());
lt_dist[x].insert(dist[i]);
}
for (auto &i: child[x]) dfs_f_dist(i);
}
void dfs_edge(int x) {
for (auto &i: child[x]) {
lt_depth[x].erase(lt_depth[x].find(max_depth[i] + 1));
if ((int)lt_depth[x].size() > 1) sp_dist[0][i] = max(sp_dist[0][i], *lt_depth[x].rbegin() + *prev(prev(lt_depth[x].end())));
else if (!lt_depth[x].empty()) sp_dist[0][i] = max(sp_dist[0][i], *lt_depth[x].rbegin());
int V = (lt_depth[x].empty() ? 0 : *lt_depth[x].rbegin());
sp_split[0][i].posde = V + depth[x];
sp_split[0][i].negde = V - depth[x];
lt_depth[x].insert(max_depth[i] + 1);
}
for (auto &i: child[x]) dfs_edge(i);
}
void dfs_child(int x, int prev = -1) {
sp[0][x] = prev;
for (auto &i: tree[x]) if (i != prev) {
depth[i] = depth[x] + 1;
child[x].push_back(i);
dfs_child(i, x);
}
}
int lca(int u, int v) {
if (depth[u] < depth[v]) swap(u, v);
int diff = depth[u] - depth[v];
for (int t = 18; t >= 0; t--) if (diff >= 1 << t) {
diff -= 1 << t;
u = sp[t][u];
}
if (u == v) return u;
for (int t = 18; t >= 0; t--) if (sp[t][u] != -1 && sp[t][v] != -1 && sp[t][u] != sp[t][v]) {
u = sp[t][u];
v = sp[t][v];
}
return sp[0][u];
}
int pr(int x, int y) {
for (int t = 18; t >= 0; t--) if (y >= 1 << t) {
y -= 1 << t;
x = sp[t][x];
}
return x;
}
int query_sp_dist(int u, int v, int l, int A, int B) {
int ret = 0;
if (u != l) {
ret = max(prev_depth[u][1], prev_dist[u]);
u = sp[0][u];
}
if (v != l) {
ret = max(prev_depth[v][1], prev_dist[v]);
v = sp[0][v];
}
for (int t = 18; t >= 0; t--) if (sp[t][u] != -1 && depth[sp[t][u]] > depth[l]) {
ret = max(ret, sp_dist[t][u]);
u = sp[t][u];
}
for (int t = 18; t >= 0; t--) if (sp[t][v] != -1 && depth[sp[t][v]] > depth[l]) {
ret = max(ret, sp_dist[t][v]);
v = sp[t][v];
}
if (A != -1) lt_dist[l].erase(lt_dist[l].find(dist[A]));
if (B != -1) lt_dist[l].erase(lt_dist[l].find(dist[B]));
ret = max(ret, lt_dist[l].empty() ? 0 : *lt_dist[l].rbegin());
if (A != -1) lt_dist[l].insert(dist[A]);
if (B != -1) lt_dist[l].insert(dist[B]);
if (A != -1) lt_depth[l].erase(lt_depth[l].find(max_depth[A] + 1));
if (B != -1) lt_depth[l].erase(lt_depth[l].find(max_depth[B] + 1));
if (!lt_depth[l].empty()) ret = max(ret, *lt_depth[l].rbegin() + rev_max_depth[l]);
else ret = max(ret, rev_max_depth[l]);
if ((int)lt_depth[l].size() > 1) ret = max(ret, *lt_depth[l].rbegin() + *prev(prev(lt_depth[l].end())));
if (A != -1) lt_depth[l].insert(max_depth[A] + 1);
if (B != -1) lt_depth[l].insert(max_depth[B] + 1);
return ret;
}
int main() {
scanf("%d%d", &n, &m);
while (m--) {
int x, y, w;
scanf("%d%d%d", &x, &y, &w);
if (w == 1) {
tree[x].push_back(y);
tree[y].push_back(x);
} else {
adj[x].push_back({ y, w });
adj[y].push_back({ x, w });
}
}
dfs_child(0);
dfs_dist(0);
dfs_rev_dist(0);
for (int i = 0; i < n; i++) for (auto &j: child[i]) {
lt_depth[i].insert(max_depth[j] + 1);
lt_dist[i].insert(dist[j]);
}
for (int i = 0; i < n; i++) {
prev_dist[i] = (lt_dist[i].empty() ? (int)-1e9 : *lt_dist[i].rbegin());
prev_depth[i][0] = (lt_depth[i].empty() ? (int)-1e9 : *lt_depth[i].rbegin());
prev_depth[i][1] = ((int)lt_depth[i].size() < 2 ? (int)-1e9 : *lt_depth[i].rbegin() + *prev(prev(lt_depth[i].end())));
}
dfs_f_dist(0);
dfs_edge(0);
for (int t = 1; t < 19; t++) for (int i = 0; i < n; i++) {
if (sp[t - 1][i] == -1) {
sp[t][i] = -1;
sp_dist[t][i] = sp_dist[t - 1][i];
sp_split[t][i] = sp_split[t - 1][i];
} else {
sp[t][i] = sp[t - 1][sp[t - 1][i]];
sp_dist[t][i] = max(sp_dist[t - 1][i], sp_dist[t - 1][sp[t - 1][i]]);
sp_split[t][i] = f(sp_split[t - 1][sp[t - 1][i]], sp_split[t - 1][i]);
}
}
int zero = 2 * (n - 1) - dist[0], one = (int)1e9;
for (int i = 0; i < n; i++) for (auto &j: adj[i]) if (i < j.first) {
int l = lca(i, j.first);
int ds = depth[i] + depth[j.first] - depth[l] - depth[l];
int curr = j.second + 2 * (n - 1) - ds - 1;
int A = (i == l ? -1 : pr(i, depth[i] - depth[l] - 1));
int B = (j.first == l ? -1 : pr(j.first, depth[j.first] - depth[l] - 1));
int y = max(rev_dist[l] - 1, query_sp_dist(i, j.first, l, A, B) - 1);
int Ap = (depth[i] - depth[l] - 2 >= 0 ? pr(i, depth[i] - depth[l] - 2) : -1);
int Bp = (depth[j.first] - depth[l] - 2 >= 0 ? pr(j.first, depth[j.first] - depth[l] - 2) : -1);
if (A != -1) lt_depth[l].erase(lt_depth[l].find(max_depth[A] + 1));
if (B != -1) lt_depth[l].erase(lt_depth[l].find(max_depth[B] + 1));
int G = 0;
if (!lt_depth[l].empty()) G = *lt_depth[l].rbegin();
else y = max(y, rev_max_depth[l] - 1);
if ((int)lt_depth[l].size() > 1) y = max(y, *lt_depth[l].rbegin() + *prev(prev(lt_depth[l].end())) - 1);
if (A != -1) lt_depth[l].insert(max_depth[A] + 1);
if (B != -1) lt_depth[l].insert(max_depth[B] + 1);
int Alt = (A == -1 ? (int)-1e9 : query_sp_half(Ap, i) + depth[l]);
int Brt = (B == -1 ? (int)-1e9 : query_sp_half(Bp, j.first) + depth[l]);
int Lt = max(rev_max_depth[l], G);
y = max(y, Alt + max(Brt, Lt) + 1);
y = max(y, max(Alt, Lt) + Brt + 1);
if (Ap != -1) y = max(y, query_sp_res(Ap, i) + 1);
if (Bp != -1) y = max(y, query_sp_res(Bp, j.first) + 1);
curr -= y;
one = min(one, curr);
}
printf("%d", min(zero, one));
}
Compilation message
Compilation timeout while compiling Main
