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3242. [Noi2013] 快餐店

https://hydro.ac/d/bzoj/record/63a45935cf75a716a1673079
This commit is contained in:
Baoshuo Ren 2022-12-22 21:18:54 +08:00
parent 08b27afab5
commit 00d78dea6c
Signed by: baoshuo
GPG Key ID: 00CB9680AB29F51A
41 changed files with 272 additions and 0 deletions

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#include <iostream>
#include <algorithm>
#include <iomanip>
#include <iterator>
#include <numeric>
#include <queue>
#include <unordered_set>
#include <utility>
#include <vector>
using std::cin;
using std::cout;
const char endl = '\n';
const int N = 1e5 + 5;
const long long INF = 0x3f3f3f3f'3f3f3f3f;
int n;
long long dist[N], dep[N], pre[N], suf[N], a[N], b[N], c[N], d[N], ans1, ans2;
std::vector<std::pair<int, int>> g[N], circle;
bool vis[N], on_circle[N];
bool dfs(int u, int f) {
if (vis[u]) return true;
vis[u] = true;
for (auto e : g[u]) {
int v = e.first,
w = e.second;
if (v == f) continue;
if (dfs(v, u)) {
circle.emplace_back(v, w);
on_circle[v] = true;
return true;
}
}
return false;
}
std::pair<int, long long> bfs(int s) {
int res = s;
std::queue<int> q;
std::unordered_set<int> set;
q.emplace(s);
set.emplace(s);
dist[s] = 0;
vis[s] = true;
while (!q.empty()) {
int u = q.front();
q.pop();
for (auto e : g[u]) {
int v = e.first,
w = e.second;
if (!vis[v] && !on_circle[v]) {
dist[v] = dist[u] + w;
if (dist[v] > dist[res]) res = v;
q.emplace(v);
set.emplace(v);
vis[v] = true;
}
}
}
long long dist_res = dist[res];
for (int u : set) {
vis[u] = false;
dist[u] = INF;
}
return {res, dist_res};
}
int main() {
std::ios::sync_with_stdio(false);
cin.tie(nullptr);
cin >> n;
for (int i = 1, u, v, w; i <= n; i++) {
cin >> u >> v >> w;
g[u].emplace_back(v, w);
g[v].emplace_back(u, w);
}
dfs(1, 0);
std::reverse(circle.begin(), circle.end());
std::fill(std::begin(vis), std::end(vis), false);
std::fill(std::begin(dist), std::end(dist), INF);
for (int i = 1; i <= circle.size(); i++) {
int u = circle[i - 1].first;
on_circle[u] = false;
auto o = bfs(u);
dep[i] = o.second;
ans1 = std::max(ans1, bfs(o.first).second);
on_circle[u] = true;
}
for (int i = 2; i <= circle.size(); i++) {
pre[i] = pre[i - 1] + circle[i - 1].second;
}
for (int i = circle.size() - 1; i; i--) {
suf[i] = suf[i + 1] + circle[i].second;
}
for (int i = 1; i <= circle.size(); i++) {
a[i] = std::max(a[i - 1], dep[i] + pre[i]);
}
for (int i = circle.size(); i; i--) {
b[i] = std::max(b[i + 1], dep[i] + suf[i]);
}
long long max = 0;
for (int i = 1; i <= circle.size(); i++) {
c[i] = std::max(c[i - 1], max + dep[i] + pre[i]);
max = std::max(max, dep[i] - pre[i]);
}
max = 0;
for (int i = circle.size(); i; i--) {
d[i] = std::max(d[i + 1], max + dep[i] + suf[i]);
max = std::max(max, dep[i] - suf[i]);
}
ans2 = INF;
for (int i = 1; i < circle.size(); i++) {
ans2 = std::min(ans2, std::max({a[i] + b[i + 1] + circle[0].second, c[i], d[i + 1]}));
}
cout << std::fixed << std::setprecision(1) << static_cast<double>(std::max(ans1, ans2)) / 2 << endl;
return 0;
}

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