P1399 [NOI2013] 快餐店

https://www.luogu.com.cn/record/97012047

Luogu/P1399/P1399.cpp

@@ -0,0 +1,152 @@
+#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;
+}