From becee5f04e9b86e6029f376837770ba5247aa38d Mon Sep 17 00:00:00 2001
From: Baoshuo <i@baoshuo.ren>
Date: Thu, 16 Feb 2023 18:58:29 +0800
Subject: [PATCH] P6869 [COCI2019-2020#5] Putovanje

https://www.luogu.com.cn/record/102258049
---
 Luogu/P6869/P6869.cpp | 106 ++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 106 insertions(+)
 create mode 100644 Luogu/P6869/P6869.cpp

diff --git a/Luogu/P6869/P6869.cpp b/Luogu/P6869/P6869.cpp
new file mode 100644
index 00000000..02b8f347
--- /dev/null
+++ b/Luogu/P6869/P6869.cpp
@@ -0,0 +1,106 @@
+#include <iostream>
+#include <utility>
+#include <vector>
+
+using std::cin;
+using std::cout;
+const char endl = '\n';
+
+const int N = 2e5 + 5;
+
+int n, c1[N], c2[N], c[N];
+long long ans;
+int id[N], rid[N], fa[N], dep[N], siz[N], son[N], top[N];
+std::vector<std::pair<int, int>> g[N];
+
+void dfs1(int u, int f) {
+    fa[u] = f;
+    dep[u] = dep[f] + 1;
+    siz[u] = 1;
+
+    for (auto e : g[u]) {
+        int v = e.first;
+
+        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) {
+    static int cnt = 0;
+
+    rid[id[u] = ++cnt] = u;
+    top[u] = t;
+
+    if (son[u]) dfs2(son[u], t);
+
+    for (auto e : g[u]) {
+        int v = e.first;
+
+        if (v == fa[u] || 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) {
+    int fa_edge_id = 0;
+
+    for (auto e : g[u]) {
+        int v = e.first,
+            id = e.second;
+
+        if (v == fa[u]) {
+            fa_edge_id = id;
+
+            continue;
+        }
+
+        dfs3(v);
+
+        c[u] += c[v];
+    }
+
+    ans += std::min<long long>(static_cast<long long>(c1[fa_edge_id]) * c[u], c2[fa_edge_id]);
+}
+
+int main() {
+    std::ios::sync_with_stdio(false);
+    cin.tie(nullptr);
+
+    cin >> n;
+
+    for (int i = 1, u, v; i < n; i++) {
+        cin >> u >> v >> c1[i] >> c2[i];
+
+        g[u].emplace_back(v, i);
+        g[v].emplace_back(u, i);
+    }
+
+    dfs1(1, 1);
+    dfs2(1, 1);
+
+    for (int i = 1; i < n; i++) {
+        c[i]++, c[i + 1]++;
+        c[lca(i, i + 1)] -= 2;
+    }
+
+    dfs3(1);
+
+    cout << ans << endl;
+
+    return 0;
+}