From 3c57af7b92f6f02fb4a27c364c3cb96060844868 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?=E9=BB=84=E6=B5=B7?= <10402852@qq.com>
Date: Tue, 9 Jan 2024 13:49:05 +0800
Subject: [PATCH] 'commit'

---
 TangDou/Topic/HuanGenDp/CF1406.cpp     | 52 -------------------
 TangDou/Topic/HuanGenDp/CF1406C.cpp    | 71 ++++++++++++++++++++++++++
 TangDou/Topic/【换根】dfs专题.md |  5 +-
 3 files changed, 74 insertions(+), 54 deletions(-)
 delete mode 100644 TangDou/Topic/HuanGenDp/CF1406.cpp
 create mode 100644 TangDou/Topic/HuanGenDp/CF1406C.cpp

diff --git a/TangDou/Topic/HuanGenDp/CF1406.cpp b/TangDou/Topic/HuanGenDp/CF1406.cpp
deleted file mode 100644
index a291eb3..0000000
--- a/TangDou/Topic/HuanGenDp/CF1406.cpp
+++ /dev/null
@@ -1,52 +0,0 @@
-#include <bits/stdc++.h>
-using namespace std;
-const int N = 1e5 + 10;
-#define int long long
-#define endl "\n"
-
-vector<int> g[N];
-int siz[N], son[N];
-int r1, r2, n;
-void dfs(int u, int fa) {
-    siz[u] = 1;
-    son[u] = 0;
-    for (int i = 0; i < g[u].size(); i++) {
-        int v = g[u][i];
-        if (v == fa) continue;
-        dfs(v, u);
-        siz[u] += siz[v];
-        son[u] = max(son[u], siz[v]);
-    }
-    son[u] = max(son[u], n - siz[u]);
-    if ((son[u] << 1) <= n) r2 = r1, r1 = u;
-}
-signed main() {
-    int t;
-    cin >> t;
-    while (t--) {
-        cin >> n;
-        for (int i = 0; i <= n + 10; i++) g[i].clear(), siz[i] = 0, son[i] = 0;
-        for (int i = 1; i < n; i++) {
-            int x, y;
-            cin >> x >> y;
-            g[x].push_back(y);
-            g[y].push_back(x);
-        }
-        r1 = r2 = 0;
-        dfs(1, 0);
-        if (!r2) {
-            int r3 = g[r1][0];
-            cout << r1 << " " << r3 << endl;
-            cout << r1 << " " << r3 << endl;
-        } else {
-            int r3 = r1;
-            for (int i = 0; i < g[r2].size(); i++) {
-                r3 = g[r2][i];
-                if (r3 != r1) break;
-            }
-            cout << r3 << " " << r2 << endl;
-            cout << r3 << " " << r1 << endl;
-        }
-    }
-    return 0;
-}
\ No newline at end of file
diff --git a/TangDou/Topic/HuanGenDp/CF1406C.cpp b/TangDou/Topic/HuanGenDp/CF1406C.cpp
new file mode 100644
index 0000000..4ef55ac
--- /dev/null
+++ b/TangDou/Topic/HuanGenDp/CF1406C.cpp
@@ -0,0 +1,71 @@
+#include <bits/stdc++.h>
+#define N 100005
+using namespace std;
+int n, head[N], ver[2 * N], Next[2 * N], tot = 0;
+void add(int x, int y) {
+    ver[++tot] = y, Next[tot] = head[x], head[x] = tot;
+}
+vector<int> c;
+int mx[N], sz[N];
+int mn = 0x3f3f3f3f;
+void dfs(int x, int pre) {
+    for (int i = head[x]; i; i = Next[i]) {
+        int y = ver[i];
+        if (y == pre) continue;
+        dfs(y, x);
+        sz[x] += (sz[y] + 1);
+        mx[x] = max(mx[x], sz[y] + 1);
+    }
+    mx[x] = max(mx[x], n - 1 - sz[x]);
+    mn = min(mn, mx[x]);
+}
+void solve() {
+    cin >> n;
+    tot = 0;
+    mn = 0x3f3f3f3f;
+    c.clear();
+    for (int i = 0; i <= n; i++) {
+        head[i] = 0;
+        mx[i] = 0;
+        sz[i] = 0;
+    }
+    for (int i = 1; i < n; i++) {
+        int x, y;
+        cin >> x >> y;
+        add(x, y);
+        add(y, x);
+    }
+    dfs(1, 0);
+    for (int i = 1; i <= n; i++) {
+        if (mx[i] == mn) {
+            c.push_back(i);
+        }
+    }
+    if (c.size() == 1) {
+        for (int i = head[c[0]]; i; i = Next[i]) {
+            int y = ver[i];
+            cout << c[0] << " " << y << endl;
+            cout << c[0] << " " << y << endl;
+            return;
+        }
+    } else {
+        int tmp;
+        for (int i = head[c[0]]; i; i = Next[i]) {
+            int y = ver[i];
+            if (y == c[1]) continue;
+            cout << c[0] << " " << y << endl;
+            tmp = y;
+            break;
+        }
+        cout << c[1] << " " << tmp << endl;
+        return;
+    }
+}
+int main() {
+    int T;
+    cin >> T;
+    while (T--) {
+        solve();
+    }
+    return 0;
+}
diff --git a/TangDou/Topic/【换根】dfs专题.md b/TangDou/Topic/【换根】dfs专题.md
index 43a5928..ede4e2c 100644
--- a/TangDou/Topic/【换根】dfs专题.md
+++ b/TangDou/Topic/【换根】dfs专题.md
@@ -141,9 +141,10 @@ signed main() {
 
 1、先任选一个结点作为根节点(比如$1$号节点)，把无根树变成有根树。然后设$sz[i]$表示以$i$为根节点的子树节点个数。转移方程为$\displaystyle sz[u]=\sum_{fa[v]=u} (sz[v])$
 
-2、设$son[i]$表示删去节点$x$后剩下的连通分量中最大子树节点个数。其中一部分在原来$i$其为根的子树。$son[i]=max(son[i],siz[i的儿子节点])$;
+2、设$son[i]$表示删去节点$i$后剩下的连通分量中最大子树节点个数。其中一部分在原来$i$其为根的子树。$\displaystyle son[i]=max(son[i],sz[j])$ 
+> **解释**：$j$的含义是$i$的所有儿子节点
 
-另外一部分在$i$的“上方”子树有$n-sz[i]$个。  
+另外一部分在$i$的 **上方** 子树有$n-sz[i]$个。  
 $$son[i]=max(son[i],n-sz[i])$$
 
 ![](https://dsideal.obs.cn-north-1.myhuaweicloud.com/HuangHai/BlogImages/202401091310362.png)