From 6f7afdc56e9f82ea77724351b733e0e90d10c94d Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?=E9=BB=84=E6=B5=B7?= <10402852@qq.com>
Date: Tue, 16 Jan 2024 15:04:57 +0800
Subject: [PATCH] 'commit'

---
 TangDou/Topic/HuanGenDp/P6419.cpp     | 34 ++++++++++++++++-----------
 TangDou/Topic/【换根DP】专题.md | 20 +++++++++++++++-
 2 files changed, 39 insertions(+), 15 deletions(-)

diff --git a/TangDou/Topic/HuanGenDp/P6419.cpp b/TangDou/Topic/HuanGenDp/P6419.cpp
index 4fde328..8c8ec74 100644
--- a/TangDou/Topic/HuanGenDp/P6419.cpp
+++ b/TangDou/Topic/HuanGenDp/P6419.cpp
@@ -11,24 +11,29 @@ void add(int a, int b, int c = 0) {
     e[idx] = b, ne[idx] = h[a], w[idx] = c, h[a] = idx++;
 }
 
-int pos[N];
-int sz[N], f[N], g[N];
+int sz[N]; // 哪个点上有人
 int len[N], id[N], slen[N];
+int f[N], g[N];
 
 void dfs1(int u, int fa) {
-    if (pos[u]) sz[u] = 1;
     for (int i = h[u]; ~i; i = ne[i]) {
         int v = e[i];
         if (v == fa) continue;
-        dfs1(v, u);
-        if (sz[v]) {
-            f[u] += f[v] + 2 * w[i];
-            int now = len[v] + w[i];
-            if (now >= len[u])
-                slen[u] = len[u], len[u] = now, id[u] = v;
-            else if (now > slen[u])
-                slen[u] = now;
-        }
+        dfs1(v, u); // 由底向上，先递归，再更新统计信息
+
+        // 如果v这个节点，及它的子节点上有人，那么需要汇总统计信息到sz[u]上去
+        // 如果v上就没有人，那就不用统计了
+        if (sz[v] == 0) continue;
+
+        // ①  u->v,v->u一来一回，路径翻倍 2*w[i]
+        // ②  所有子节点都对u有贡献，所以f[u]+
+        // ③  跑完v为根的子树后，v子树的贡献要累加到u子树上，所以f[u]+=f[v]+2*w[i]
+        f[u] += f[v] + 2 * w[i];
+        int now = len[v] + w[i];
+        if (now >= len[u])
+            slen[u] = len[u], len[u] = now, id[u] = v;
+        else if (now > slen[u])
+            slen[u] = now;
         sz[u] += sz[v];
     }
 }
@@ -64,11 +69,12 @@ signed main() {
         cin >> a >> b >> c;
         add(a, b, c), add(b, a, c);
     }
-    for (int i = 1; i <= m; i++) {
+    for (int i = 1; i <= m; i++) { // 有m个人
         int x;
         cin >> x;
-        pos[x] = 1;
+        sz[x] = 1; // x号点上有人
     }
+
     dfs1(1, 0);
     g[1] = f[1];
 
diff --git a/TangDou/Topic/【换根DP】专题.md b/TangDou/Topic/【换根DP】专题.md
index 7299d43..371e48d 100644
--- a/TangDou/Topic/【换根DP】专题.md
+++ b/TangDou/Topic/【换根DP】专题.md
@@ -998,7 +998,25 @@ int main() {
 
 先放第一次$dfs$的代码：
 
-
+```cpp {.line-numbers}
+void dfs1(int u, int fa) {
+    if (pos[u]) sz[u] = 1;
+    for (int i = h[u]; ~i; i = ne[i]) {
+        int v = e[i];
+        if (v == fa) continue;
+        dfs1(v, u);
+        if (sz[v]) {
+            f[u] += f[v] + 2 * w[i];
+            int now = len[v] + w[i];
+            if (now >= len[u])
+                slen[u] = len[u], len[u] = now, id[u] = v;
+            else if (now > slen[u])
+                slen[u] = now;
+        }
+        sz[u] += sz[v];
+    }
+}
+```