From 8894e598511d6008253a1636951aadd520150467 Mon Sep 17 00:00:00 2001
From: Zengtudor <Zengtudor@outlook.com>
Date: Sat, 30 Aug 2025 13:43:05 +0800
Subject: [PATCH] =?UTF-8?q?feat:=20=E6=B7=BB=E5=8A=A0P2016.cpp=E5=AE=9E?=
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实现了一个动态规划算法来解决树结构的最小顶点覆盖问题。使用深度优先搜索遍历树结构，并通过动态规划计算每个节点的两种状态值，最终输出根节点的最优解。
---
 src/8/30/P2016.cpp | 57 ++++++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 57 insertions(+)
 create mode 100644 src/8/30/P2016.cpp

diff --git a/src/8/30/P2016.cpp b/src/8/30/P2016.cpp
new file mode 100644
index 0000000..2294208
--- /dev/null
+++ b/src/8/30/P2016.cpp
@@ -0,0 +1,57 @@
+/*
+
+
+
+*/
+#include <algorithm>
+#include <cstdint>
+#include <cstdio>
+#include <iostream>
+#include <istream>
+#include <vector>
+using ll = int64_t;
+
+const ll inf = 1e9;
+ll n;
+std::vector<std::vector<ll>> edg,dp;
+
+static inline void dfs(ll f,ll u){
+    for(ll v:edg[u]){
+        if(v==f)continue;
+        dfs(u,v);
+        dp[u][1]+=std::min(
+            dp[v][0],
+            dp[v][1]
+        );
+        dp[u][0]+=dp[v][1];
+    }
+}
+
+
+int main(){
+    std::iostream::sync_with_stdio(false);
+    std::cin.tie(nullptr);
+
+    std::cin>>n;
+    edg.resize(n);
+    dp.resize(n,std::vector<ll>(2,0));
+    for(ll i=1;i<=n;++i){
+        dp[i-1][1]=1;
+        ll u,k;
+        std::cin>>u>>k;
+        for(ll j=1;j<=k;++j){
+            ll v;
+            std::cin>>v;
+            edg[u].push_back(v);
+            edg[v].push_back(u);
+        }
+    }
+
+    dfs(0, 0);
+    // for(ll i=0;i<n;i++){
+    //     for(ll j=0;j<2;j++){
+    //         printf("dp[%lld][%lld]=%lld\n",i,j,dp[i][j]);
+    //     }
+    // }
+    std::cout<<std::min(dp[0][0],dp[0][1])<<"\n";
+}
\ No newline at end of file