From 5e23f171330bbdf6cd9edf72db584f717933365b Mon Sep 17 00:00:00 2001
From: Zengtudor <Zengtudor@outlook.com>
Date: Fri, 29 Aug 2025 15:59:18 +0800
Subject: [PATCH] =?UTF-8?q?feat:=20=E6=B7=BB=E5=8A=A0P2014=E9=A2=98?=
 =?UTF-8?q?=E7=9B=AE=E8=A7=A3=E5=86=B3=E6=96=B9=E6=A1=88=E5=AE=9E=E7=8E=B0?=
 =?UTF-8?q?=E5=8A=A8=E6=80=81=E8=A7=84=E5=88=92=E7=AE=97=E6=B3=95?=
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8
Content-Transfer-Encoding: 8bit

实现基于树形动态规划的课程选修问题解决方案，计算在限定课程数量下能获得的最大学分。使用深度优先搜索遍历课程依赖关系，并通过动态规划状态转移求解最优解。
---
 src/8/29/P2014.cpp | 55 ++++++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 55 insertions(+)
 create mode 100644 src/8/29/P2014.cpp

diff --git a/src/8/29/P2014.cpp b/src/8/29/P2014.cpp
new file mode 100644
index 0000000..9939882
--- /dev/null
+++ b/src/8/29/P2014.cpp
@@ -0,0 +1,55 @@
+/*
+
+dp[i][j]=修第i个课程时(以i为根)，总共选修了j门课程学习的最大学分是多少
+
+dp[u][j]=max(
+    dp[u][j],
+    dp[v][1~j-1]+v[u]
+)
+
+*/
+
+#include <algorithm>
+#include <cstdint>
+#include <iostream>
+#include <istream>
+#include <vector>
+using ll = int64_t;
+
+ll n,m;
+std::vector<ll> f,val;
+std::vector<std::vector<ll>> dp;
+std::vector<std::vector<ll>> edg;
+
+static inline void dfs(const ll u){
+    dp[u][1]=val[u];
+    for(auto v:edg[u]){
+        dfs(v);
+        for(ll i=m;i>=1;--i){
+            for(ll j=i-1;j>=1;--j){
+                dp[u][i]=std::max(
+                    dp[u][i],
+                    dp[v][j]+dp[u][i-j]
+                );
+            }
+        }
+    }
+}
+
+int main(){
+    std::iostream::sync_with_stdio(false);
+    std::cin.tie(nullptr);
+
+    std::cin>>n>>m;
+    ++m;
+    f.resize(n+1);
+    val.resize(n+1);
+    dp.resize(n+1,std::vector<ll>(m+1));
+    edg.resize(n+1);
+    for(ll i=1;i<=n;++i){
+        std::cin>>f[i]>>val[i];
+        edg[f[i]].push_back(i);
+    }
+    dfs(0);
+    std::cout<<dp[0][m]<<"\n";
+}   
\ No newline at end of file