第五届上海理工大学程序设计全国挑战赛A. Another Walk Alone Problem · znzryb

## 思路讲解

看了题解以后，我们发现有些时候我们不一定要全部依赖树状dp得出答案。

```cpp
	auto dfs=[&](auto &&self,ll u,ll cur,ll gain,ll de)->void{    // 在外面调用的时候dfs(dfs,u)
		vis[u]=true;dp[u]=cur;
		for(int i=0;i<g[u].size();++i){
			ll v=g[u][i][0],w=g[u][i][1];
			if(vis[v]) continue;
			if(cur+gain+A[u]-de>=w){
				self(self,v,cur,gain+A[u],de+w);
			}else{
				self(self,v,w-gain-A[u]+de,gain+A[u],de+w);
			}
		}
		for(int i=0;i<g[u].size();++i){
			ll w=g[u][i][1],v=g[u][i][0];
			if(w*2<A[u]+A[v] && A[u]>=w){
				inf.push_back(dp[u]);  // 无限循环所需要的值
				break;
			}
		}
	};
```

## AC代码

[https://ac.nowcoder.com/acm/contest/view-submission?submissionId=78031630](https://ac.nowcoder.com/acm/contest/view-submission?submissionId=78031630)



::: 源代码

```cpp
// Problem: Another Walk Alone Problem
// Contest: NowCoder
// URL: https://ac.nowcoder.com/acm/contest/111679/A
// Memory Limit: 2048 MB
// Time Limit: 4000 ms
// 
// Powered by CP Editor (https://cpeditor.org)

#include <bits/stdc++.h>
#define debug(x) cerr<<#x<<":"<<x<<"\n";

using namespace std;

using  ll = long long;
constexpr ll MAXN=(ll)1e6+10;constexpr ll INF=(ll)1e17+9;
constexpr ll mod=(ll)1e9+7;constexpr double eps=1e-8;const double pi=acos(-1.0);
/*

*/
ll A[MAXN];
inline void solve(){
	ll N;cin>>N;
	vector<vector<array<ll,2> > > g(N+5);
	for(int i=2;i<=N;++i){
		cin>>A[i];
	}
	for(int i=1;i<=N-1;++i){
		ll u,v,w;cin>>u>>v>>w;
		g[u].push_back({v,w});g[v].push_back({u,w});
	}
	vector<ll> inf,dp(N+5,0);
	vector<bool> vis(N+5,0),isinf(N+5,0);
	// map<array<ll,2>,2> mp;
	auto dfs=[&](auto &&self,ll u,ll cur,ll gain,ll de)->void{    // 在外面调用的时候dfs(dfs,u)
		vis[u]=true;dp[u]=cur;
		for(int i=0;i<g[u].size();++i){
			ll v=g[u][i][0],w=g[u][i][1];
			if(vis[v]) continue;
			if(cur+gain+A[u]-de>=w){
				self(self,v,cur,gain+A[u],de+w);
			}else{
				self(self,v,w-gain-A[u]+de,gain+A[u],de+w);
			}
		}
		for(int i=0;i<g[u].size();++i){
			ll w=g[u][i][1],v=g[u][i][0];
			if(w*2<A[u]+A[v] && A[u]>=w){
				inf.push_back(dp[u]);
#ifdef LOCAL
    debug(w);debug(A[u]);debug(u);
#endif
				break;
			}
		}
	};
	dfs(dfs,1,0,0,0);
#ifdef LOCAL
    for(int i=2;i<=N;++i){
    	cerr<<dp[i]<<" ";
    }
    cerr<<"\n";
    for(int i=0;i<inf.size();++i){
    	cerr<<inf[i]<<" ";
    }
    cerr<<"\n";
#endif
	ll mn=inf.empty()?INF:*min_element(inf.begin(),inf.end());
	for(int i=2;i<=N;++i){
		cout<<min(dp[i],mn)<<" ";
	}
	cout<<"\n";
}

int main()
{
	ios::sync_with_stdio(false);
	cin.tie(0);cout.tie(0);
	ll lT;
	cin>>lT;
	while(lT--){
		solve();
	}
	// solve();
	return 0;
}
/*

*/
```


:::


## 心路历程（WA，TLE，MLE……）