我也没发现哪里复杂度假了呀。

#include<bits/stdc++.h>
using namespace std;
const int maxn=3e5+5;
class edge{
	public:
		int to,nex;
		edge(int to,int nex):to(to),nex(nex) {}
		edge() {}
};
edge e[maxn<<1];
int head[maxn],tot;
inline void add_edge(int from,int to){
	e[++tot]=edge(to,head[from]),head[from]=tot;
}
long long hit[maxn];
int fa[maxn],maxround;
inline void pre_work(int u,int father){
	fa[u]=father;
	for(int i=head[u];i;i=e[i].nex){
		int v=e[i].to;
		if(v!=father){
			pre_work(v,u);
		}
	}
}
long long f[maxn][21];
inline void Solve(int u){
	f[u][0]=0x7f7f7f7f7f7f7f7f;
	long long sum=0;
	for(int i=head[u];i;i=e[i].nex){
		int v=e[i].to;
		if(v!=fa[u]){
			Solve(v);
			int min_it=0,c_min_it=0;
			for(int j=1;j<=maxround;++j){
				if(f[v][j]<f[v][min_it]){
					c_min_it=min_it;
					min_it=j;
				}
				else if(f[v][j]<f[v][c_min_it]){
					c_min_it=j;
				}
			}
			f[u][min_it]+=f[v][c_min_it]-f[v][min_it];
			sum+=f[v][min_it];
		}
	}
	for(int i=1;i<=maxround;++i){
		f[u][i]+=sum+hit[u]*i;
	}
}
int main(){
	//freopen("CF Round 958 D.in","r",stdin);
	int T;
	scanf("%d",&T);
	while(T--){
		memset(f,0,sizeof(f)),memset(head,0,sizeof(head)),tot=0;
		int n;
		scanf("%d",&n);
		maxround=ceil(log2(n))+1;
		for(int i=1;i<=n;++i){
			scanf("%lld",&hit[i]);
		}
		for(int i=1;i<n;++i){
			int u,v;
			scanf("%d%d",&u,&v);
			add_edge(u,v),add_edge(v,u);
		}
		pre_work(1,0);
		Solve(1);
		long long minn=0x7f7f7f7f7f7f7f7f;
		for(int i=1;i<=maxround;++i){
			minn=min(minn,f[1][i]);
		}
		printf("%lld\n",minn);
	}
	return 0;
}

$O(n\ \log n)$