BZOJ 3991 [SDOI2015]寻宝游戏

题解：按照点的Dfs序走

用Splay维护Dfs序即可

插入时找前驱和后继，插在中间

#include<iostream>
#include<cstdio>
#include<cstring>
using namespace std;
const int maxn=200009;
typedef long long Lint;

int n,m;
int nn;
int htr[maxn];
Lint ans;
int cntedge;
int head[maxn];
int to[maxn],nex[maxn],dist[maxn];
void Addedge(int x,int y,int z){
	nex[++cntedge]=head[x];
	to[cntedge]=y;
	dist[cntedge]=z;
	head[x]=cntedge;
}

int dfsclock;
int idt[maxn],father[maxn],depth[maxn];
Lint d[maxn];
void Dfs(int now,int fa){
	father[now]=fa;
	depth[now]=depth[fa]+1;
	idt[now]=++dfsclock;
	for(int i=head[now];i;i=nex[i]){
		if(to[i]==fa)continue;
		d[to[i]]=d[now]+dist[i];
		Dfs(to[i],now);
	}
}

int f[maxn][20];
void LCAinit(){
	for(int i=1;i<=n;++i)f[i][0]=father[i];
	for(int j=1;j<=19;++j){
		for(int i=1;i<=n;++i){
			f[i][j]=f[f[i][j-1]][j-1];
		}
	}
}
int Getlca(int u,int v){
	if(depth[u]<depth[v])swap(u,v);
	for(int j=19;j>=0;--j){
		if(depth[f[u][j]]>=depth[v])u=f[u][j];
	}
	if(u==v)return u;
	for(int j=19;j>=0;--j){
		if(f[u][j]!=f[v][j]){
			u=f[u][j];v=f[v][j];
		}
	}
	return f[u][0];
}

Lint Getd(int u,int v){
	int lca=Getlca(u,v);
	return d[u]+d[v]-2*d[lca];
}

int root;
int fa[maxn],ch[maxn][2];
inline int son(int x){
	if(ch[fa[x]][1]==x)return 1;
	else return 0;
}
inline void Rotate(int x){
	int y=fa[x];
	int z=fa[y];
	int b=son(x),c=son(y);
	int a=ch[x][b^1];
	if(z)ch[z][c]=x;
	else root=x;
	fa[x]=z;
	if(a)fa[a]=y;
	ch[y][b]=a;
	fa[y]=x;ch[x][b^1]=y;
}
void Splay(int x,int i){
	while(fa[x]!=i){
		int y=fa[x];
		int z=fa[y];
		if(z==i){
			Rotate(x);
		}else{
			if(son(x)==son(y)){
				Rotate(y);Rotate(x);
			}else{
				Rotate(x);Rotate(x);
			}
		}
	}
}

void Ins(int p){
	int x=root,y=0;
	while(x){
		y=x;
		if(idt[p]>idt[x])x=ch[x][1];
		else x=ch[x][0];
	}
	
	x=p;
	fa[x]=y;ch[x][0]=ch[x][1]=0;
	if(y){
		if(idt[x]>idt[y])ch[y][1]=x;
		else ch[y][0]=x;
	}else{
		root=x;
	}
	Splay(x,0);
}
void Del(int x){
	Splay(x,0);
	if(ch[x][0]==0&&ch[x][1]==0){
		root=0;
	}else if(ch[x][0]==0){
		root=ch[x][1];fa[ch[x][1]]=0;
	}else if(ch[x][1]==0){
		root=ch[x][0];fa[ch[x][0]]=0;
	}else{
		int p=ch[x][0];
		while(ch[p][1])p=ch[p][1];
		Splay(p,x);
		ch[p][1]=ch[x][1];fa[ch[x][1]]=p;
		root=p;fa[p]=0;
	}
	fa[x]=ch[x][0]=ch[x][1]=0;
}

int Getpre(){
	int x=ch[root][0];
	if(x==0)return 0;
	while(ch[x][1])x=ch[x][1];
	return x;
}
int Getsuf(){
	int x=ch[root][1];
	if(x==0)return 0;
	while(ch[x][0])x=ch[x][0];
	return x;
}
int Gettop(){
	int x=root;
	if(x==0)return 0;
	while(ch[x][0])x=ch[x][0];
	return x;
}
int Getbot(){
	int x=root;
	if(x==0)return 0;
	while(ch[x][1]){
		x=ch[x][1];
	}
	return x;
}


int main(){
	scanf("%d%d",&n,&m);
	for(int i=1;i<=n-1;++i){
		int x,y,z;
		scanf("%d%d%d",&x,&y,&z);
		Addedge(x,y,z);
		Addedge(y,x,z);
	}
	
	Dfs(1,0);
	LCAinit();
	
//	cout<<"eating shti"<<endl;
	while(m--){
		int x;scanf("%d",&x);
		if(htr[x]){
			htr[x]=0;--nn;
			Splay(x,0);
			int pre=Getpre();
			int suf=Getsuf();
			if(pre&&suf){
				ans-=Getd(pre,x);
				ans-=Getd(suf,x);
				ans+=Getd(pre,suf);
			}else if(pre){
				ans-=Getd(pre,x);
				int toppoint=Gettop();
				ans-=Getd(x,toppoint);
				ans+=Getd(pre,toppoint);
			}else if(suf){
				ans-=Getd(suf,x);
				int botpoint=Getbot();
				ans-=Getd(x,botpoint);
				ans+=Getd(suf,botpoint);
			}
			Del(x);
		}else{
			htr[x]=1;++nn;
			Ins(x);
			
			int pre=Getpre();
			int suf=Getsuf();
			
			if(pre&&suf){
				ans-=Getd(pre,suf);
				ans+=Getd(pre,x);
				ans+=Getd(suf,x);
			}else if(pre){
				ans+=Getd(pre,x);
				int toppoint=Gettop();
				ans-=Getd(toppoint,pre);
				ans+=Getd(toppoint,x);
			}else if(suf){
				ans+=Getd(x,suf);
				int botpoint=Getbot();
				ans-=Getd(botpoint,suf);
				ans+=Getd(botpoint,x);
			}
		}
		printf("%lld
",ans);
	}
	return 0;
}