[ZOJ3522]Hide and seek

题意：给一棵带边权的树，多次询问$(x,y,l)$表示如果加一条连接$x$和$y$的长为$l$的边，所有点到$x$和到$y$的最短路减少了多少

先把题目中的图放上来（雾

考虑用lct维护，先把路径提出来，然后在splay上二分找到最短路大小改变的临界点$p$，再统计答案

容易看出$p\rightarrow y$上的所有点的子树都对答案有贡献，对于一个点$p_1$，它和它的虚子树对答案的贡献都是$dis_{x,p_1}-dis_{p_1,y}-l$，即$dis_{x,y}-2dis_{p_1,y}-l$，于是我们可以维护每个点在splay中往左往右的答案（因为要换根，有区间翻转操作），再维护一下虚子树大小即可

车万题吼啊！

#include<stdio.h>
#include<string.h>
typedef long long ll;
template<class C>void swap(C&a,C&b){a^=b^=a^=b;}
int ch[100010][2],fa[100010],r[100010],siz[100010],vsiz[100010];
ll lsum[100010],rsum[100010],s[100010],v[100010];
#define ls ch[x][0]
#define rs ch[x][1]
void rev(int x){
	r[x]^=1;
	swap(ls,rs);
	swap(lsum[x],rsum[x]);
}
void pushdown(int x){
	if(r[x]){
		if(ls)rev(ls);
		if(rs)rev(rs);
		r[x]=0;
	}
}
void pushup(int x){
	siz[x]=siz[ls]+siz[rs]+vsiz[x];
	s[x]=s[ls]+s[rs]+v[x];
	lsum[x]=lsum[ls]+lsum[rs]+(s[ls]+v[x])*siz[rs]+vsiz[x]*s[ls];
	rsum[x]=rsum[ls]+rsum[rs]+(s[rs]+v[x])*siz[ls]+vsiz[x]*s[rs];
}
void rot(int x){
	int y,z,f,b;
	y=fa[x];
	z=fa[y];
	f=ch[y][0]==x;
	b=ch[x][f];
	fa[x]=z;
	fa[y]=x;
	if(b)fa[b]=y;
	ch[x][f]=y;
	ch[y][f^1]=b;
	if(ch[z][0]==y)ch[z][0]=x;
	if(ch[z][1]==y)ch[z][1]=x;
	pushup(y);
	pushup(x);
}
bool isrt(int x){return ch[fa[x]][0]!=x&&ch[fa[x]][1]!=x;}
void gao(int x){
	if(!isrt(x))gao(fa[x]);
	pushdown(x);
}
void splay(int x){
	gao(x);
	int y,z;
	while(!isrt(x)){
		y=fa[x];
		z=fa[y];
		if(!isrt(y))rot((ch[z][0]==y&&ch[y][0]==x)||(ch[z][1]==y&&ch[y][1]==x)?y:x);
		rot(x);
	}
}
void access(int x){
	int y=0;
	while(x){
		splay(x);
		vsiz[x]+=siz[rs];
		rs=y;
		vsiz[x]-=siz[y];
		pushup(x);
		y=x;
		x=fa[x];
	}
}
void makert(int x){
	access(x);
	splay(x);
	rev(x);
}
int find(int x,ll d){
	int c=0;
	ll al=s[x];
	while(x){
		pushdown(x);
		if((s[ls]+v[x])*2<=al+d){
			c=x;
			d-=(s[ls]+v[x])*2;
			x=rs;
		}else
			x=ls;
	}
	return c;
}
ll query(int x,int y,ll z){
	if(x==y)return 0;
	makert(x);
	access(y);
	splay(y);
	if(s[y]<=z)return 0;
	x=find(y,z);
	splay(x);
	return siz[rs]*(s[x]-z)-rsum[rs]*2;
}
int h[100010],nex[200010],to[200010],M;
void add(int a,int b){
	M++;
	to[M]=b;
	nex[M]=h[a];
	h[a]=M;
}
void dfs(int x){
	for(int i=h[x];i;i=nex[i]){
		if(to[i]!=fa[x]){
			fa[to[i]]=x;
			dfs(to[i]);
			siz[x]+=siz[to[i]];
		}
	}
	vsiz[x]=siz[x];
}
int main(){
	int n,m,i,x,y,z;
	while(~scanf("%d",&n)){
		memset(h,0,sizeof(h));
		memset(fa,0,sizeof(fa));
		memset(ch,0,sizeof(ch));
		memset(siz,0,sizeof(siz));
		memset(r,0,sizeof(r));
		memset(lsum,0,sizeof(lsum));
		memset(rsum,0,sizeof(rsum));
		memset(s,0,sizeof(s));
		memset(v,0,sizeof(v));
		M=0;
		for(i=1;i<=n;i++)siz[i]=1;
		for(i=1;i<n;i++){
			scanf("%d%d%d",&x,&y,&z);
			v[n+i]=s[n+i]=z;
			add(x,n+i);
			add(n+i,x);
			add(y,n+i);
			add(n+i,y);
		}
		dfs(1);
		scanf("%d",&m);
		while(m--){
			scanf("%d%d%d",&x,&y,&z);
			printf("%lld\n",query(x,y,z)+query(y,x,z));
		}
	}
}