[UOJ#207]共价大爷游长沙

题目大意

一颗会动的树。

有一个点对集合会变。

每次询问一条树边，问集合内所有点对之间的路径是否都经过该边。

维护虚边信息的LCT

终于无聊来补了这题

每个点对随机一个10^9内的权值

然后给两端点的点权分别异或给权值。

询问一条边是否被全部经过，就是询问每个点对是否都被这条边分开。

那么比如这条边是(u,v)，断开后u的子树异或和应该要等于当前所有路径权值异或和。

就可以判了，出错率当然是很低啦。

#include<cstdio>
#include<algorithm>
#include<ctime>
#define fo(i,a,b) for(i=a;i<=b;i++)
using namespace std;
typedef long long ll;
const int maxn=100000+10,maxm=300000+10,md=1000000000;
int ask[maxm][5],size[maxm*4],c[maxm],b[maxm];
int key[maxn],num[maxn],siz[maxn],father[maxn],tree[maxn][2],pp[maxn],sum[maxn],sta[maxn];
bool bz[maxn];
int h[maxn],go[maxn*2],next[maxn*2];
int i,j,k,u,v,l,t,n,m,tot,top,wdc,ans,id;
int random(int x){
ll t=rand()%10000;
t=t*10000+rand()%10000;
t=t*10000+rand()%10000;
return t%x;
}
int read(){
int x=0,f=1;
char ch=getchar();
while (ch<'0'||ch>'9'){
if (ch=='-') f=-1;
ch=getchar();
}
while (ch>='0'&&ch<='9'){
x=x*10+ch-'0';
ch=getchar();
}
return x*f;
}
void add(int x,int y){
go[++tot]=y;
next[tot]=h[x];
h[x]=tot;
}
void dfs(int x,int y){
pp[x]=y;
int t=h[x];
while (t){
if (go[t]!=y) dfs(go[t],x);
t=next[t];
}
}
int pd(int x){
return tree[father[x]][1]==x;
}
void update(int x){
siz[x]=siz[tree[x][0]]^siz[tree[x][1]]^key[x];
num[x]=num[tree[x][0]]^num[tree[x][1]]^sum[x];
}
void rotate(int x){
int y=father[x],z=pd(x);
father[x]=father[y];
if (father[y]) tree[father[y]][pd(y)]=x;
tree[y][z]=tree[x][1-z];
if (tree[x][1-z]) father[tree[x][1-z]]=y;
tree[x][1-z]=y;
father[y]=x;
update(y);
update(x);
if (pp[y]) pp[x]=pp[y],pp[y]=0;
}
void clear(int x){
if (bz[x]){
if (tree[x][0]) bz[tree[x][0]]^=1;
if (tree[x][1]) bz[tree[x][1]]^=1;
swap(tree[x][0],tree[x][1]);
bz[x]=0;
}
}
void remove(int x,int y){
top=0;
while (x!=y){
sta[++top]=x;
x=father[x];
}
while (top){
clear(sta[top]);
top--;
}
}
void splay(int x,int y){
remove(x,y);
while (father[x]!=y){
if (father[father[x]]!=y)
if (pd(x)==pd(father[x])) rotate(father[x]);else rotate(x);
rotate(x);
}
}
int find_left(int x){
if (!x) return 0;
clear(x);
if (!tree[x][0]) return x;
else return find_left(tree[x][0]);
}
int getnum(int x){
splay(x,0);
return sum[x]^num[tree[x][1]]^siz[tree[x][1]]^key[x];
}
void real_empty(int x,int y){
int t=getnum(x);
splay(y,0);
splay(x,y);
tree[y][1]=0;
father[x]=0;
pp[x]=y;
sum[y]^=t;
update(y);
}
void empty_real(int x,int y){
int t=getnum(x);
splay(y,0);
splay(x,0);
tree[y][1]=x;
father[x]=y;
pp[x]=0;
sum[y]^=t;
update(y);
}
void access(int x){
int y,z;
splay(x,0);
z=find_left(tree[x][1]);
if (z){
splay(z,x);
real_empty(z,x);
}
while (pp[x]){
y=pp[x];
splay(y,0);
z=find_left(tree[y][1]);
if (z){
splay(z,y);
real_empty(z,y);
}
splay(x,0);
z=find_left(x);
splay(z,0);
empty_real(z,y);
splay(x,0);
}
}
void makeroot(int x){
access(x);
splay(x,0);
bz[x]^=1;
}
void cut(int x,int y){
makeroot(x);
access(x);
int t=getnum(y);
splay(x,0);
sum[x]^=t;
update(x);
splay(y,0);
pp[y]=0;
}
void link(int x,int y){
makeroot(x);
makeroot(y);
int t=getnum(y);
splay(x,0);
sum[x]^=t;
update(x);
splay(y,0);
pp[y]=x;
}
void insert(int p,int l,int r,int a,int b){
if (l==r){
size[p]+=b;
return;
}
int mid=(l+r)/2;
if (a<=mid) insert(p*2,l,mid,a,b);else insert(p*2+1,mid+1,r,a,b);
size[p]=size[p*2]+size[p*2+1];
}
int kth(int p,int l,int r,int k){
if (l==r) return l;
int mid=(l+r)/2;
if (k<=size[p*2]) return kth(p*2,l,mid,k);else return kth(p*2+1,mid+1,r,k-size[p*2]);
}
int main(){
//freopen("data.in","r",stdin);freopen("data.out","w",stdout);
srand(time(0));
id=read();
n=read();m=read();
fo(i,1,n-1){
j=read();k=read();
add(j,k);add(k,j);
}
dfs(1,0);
tot=0;
fo(i,1,m){
ask[i][0]=read();
ask[i][1]=read();
if (ask[i][0]!=3) ask[i][2]=read();
if (ask[i][0]==1) ask[i][3]=read(),ask[i][4]=read();
if (ask[i][0]==2) ask[i][3]=++tot,c[tot]=i;
}
fo(i,1,m){
if (ask[i][0]==1){
j=ask[i][1];k=ask[i][2];u=ask[i][3];v=ask[i][4];
cut(j,k);
link(u,v);
}
else if (ask[i][0]==2){
insert(1,1,tot,ask[i][3],1);
j=ask[i][1];k=ask[i][2];
b[ask[i][3]]=random(md)+1;
access(j);
splay(j,0);
key[j]^=b[ask[i][3]];
update(j);
access(k);
splay(k,0);
key[k]^=b[ask[i][3]];
update(k);
wdc^=b[ask[i][3]];
}
else if (ask[i][0]==3){
//t=kth(1,1,tot,ask[i][1]);
t=ask[i][1];
insert(1,1,tot,t,-1);
j=ask[c[t]][1];k=ask[c[t]][2];
access(j);
splay(j,0);
key[j]^=b[ask[c[t]][3]];
update(j);
access(k);
splay(k,0);
key[k]^=b[ask[c[t]][3]];
update(k);
wdc^=b[ask[c[t]][3]];
}
else{
j=ask[i][1];k=ask[i][2];
cut(j,k);
makeroot(j);
ans=getnum(j);
if (ans==wdc) printf("YES\n");else printf("NO\n");
link(j,k);
}
}
}