【bzoj4129】Haruna’s Breakfast 树上莫队+分块

AC通道：http://www.lydsy.com/JudgeOnline/problem.php?id=4129

【题解】

这题是糖果公园和mex的结合，仿照糖果公园搞树上莫队，然后分块统计答案。

注意不要把块状树和分块搞混，博主因为这个搞了2天。。。

另外这题跑了7.92s，和糖果公园的100s不成正比，我也只能说莫队是玄学。

/************
bzoj 4129
by chty
2016.12.1
************/
#include<iostream>
#include<cstdio>
#include<cstdlib>
#include<cstring>
#include<ctime>
#include<cmath>
#include<algorithm>
using namespace std;
typedef long long ll;
#define FILE "read"
#define MAXN 50010
#define up(i,j,n) for(int i=j;i<=n;i++)
#define down(i,j,n) for(int i=j;i>=n;i--)
struct node{int y,next;}e[MAXN*2];
struct NODE{int x,y,id,time,pre;}b[MAXN],c[MAXN];
int n,m,len,cnt1,cnt2,block,top,bcnt;
int a[MAXN],Link[MAXN],pre[MAXN],deep[MAXN],belong[MAXN],vis[MAXN],cnt[MAXN],ans[MAXN],blo[MAXN],stack[MAXN],bin[20],l[MAXN],r[MAXN],Belong[MAXN],anc[MAXN][20];
void insert(int x,int y){e[++len].next=Link[x];Link[x]=len;e[len].y=y;}
namespace INIT{
char buf[1<<15],*fs,*ft;
inline char getc(){return (fs==ft&&(ft=(fs=buf)+fread(buf,1,1<<15,stdin),fs==ft))?0:*fs++;}
inline int read(){
int x=0,f=1; char ch=getc();
while(!isdigit(ch)) {if(ch=='-') f=-1; ch=getc();}
while(isdigit(ch)) {x=x*10+ch-'0'; ch=getc();}
return x*f;
}
}using namespace INIT;
bool operator <(NODE a,NODE b){
if(belong[a.x]==belong[b.x]&&belong[a.y]==belong[b.y]) return a.time<b.time;
else if(belong[a.x]==belong[b.x]) return belong[a.y]<belong[b.y];
else return belong[a.x]<belong[b.x];
}
int dfs(int x){
int size=0;
up(i,1,16)if(deep[x]>=bin[i])anc[x][i]=anc[anc[x][i-1]][i-1];else break;
for(int i=Link[x];i;i=e[i].next)if(e[i].y!=anc[x][0]){
anc[e[i].y][0]=x;
deep[e[i].y]=deep[x]+1;
size+=dfs(e[i].y);
if(size>=block){
bcnt++;
up(j,1,size) belong[stack[top--]]=bcnt;
size=0;
}
}
stack[++top]=x;
return size+1;
}
void cal(int x){
if(a[x]>n) return;
if(vis[x]) {if(!--cnt[a[x]])blo[Belong[a[x]]]--;}
else {if(!cnt[a[x]]++)blo[Belong[a[x]]]++;}
vis[x]^=1;
}
void change(int x,int v){
if(vis[x]) {cal(x); a[x]=v; cal(x);}
else a[x]=v;
}
void solve(int x,int y){
while(x!=y){
if(deep[x]>deep[y]) cal(x),x=anc[x][0];
else cal(y),y=anc[y][0];
}
}
int query(){
if(!cnt[0]) return 0;
int i;
for(i=1;l[i];i++) if(r[i]-l[i]+1!=blo[i]) break;
int temp=i;
up(i,l[temp],r[temp]) if(!cnt[i]) return i;
return n;
}
int lca(int x,int y){
if(deep[x]<deep[y])swap(x,y);
int t=deep[x]-deep[y];
for(int i=0;bin[i]<=t;i++)if(bin[i]&t)x=anc[x][i];
down(i,16,0)if(anc[x][i]!=anc[y][i])x=anc[x][i],y=anc[y][i];
if(x==y)return x;
return anc[x][0];
}
void init(){
n=read(); m=read(); block=(int)sqrt(n*1.0);
for(int i=1;(i-1)*block+1<=n;i++) l[i]=(i-1)*block+1,r[i]=min(i*block,n);
up(i,1,n) Belong[i]=(i-1)/block+1;
up(i,1,n) pre[i]=a[i]=read();
bin[0]=1; up(i,1,16) bin[i]=bin[i-1]<<1;
up(i,1,n-1) {int x=read(),y=read();insert(x,y);insert(y,x);}
dfs(1);
while(top) belong[stack[top--]]=bcnt;
up(i,1,m){
int flag=read(),x=read(),y=read();
if(flag==0) {b[++cnt1].x=x; b[cnt1].y=y; b[cnt1].pre=pre[x]; pre[x]=y;}
else {c[++cnt2].x=x; c[cnt2].y=y; c[cnt2].time=cnt1; c[cnt2].id=cnt2;}
}
}
void work(){
sort(c+1,c+cnt2+1);
up(i,1,c[1].time) change(b[i].x,b[i].y);
solve(c[1].x,c[1].y);
int t=lca(c[1].x,c[1].y);
cal(t); ans[c[1].id]=query(); cal(t);
up(i,2,cnt2){
up(j,c[i-1].time+1,c[i].time) change(b[j].x,b[j].y);
down(j,c[i-1].time,c[i].time+1) change(b[j].x,b[j].pre);
solve(c[i].x,c[i-1].x);
solve(c[i].y,c[i-1].y);
int t=lca(c[i].x,c[i].y);
cal(t); ans[c[i].id]=query(); cal(t);
}
up(i,1,cnt2) printf("%d\n",ans[i]);
}
int main(){
freopen(FILE".in","r",stdin);
freopen(FILE".out","w",stdout);
init();
work();
return 0;
}