「bzoj3786」星系探索 - Dfs序/ETT | Bill Yang's Blog
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「bzoj3786」星系探索 - Dfs序/ETT

题目大意

    维护一棵树,支持如下操作:

  • $Q\,d_i$,查询$d_i$到根的权值和
  • $C\,x_i\,y_i$,将$x_i$的父亲换为$y_i$
  • $F\,p_i\,q_i$,将$p_i$的子树权值加上$q_i$

题目分析

如果没有第二个换父亲操作,本题就是很简单的树链剖分。
因为有这个换父亲操作,不难想到使用ETT维护。

考虑如何用ETT维护结点到根的权值和,我们可以使用括号序,每个结点的左括号权值为正,右括号权值为负,做一次前缀和即可得到答案。


代码

调了很久的原因是没有考虑初始权值为$0$。

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#include<algorithm>
#include<iostream>
#include<iomanip>
#include<cstring>
#include<cstdlib>
#include<climits>
#include<vector>
#include<cstdio>
#include<cmath>
#include<queue>
using namespace std;

typedef long long LL;

inline const LL Get_Int() {
LL num=0,bj=1;
char x=getchar();
while(x<'0'||x>'9') {
if(x=='-')bj=-1;
x=getchar();
}
while(x>='0'&&x<='9') {
num=num*10+x-'0';
x=getchar();
}
return num*bj;
}

const int maxn=200005;

int n,q,a[maxn],First[maxn],Last[maxn],step=2;

struct Tree {
int child[2],father,size;
int key,bj;
LL val,sum,lazy;
Tree() {}
Tree(int l,int r,int fa,int k,LL s,LL v,int _bj):father(fa),key(k),size(s),val(v),sum(v),lazy(0),bj(_bj) {
child[0]=l;
child[1]=r;
}
};

struct Splay {
int size,root;
Tree tree[maxn];
#define ls(x) tree[x].child[0]
#define rs(x) tree[x].child[1]
#define fa(x) tree[x].father
#define key(x) tree[x].key
#define val(x) tree[x].val
#define sum(x) tree[x].sum
#define size(x) tree[x].size
#define lazy(x) tree[x].lazy
Splay() {
tree[++size]=Tree(0,2,0,-INT_MAX,0,0,0);
tree[++size]=Tree(0,0,1,INT_MAX,0,0,0);
root=size;
}
bool checkson(int index) {
return rs(fa(index))==index;
}
void modify(int index,LL v) {
lazy(index)+=v;
val(index)+=tree[index].bj*v;
sum(index)+=v*size(index);
}
void push_down(int index) {
if(!lazy(index))return;
if(ls(index))modify(ls(index),lazy(index));
if(rs(index))modify(rs(index),lazy(index));
lazy(index)=0;
}
void push_up(int index) {
if(!index)return;
sum(index)=val(index);
size(index)=tree[index].bj;
if(ls(index))sum(index)+=sum(ls(index)),size(index)+=size(ls(index));
if(rs(index))sum(index)+=sum(rs(index)),size(index)+=size(rs(index));
}
void rotate(int index) {
int father=fa(index),grand=fa(father),side=checkson(index);
if(grand)tree[grand].child[checkson(father)]=index;
tree[father].child[side]=tree[index].child[side^1];
fa(tree[father].child[side])=father;
fa(father)=index;
tree[index].child[side^1]=father;
fa(index)=grand;
push_up(father);
push_up(index);
}
void splay(int index,int target=0) {
push_down(index);
for(int father; (father=fa(index))!=target; rotate(index)) {
int grand=fa(father);
if(grand)push_down(grand);
push_down(father);
push_down(index);
if(fa(father)!=target)rotate(checkson(index)==checkson(father)?father:index);
}
if(target==0)root=index;
}
int insert(int k,LL v,int bj) {
int now=root,father=0;
while(now) {
father=now;
now=tree[now].child[key(now)<k];
}
tree[now=++size]=Tree(0,0,father,k,bj,v,bj);
if(father)tree[father].child[key(father)<k]=now;
splay(now);
return now;
}
int pre_suc(bool bj) {
push_down(root);
int now=tree[root].child[bj];
while(tree[now].child[bj^1])push_down(now),now=tree[now].child[bj^1];
push_down(now);
return now;
}
int pre_suc(int index,bool bj) {
splay(index);
return pre_suc(bj);
}
int split(int Left,int Right) {
int pre=pre_suc(Left,0),suc=pre_suc(Right,1);
splay(pre);
splay(suc,pre);
push_down(pre),push_down(suc);
return ls(suc);
}
int cut(int x) { //将x子树分离
int pos=split(First[x],Last[x]),father=fa(pos);
ls(father)=fa(pos)=0;
push_up(father),push_up(fa(father));
return pos;
}
void link(int x,int y) { //将x子树拼接到结点y的最后面
int pre=pre_suc(Last[y],0),suc=Last[y];
splay(pre);
splay(suc,pre);
push_down(pre),push_down(suc);
ls(suc)=x;
fa(x)=suc;
push_up(suc),push_up(pre);
}
void add(int x,LL v) { //给x子树增加v
int pos=split(First[x],Last[x]),father=fa(pos);
modify(pos,v);
push_up(father),push_up(fa(father));
}
LL query(int x) { //询问x到根的和
int pos=split(First[1],First[x]);
return sum(pos);
}
} bbt;

vector<int>edges[maxn];

void AddEdge(int x,int y) {
edges[x].push_back(y);
}

void Dfs(int Now) {
First[Now]=++step;
bbt.insert(step,a[Now],1);
for(int Next:edges[Now])Dfs(Next);
Last[Now]=++step;
bbt.insert(step,-a[Now],-1);
}

int main() {
n=Get_Int();
for(int i=2; i<=n; i++)AddEdge(Get_Int(),i);
for(int i=1; i<=n; i++)a[i]=Get_Int();
Dfs(1);
q=Get_Int();
while(q--) {
char opt=' ';
while(!isalpha(opt))opt=getchar();
int x=Get_Int();
if(opt=='Q')printf("%lld\n",bbt.query(x));
else if(opt=='C') {
int pos=bbt.cut(x);
bbt.link(pos,Get_Int());
} else if(opt=='F')bbt.add(x,Get_Int());
}
return 0;
}

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