BZOJ2843 极地旅行社 LCT

题意：初始时给定一个没有边的图，维护：1、添加一条边  2、修改单点权  3、询问u到v的点权和

题解：因为只有加边的操作，所以可以用LCT来维护，剩下的就是裸的操作了。

#include <cstdio>
#include <cstring>
#include <cstdlib>
#include <iostream>
#include <algorithm>
using namespace std;

const int MAXN=30000+2;
typedef struct NODE{
    NODE *child[2],*f;
    int s,v;
    bool rev;
    NODE(){}
    NODE(NODE *_f):f(_f),rev(0){}
} *TREE;
TREE root,Null,mark[MAXN];
int N,M;
char s[10+2];

TREE NewNode(TREE f){
    TREE x=new NODE(f);
    x->child[0]=x->child[1]=Null;
    return x;
}

void Initialize(int N){
    Null=NewNode(0);
    for(int i=1;i<=N;i++) mark[i]=NewNode(Null);
}

void Pushup(TREE &x){ x->s=x->child[0]->s+x->child[1]->s+x->v;}

void Pushdown(TREE &x){
    if(x->f->child[0]==x || x->f->child[1]==x) Pushdown(x->f);
    
    if(x->rev){
        swap(x->child[0],x->child[1]);
        x->child[0]->rev^=1,x->child[1]->rev^=1;
        x->rev=0;
    }
}

void Rotate(TREE &x,bool t){
    TREE y=x->f;
    
    y->child[!t]=x->child[t],x->child[t]->f=y,x->f=y->f;
    if(y->f->child[0]==y) y->f->child[0]=x;
    if(y->f->child[1]==y) y->f->child[1]=x;
    y->f=x,x->child[t]=y;
    
    Pushup(y),Pushup(x);
}

void Splay(TREE &x){
    TREE y=x->f;
    Pushdown(x);
    while(y->child[1]==x || y->child[0]==x){
        if(x==y->child[0]){
            if(y==y->f->child[0]) Rotate(y,1);
            Rotate(x,1);
        }
        else{
            if(y==y->f->child[1]) Rotate(y,0);
            Rotate(x,0);
        }
        y=x->f;
    }
    Pushup(x);
}

void Access(TREE &x){
    TREE y=Null,z=x;
    while(z!=Null){
        Splay(z);
        z->child[1]=y;
        Pushup(z);
        y=z,z=z->f;
    }
}

void Move(TREE &x){
    Access(x),Splay(x);
    x->rev=1,Pushdown(x);
}

void Link(TREE &x,TREE &y){
    Move(x);
    x->child[0]=Null,x->f=y;
}

TREE Find(TREE &x){
    TREE y=x;
    while(y->f!=Null) y=y->f;
    return y;
}

void Update(TREE &x,int a){ Move(x),x->v=a,Pushup(x);}

int Query(TREE &x,TREE &y){
    Move(x),Access(y),Splay(y);
    Pushup(y);
    return y->s;
}

int main(){
    scanf("%d",&N);
    Initialize(N);
    for(int i=1;i<=N;i++) scanf("%d",&mark[i]->s),mark[i]->v=mark[i]->s;
    
    scanf("%d",&M);
    for(int i=1,a,b;i<=M;i++){
        scanf("%s %d %d",s,&a,&b);
        if(strstr(s,"bridge"))
            if(Find(mark[a])==Find(mark[b])) puts("no");
            else Link(mark[a],mark[b]),puts("yes");
        if(strstr(s,"penguins")) Update(mark[a],b);
        if(strstr(s,"excursion"))
            if(Find(mark[a])==Find(mark[b])) printf("%d\n",Query(mark[a],mark[b]));
            else puts("impossible");
    }

    return 0;
}