Link-cut-Tree

Posted 2020-10-19 Grary

#include<bits/stdc++.h>
#define N 300005
using namespace std;
int n,m,val[N];
struct Link_Cut_Tree{
    int top,c[N][2],fa[N],xr[N],q[N],rev[N];
    inline void pushup(int x){xr[x]=xr[c[x][0]]^xr[c[x][1]]^val[x];}
    inline void pushdown(int x){
        int l=c[x][0],r=c[x][1];
        if(rev[x]){
            rev[l]^=1;rev[r]^=1;rev[x]^=1;
            swap(c[x][0],c[x][1]);
        }
    }
    inline bool isroot(int x){return c[fa[x]][0]!=x&&c[fa[x]][1]!=x;}
    void rotate(int x){
        int y=fa[x],z=fa[y],l,r;
        if(c[y][0]==x)l=0;else l=1;r=l^1;
        if(!isroot(y)){if(c[z][0]==y)c[z][0]=x;else c[z][1]=x;}
        fa[x]=z;fa[y]=x;fa[c[x][r]]=y;
        c[y][l]=c[x][r];c[x][r]=y;
        pushup(y);pushup(x);
    }
    void splay(int x){
        top=1;q[top]=x;
        for(int i=x;!isroot(i);i=fa[i])q[++top]=fa[i];
        for(int i=top;i;i--)pushdown(q[i]);
        while(!isroot(x)){
            int y=fa[x],z=fa[y];
            if(!isroot(y)){
                if((c[y][0]==x)^(c[z][0]==y))rotate(x);
                else rotate(y);
            }rotate(x);
        }
    }
    void access(int x){for(int t=0;x;t=x,x=fa[x])splay(x),c[x][1]=t,pushup(x);}
    void makeroot(int x){access(x);splay(x);rev[x]^=1;}
    int find(int x){access(x);splay(x);while(c[x][0])x=c[x][0];return x;}
    void split(int x,int y){makeroot(x);access(y);splay(y);}
    void cut(int x,int y){split(x,y);if(c[y][0]==x)c[y][0]=0,fa[x]=0;}
    void link(int x,int y){makeroot(x);fa[x]=y;}
}T;

inline 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;
}
int main(){
    n=read();m=read();
    for(int i=1;i<=n;i++)val[i]=read(),T.xr[i]=val[i];
    while(m--){
        int opt=read();
        if(opt==0){
            int x=read(),y=read();T.split(x,y);
            printf("%d\n",T.xr[y]);
        }
        if(opt==1){
            int x=read(),y=read(),xx=T.find(x),yy=T.find(y);
            if(xx!=yy)T.link(x,y);
        }
        if(opt==2){
            int x=read(),y=read(),xx=T.find(x),yy=T.find(y);
            if(xx==yy)T.cut(x,y);
        }
        if(opt==3){
            int x=read(),y=read();
            T.access(x);T.splay(x);val[x]=y;T.pushup(x);
        }
    }
    return 0;
}