luogu3690

Posted 2020-11-07 せみしぐれ

非常好的一篇博客

写下之前自己被困住的几个点吧：

1.access找的不是到真实的根的一条路径，而是到能找到的最上面的splay的根(makeroot同理)

2.findroot找的是x所在原树的树根（深度最小），并旋转至当前一棵splay的根

tips:具体的还是没特别懂，多做题吧

#include<cstdio>
#include<cctype>
#include<algorithm>
#define ls tr[x][0]
#define rs tr[x][1]
#define maxn 300002
using namespace std;
int n,m,res[maxn],tr[maxn][2],rev[maxn],w[maxn],tmp[maxn],f[maxn];
inline void pushup(int x){res[x]=res[ls]^res[rs]^w[x];}
inline void pushr(int x){swap(ls,rs);rev[x]^=1;}
inline void pushdown(int x){if(rev[x]){if(ls)pushr(ls);if(rs)pushr(rs);rev[x]=0;}}
inline void read(int &x){
    char ch=getchar();x=0;int f=1;
    while(!isdigit(ch)){if(ch==\'-\')f=-1;ch=getchar();}
    while(isdigit(ch)){x=(x<<1)+(x<<3)+ch-\'0\';ch=getchar();}
    x*=f;
}
inline bool isroot(int x){return (tr[f[x]][0]==x||tr[f[x]][1]==x);}
inline void rotate(int x){
    int fa=f[x],gfa=f[fa],whicx=tr[fa][1]==x,flag=isroot(fa);//注意flag要先赋值，因为若之后其父亲会变为x 
    tr[fa][whicx]=tr[x][whicx^1];if(tr[fa][whicx])f[tr[fa][whicx]]=fa;
    tr[x][whicx^1]=fa;f[fa]=x;
    f[x]=gfa;
    if(flag)tr[gfa][tr[gfa][1]==fa]=x;
    pushup(fa);
}
inline void splay(int x){
    int y=x,siz=0,z;
    tmp[++siz]=y;
    while(isroot(y))tmp[++siz]=y=f[y];
    while(siz)pushdown(tmp[siz--]);
    while(isroot(x)){
        y=f[x];z=f[y];
        if(isroot(y))rotate((tr[y][1]==x)==(tr[z][1]==y)?y:x);
        rotate(x);
    }
    pushup(x);
}
inline void access(int x){
    for(int y=0;x;x=f[y=x])splay(x),rs=y,pushup(x);
}
inline void makeroot(int x){access(x);splay(x);pushr(x);}
inline void split(int x,int y){makeroot(x);access(y);splay(y);}
inline int findroot(int x){
    access(x);splay(x);
    while(ls)pushdown(x),x=ls;
    return x;
}
inline void link(int x,int y){makeroot(x);if(findroot(y)!=x)f[x]=y;}
inline void cut(int x,int y){
    makeroot(x);if(findroot(y)==x&&f[x]==y&&!rs){f[x]=tr[y][0]=0;pushup(y);}
}
int main(){
    read(n);read(m);
    int typ,x,y;
    for(int i=1;i<=n;i++)read(w[i]);
    while(m--){
        read(typ);read(x);read(y);
        switch(typ){
            case 0:split(x,y);printf("%d\\n",res[y]);break;
            case 1:link(x,y);break;
            case 2:cut(x,y);break;
            case 3:makeroot(x);w[x]=y;pushup(x);
        }
    }
}