[模板]Link-Cut-Tree动态树

做法以后再补，先写一些注意事项。

做法以后也不补了，直接看这个吧。https://www.cnblogs.com/candy99/p/6271344.html

1.rotate其实是最容易写错的地方（对于丝毫没有掌握splay蒟蒻我来说），一定要仔细检查

2.splay之前需要先从根开始往下pushdown一遍

3.注意getRoot(findRoot)和setRoot(makeRoot)对节点位置带来的影响

4.access的结束条件是x==0!!不是fa[x]!!（这个zz才会写错吧） （没错就是我写错了还查了半天）

5.pushdown的位置、是否splay(x)所带来的玄学问题（我哪想的明白啊）

luogu3690（连边、断边、改点值、查询链上异或和）

 #include<cstdio>
 #include<cstring>
 #include<algorithm>
 #include<vector>
 #include<queue>
 #include<map>
 #include<cmath>
 #include<ctime>
 #include<set>
 #define pa pair<int,int>
 #define lowb(x) ((x)&(-(x)))
 #define REP(i,n0,n) for(i=n0;i<=n;i++)
 #define PER(i,n0,n) for(i=n;i>=n0;i--)
 #define MAX(a,b) ((a>b)?a:b)
 #define MIN(a,b) ((a<b)?a:b)
 #define CLR(a,x) memset(a,x,sizeof(a))
 #define rei register int
 using namespace std;
 typedef long long ll;
 const int maxn=;

 ll rd(){
     ll x=;char c=getchar();int neg=;
     while(c<''||c>''){if(c=='-') neg=-;c=getchar();}
     while(c>=''&&c<='') x=x*+c-'',c=getchar();
     return x*neg;
 }

 int N,M;
 int ch[maxn][],v[maxn],xs[maxn],fa[maxn];
 bool rev[maxn];

 inline void pushrev(int x){swap(ch[x][],ch[x][]);rev[x]^=;}
 inline void update(int x){xs[x]=xs[ch[x][]]^xs[ch[x][]]^v[x];}
 inline void pushdown(int x){
     if(!rev[x]) return;
     if(ch[x][]) pushrev(ch[x][]);
     if(ch[x][]) pushrev(ch[x][]);
     rev[x]=;
 }
 inline bool isRoot(int x){return ch[fa[x]][]!=x&&ch[fa[x]][]!=x;}
 inline bool isRson(int x){return x==ch[fa[x]][];}
 inline void rotate(int x){
     int f=fa[x],ff=fa[f];bool b=isRson(x);
     if(ch[x][b^]) fa[ch[x][b^]]=f;ch[f][b]=ch[x][b^];
     if(!isRoot(f)) ch[ff][isRson(f)]=x;fa[x]=ff;
     fa[f]=x;ch[x][b^]=f;update(f);update(x);
 }
 void pushall(int x){
     if(!isRoot(x)) pushall(fa[x]);
     pushdown(x);
 }
 inline void splay(int x){
     pushall(x);
     while(!isRoot(x)&&!isRoot(fa[x])){
         if(isRson(x)==isRson(fa[x])) rotate(fa[x]);rotate(x);
     }if(!isRoot(x)) rotate(x);
 }
 inline void access(int x){
     for(int lst=;x;lst=x,x=fa[x]){
         splay(x);ch[x][]=lst;update(x);
     }
 }
 inline int getRoot(int x){
     access(x);splay(x);
     while(ch[x][]){pushdown(x);x=ch[x][];}return x;
 }
 inline void setRoot(int x){
     access(x);splay(x);pushrev(x);
 }
 inline void link(int x,int y){
     setRoot(x);
     if(getRoot(y)!=x) fa[x]=y;
 }
 inline void cut(int x,int y){
     setRoot(x);
     if(getRoot(y)!=x||fa[x]!=y||ch[x][]) return;
     ch[y][]=fa[x]=;update(y);
 }
 inline void change(int x,int k){
     splay(x);v[x]=k;update(x);
 }
 inline int query(int x,int y){
     setRoot(x);access(y);splay(y);
     return xs[y];
 }

 int main(){
     //freopen("testdata.in","r",stdin);
     rei i,j,k;
     N=rd(),M=rd();//printf("%d %d\n",N,M);
     for(i=;i<=N;i++) v[i]=xs[i]=rd();
     while(M--){
         int a=rd(),x=rd(),y=rd();
         if(a==) printf("%d\n",query(x,y));
         else if(a==) link(x,y);
         else if(a==) cut(x,y);
         else if(a==) change(x,y);
     }
     return ;
 }

luogu3690

luogu3203 弹飞绵羊（连边、断边、查询链长）

 #include<cstdio>
 #include<cstring>
 #include<algorithm>
 #include<vector>
 #include<queue>
 #include<map>
 #include<cmath>
 #include<ctime>
 #include<set>
 #define pa pair<int,int>
 #define lowb(x) ((x)&(-(x)))
 #define REP(i,n0,n) for(i=n0;i<=n;i++)
 #define PER(i,n0,n) for(i=n;i>=n0;i--)
 #define MAX(a,b) ((a>b)?a:b)
 #define MIN(a,b) ((a<b)?a:b)
 #define CLR(a,x) memset(a,x,sizeof(a))
 #define rei register int
 #define lt ch[x][0]
 #define rt ch[x][1]
 using namespace std;
 const int maxn=;
 typedef long long ll;

 ll rd(){
     ll x=;char c=getchar();int neg=;
     while(c<''||c>''){if(c=='-') neg=-;c=getchar();}
     while(c>=''&&c<='') x=x*+c-'',c=getchar();
     return x*neg;
 }

 int N,M;
 int fa[maxn],ch[maxn][],siz[maxn],to[maxn];
 bool rev[maxn];

 inline void update(int x){siz[x]=(lt?siz[lt]:)+(rt?siz[rt]:)+;}
 inline void pushrev(int x){
     rev[x]^=;swap(lt,rt);
 }
 inline void pushdown(int x){
     if(!rev[x]) return;
     if(lt) pushrev(lt);
     if(rt) pushrev(rt);
     rev[x]=;
 }
 inline bool isRoot(int x){return ch[fa[x]][]!=x&&ch[fa[x]][]!=x;}
 inline bool isRson(int x){return x==ch[fa[x]][];}
 inline void rotate(int x){
     int f=fa[x],ff=fa[f];bool b=isRson(x);
     if(!isRoot(f)) ch[ff][isRson(f)]=x;fa[x]=ff;
     if(ch[x][b^]) fa[ch[x][b^]]=f;ch[f][b]=ch[x][b^];
     ch[x][b^]=f;fa[f]=x;update(f);update(x);
 }
 inline void pushdall(int x){
     if(!isRoot(x)) pushdall(fa[x]);pushdown(x);
 }
 inline void splay(int x){
     pushdall(x);
     while(!isRoot(x)&&!isRoot(fa[x])){
         if(isRson(x)==isRson(fa[x])) rotate(fa[x]);
         else rotate(x);rotate(x);
     }if(!isRoot(x)) rotate(x);
 }
 inline void access(int x){
     for(int y=;x;y=x,x=fa[x]){
         splay(x);rt=y;update(x);
     }
 }
 inline void setRoot(int x){
     access(x);splay(x);
     pushrev(x);
 }
 inline int getRoot(int x){
     access(x);splay(x);
     while(lt){
         pushdown(x);x=lt;
     }return x;
 }
 inline void link(int x,int y){//x->y
     setRoot(x);
     access(y);splay(y);fa[x]=y;
 }
 inline void cut(int x,int y){
     setRoot(x);access(y);splay(y);
     ch[y][]=fa[x]=;update(y);
 }
 inline int query(int x,int y){
     setRoot(x);
     access(y);splay(y);
     //printf("%d %d\n",ch[y][0],ch[y][1]);
     return siz[y];
 }
 inline void change(int x,int k){
     if(x+k>N&&x+to[x]>N) return;
     if(to[x]) cut(x,MIN(x+to[x],N+));
     link(x,MIN(x+k,N+));
     to[x]=k;
 }

 int main(){
     //freopen("3203.in","r",stdin);
     rei i,j,k;N=rd();
     REP(i,,N) change(i,rd()),siz[i]=;siz[N+]=;
     M=rd();REP(i,,M){
         j=rd(),k=rd()+;
         if(j==) printf("%d\n",query(N+,k)-);
         else change(k,rd());
     }
     return ;
 }

luogu3203