洛谷 3203 HNOI2010 BOUNCE 弹飞绵羊

【题解】

　　这道题可以用Link-Cut Tree写。。

　　首先建立一个虚拟节点N+1，$i$与$N+1$连边表示$i$被弹飞了

　　对于修改操作，先$cut(i,min(n+1,i+k[i]))$，然后再$link(i,min(n+1,i+newk))$

　　对于询问操作，先$makeroot(x)$，然后$splay(n+1)$，$access(n+1)$，那么答案就是$size[n+1]-1$

 #include<cstdio>
 #include<algorithm>
 #define N (500010)
 #define ls (c[u][0])
 #define rs (c[u][1])
 using namespace std;
 int n,m,opt,k[N];
 inline int read(){
     int k=,f=; char c=getchar();
     while(c<''||c>'')c=='-'&&(f=-),c=getchar();
     while(''<=c&&c<='')k=k*+c-'',c=getchar();
     return k*f;
 }
 struct Link_Cut_Tree{
     int top,c[N][],fa[N],rev[N],size[N],q[N];
     inline void pushdown(int u){
         if(rev[u]) rev[ls]^=,rev[rs]^=,rev[u]^=,swap(ls,rs);
     }
     inline void pushup(int u){
         size[u]=;
         if(ls) size[u]+=size[ls];
         if(rs) size[u]+=size[rs];
     }
     inline bool isroot(int u){
         return c[fa[u]][]!=u&&c[fa[u]][]!=u;
     }
     inline bool which(int u){
         return c[fa[u]][]==u;
     }
     void rotate(int u){
         int f=fa[u],gf=fa[f],wh=which(u);
         if(!isroot(f)) c[gf][which(f)]=u;
         fa[u]=gf; fa[f]=u; fa[c[u][wh^]]=f;
         c[f][wh]=c[u][wh^]; c[u][wh^]=f;
         pushup(f); pushup(u);
     }
     void splay(int u){
         q[top=]=u;
         for(int i=u;!isroot(i);i=fa[i]) q[++top]=fa[i];
         for(int i=top;i;i--) pushdown(q[i]);
         while(!isroot(u)){
             if(!isroot(fa[u])) rotate(which(u)==which(fa[u])?fa[u]:u);
             rotate(u);
         }
         pushup(u);
     }
     void access(int u){
         for(int son=;u;son=u,u=fa[u])
             splay(u),c[u][]=son,pushup(u);
     }
     void makeroot(int u){
         access(u); splay(u); rev[u]^=;
     }
     int find(int u){
         access(u); splay(u);
         while(ls) u=ls; splay(u);
         return u;
     }
     void split(int x,int y){
         makeroot(x); access(y); splay(y);
     }
     void cut(int x,int y){
         int xrt=find(x),yrt=find(y);
         if(xrt!=yrt) return;
         split(x,y);
         if(c[y][]==x) c[y][]=,fa[x]=;
         pushup(y);
     }
     void link(int x,int y){
         int xrt=find(x),yrt=find(y);
         if(xrt==yrt) return;
         makeroot(x); fa[x]=y;
     }
 }t;
 int main(){
     n=read();
     for(int i=;i<=n;i++) t.link(i,min(n+,i+(k[i]=read())));
     m=read();
     while(m--){
         if((opt=read())==){
             int x=read()+;
             t.makeroot(x); t.access(n+); t.splay(n+);
             printf("%d\n",t.size[n+]-);
         }
         else{
             int x=read()+,y=read();
             if(x+y>n+&&x+k[x]>n+) continue;
             t.cut(x,min(n+,x+k[x]));
             t.link(x,min(n+,x+y));
             k[x]=y;
         }
     }
     return ;
 }