【題解】Luogu P3203 [HNOI2010]彈飛綿羊
阿新 • • 發佈:2018-12-31
原題傳送門
這題用Link-Cut-Tree解決,Link-Cut-Tree詳解
預處理:從一個點彈到另一個點就在lct裡從\(i\)連邊到\(i+k_i\),如果綿羊被彈飛了就從\(i\)連邊到\(n+1\)(一個虛擬點,方便統計)
操作1:split(x,n+1),把x到n+1路徑上的點放到同一個Splay中,答案就是T.size[n+1]-1
操作2:先把\(i\)到\(i+oldk\)的邊刪除
如果\(i+newk<=n\),從\(i\)連邊到\(i+newk\),否則就從\(i\)連邊到\(n+1\)
注意:編號是0~n-1,為了方便寫碼,把所有的編號加1
#include <bits/stdc++.h> #define N 200005 #define getchar nc using namespace std; inline char nc(){ static char buf[100000],*p1=buf,*p2=buf; return p1==p2&&(p2=(p1=buf)+fread(buf,1,100000,stdin),p1==p2)?EOF:*p1++; } inline int read() { register int x=0,f=1;register char ch=getchar(); while(ch<'0'||ch>'9'){if(ch=='-')f=-1;ch=getchar();} while(ch>='0'&&ch<='9')x=(x<<3)+(x<<1)+ch-'0',ch=getchar(); return x*f; } inline void write(register int x) { if(!x)putchar('0');if(x<0)x=-x,putchar('-'); static int sta[20];register int tot=0; while(x)sta[tot++]=x%10,x/=10; while(tot)putchar(sta[--tot]+48); } inline void Swap(register int &a,register int &b) { a^=b^=a^=b; } struct Link_Cut_Tree{ int c[N][2],fa[N],top,q[N],rev[N],size[N]; inline void pushup(register int x) { size[x]=size[c[x][0]]+size[c[x][1]]+1; } inline void pushdown(register int x){ if(rev[x]) { register int l=c[x][0],r=c[x][1]; rev[l]^=1,rev[r]^=1,rev[x]^=1; Swap(c[x][0],c[x][1]); } } inline bool isroot(register int x) { return c[fa[x]][0]!=x&&c[fa[x]][1]!=x; } inline void rotate(register int x) { int y=fa[x],z=fa[y],l,r; l=c[y][0]==x?0:1; r=l^1; if(!isroot(y)) c[z][c[z][0]==y?0:1]=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); } inline void splay(register int x) { top=1; q[top]=x; for(register int i=x;!isroot(i);i=fa[i]) q[++top]=fa[i]; for(register int i=top;i;--i) pushdown(q[i]); while(!isroot(x)) { int y=fa[x],z=fa[y]; if(!isroot(y)) rotate((c[y][0]==x)^(c[z][0]==y)?(x):(y)); rotate(x); } } inline void access(register int x) { for(register int t=0;x;t=x,x=fa[x]) { splay(x); c[x][1]=t; pushup(x); } } inline void makeroot(register int x) { access(x); splay(x); rev[x]^=1; } inline void split(register int x,register int y) { makeroot(x); access(y); splay(y); } inline void cut(register int x,register int y) { split(x,y); if(c[y][0]==x) { c[y][0]=0; fa[x]=0; } } inline void link(register int x,register int y) { makeroot(x); fa[x]=y; } }T; int n,m,val[N]; int main() { n=read(); for(register int i=1;i<=n;++i) { val[i]=read(); T.link(i,i+val[i]<=n?(i+val[i]):(n+1)); } m=read(); while(m--) { int opt=read(); if(opt==1) { int x=read()+1; T.split(x,n+1); write(T.size[n+1]-1),puts(""); } else { int x=read()+1,y=read(); T.cut(x,x+val[x]<=n?(x+val[x]):(n+1)); val[x]=y; T.link(x,x+val[x]<=n?(x+val[x]):(n+1)); } } return 0; }